WEBVTT Kind: captions Language: en-US 00:00:01.959 --> 00:00:04.890 >> Hi, and welcome back for our next discussion of statistics. 00:00:04.890 --> 00:00:09.650 This time we're discussing the Language of Hypothesis Testing. 00:00:09.650 --> 00:00:12.889 We start out with an introduction to hypothesis testing, 00:00:12.889 --> 00:00:16.270 and an initial checklist to assess the hypothesis test. 00:00:16.270 --> 00:00:19.619 Well, first, hypothesis testing can be a bit confusing. 00:00:19.619 --> 00:00:22.749 As a result, we really want to emphasize this idea that we need 00:00:22.749 --> 00:00:27.609 to read each question carefully and evaluate what is being asked before working 00:00:27.609 --> 00:00:32.740 on the mathematical side of the hypothesis test, that is, make sure we take the time 00:00:32.740 --> 00:00:35.810 to assess these questions correctly. 00:00:35.810 --> 00:00:39.010 Leading into our introduction, a hypothesis is a statement 00:00:39.010 --> 00:00:42.510 or claim regarding a characteristic of one or more populations. 00:00:42.510 --> 00:00:46.629 We technically just call this a claim, and it leads into our hypothesis testing. 00:00:46.629 --> 00:00:52.320 And our hypothesis testing is a process using sample data and probability 00:00:52.320 --> 00:00:57.920 to test claims regarding some characteristic of the populations that we're discussing. 00:00:57.920 --> 00:01:03.230 We test hypotheses using sample data because it's often impossible or unreasonable 00:01:03.230 --> 00:01:07.960 to gather data for an entire population. 00:01:07.960 --> 00:01:10.280 Well that takes us to the idea of the null hypothesis. 00:01:10.280 --> 00:01:15.710 Well, the null hypothesis is a statement of no change or difference as compared 00:01:15.710 --> 00:01:18.869 to a current situation or characteristic. 00:01:18.869 --> 00:01:21.670 On the other hand, the alternative hypothesis is 00:01:21.670 --> 00:01:24.479 a statement implicating that there is a change 00:01:24.479 --> 00:01:28.750 when compared to the current situation or characteristic that we're discussing. 00:01:28.750 --> 00:01:33.649 That is, the null hypothesis is saying that nothing has changed from the past. 00:01:33.649 --> 00:01:36.759 It's some original claim that comes typically from the past. 00:01:36.759 --> 00:01:41.229 The null hypothesis is assumed to be true, and the goal of hypothesis testing is 00:01:41.229 --> 00:01:47.210 to find evidence that supports the alternative hypothesis. 00:01:47.210 --> 00:01:50.200 So that takes us over to the idea of this assessment before we head 00:01:50.200 --> 00:01:52.450 into the math of hypothesis testing. 00:01:52.450 --> 00:01:56.570 Well, below are some initial questions to use in order to assess exactly what type 00:01:56.570 --> 00:01:58.930 of hypothesis test we're presented. 00:01:58.930 --> 00:02:01.200 We first want to ask about which parameter. 00:02:01.200 --> 00:02:05.039 Am I being asked to conduct a hypothesis test? 00:02:05.039 --> 00:02:07.200 Now this seems like it may be a little unnecessary, 00:02:07.200 --> 00:02:11.970 but we cannot tell you how many times students do the wrong hypothesis test. 00:02:11.970 --> 00:02:16.810 They do it mathematically correctly, but they do that test for the wrong parameter. 00:02:16.810 --> 00:02:20.780 And what we mean by parameter, as a refresher, is we have three options. 00:02:20.780 --> 00:02:23.850 They would be mean, proportion, and standard deviation. 00:02:23.850 --> 00:02:26.630 Now, keep in mind we do have that little caveat 00:02:26.630 --> 00:02:29.120 that is the variance from the standard deviation. 00:02:29.120 --> 00:02:31.650 But that's a small little adjustment. 00:02:31.650 --> 00:02:32.810 The next question asked would be, 00:02:32.810 --> 00:02:37.430 is this hypothesis test comparing one population or two populations? 00:02:37.430 --> 00:02:41.630 If the hypothesis test concerns only one population, we'll be comparing our sample 00:02:41.630 --> 00:02:42.630 results 00:02:42.630 --> 00:02:47.220 to some value that is a constant, as presented through the null hypothesis. 00:02:47.220 --> 00:02:50.470 However, if the hypothesis test concerns two populations, 00:02:50.470 --> 00:02:54.480 we'll be comparing the values obtained from two different samples. 00:02:54.480 --> 00:02:58.310 Now that's a big deal if the hypothesis test is on one population, 00:02:58.310 --> 00:03:01.770 we will only have one sample that we will be pulling results from. 00:03:01.770 --> 00:03:04.680 But if it's on two populations, and that means we'll have a sample 00:03:04.680 --> 00:03:09.100 from each population, or two samples altogether. 00:03:09.100 --> 00:03:13.110 And heading over to our third question then, what are the null and alternative hypotheses? 00:03:13.110 --> 00:03:17.710 First, we have some keywords to look at to determine the alternative hypothesis. 00:03:17.710 --> 00:03:19.380 And you see the list would go on, 00:03:19.380 --> 00:03:23.810 for the overall idea here is the alternative hypothesis is determined 00:03:23.810 --> 00:03:28.150 by which direction we think the data has moved, if you will, 00:03:28.150 --> 00:03:31.290 as compared to a previous value or another population. 00:03:31.290 --> 00:03:33.900 We'll ellaborate on this though with some examples later. 00:03:33.900 --> 00:03:35.080 To continue the explanation. 00:03:35.080 --> 00:03:38.730 We have three options to set up the null and alternative hypotheses. 00:03:38.730 --> 00:03:41.650 The first option presented would be for a two-tailed test. 00:03:41.650 --> 00:03:47.210 Well, a two-tailed test leads us to a not-equal sign in our alternative hypothesis. 00:03:47.210 --> 00:03:50.410 And this comes from keywords like is different or differs 00:03:50.410 --> 00:03:52.430 within the story that we're presented. 00:03:52.430 --> 00:03:56.610 And that's because the alternative hypothesis does not give us a specific direction 00:03:56.610 --> 00:03:58.790 in which we think the data moved. 00:03:58.790 --> 00:04:01.040 Our next option would be a left-tailed test, 00:04:01.040 --> 00:04:04.500 and that's where the alternative hypothesis has a less than sign 00:04:04.500 --> 00:04:07.110 in comparison to some value or population. 00:04:07.110 --> 00:04:12.680 And this comes from words such as less than or decreased within the story presented. 00:04:12.680 --> 00:04:16.090 And that takes us to our third option which would be a right-tailed test. 00:04:16.090 --> 00:04:20.280 That's where everything for the data has increased or exceeds the former value 00:04:20.280 --> 00:04:23.789 with keywords such as greater than as well. 00:04:23.789 --> 00:04:27.460 And that wraps up our initial discussion on the language of hypothesis testing. 00:04:27.460 --> 00:04:30.639 And now we're going to open up with the idea of being able 00:04:30.639 --> 00:04:33.820 to identify the null and alternative hypotheses. 00:04:33.820 --> 00:04:35.550 We jump right into an example. 00:04:35.550 --> 00:04:38.740 Right now we're working with just one population hypothesis test. 00:04:38.740 --> 00:04:41.900 We're told to determine the null hypothesis for each of the following, 00:04:41.900 --> 00:04:45.449 then state whether the test is two-tailed, left-tailed, or right-tailed, 00:04:45.449 --> 00:04:47.150 and then determine the alternative hypothesis. 00:04:47.150 --> 00:04:49.580 This is the order in which we want to go in. 00:04:49.580 --> 00:04:51.360 Of course, we're going to highlight the parameter 00:04:51.360 --> 00:04:54.229 with which we're working for each of these tests as well. 00:04:54.229 --> 00:04:55.990 So taking a look at this first one -- 00:04:55.990 --> 00:05:00.419 42% of American adults did not donate to charity despite the tax write-off. 00:05:00.419 --> 00:05:05.139 The Chairman of the Senior Citizens Association thinks that society is going down the tube 00:05:05.139 --> 00:05:07.509 and this percentage is greater today. 00:05:07.509 --> 00:05:11.599 Well, the first word that we're going to highlight now would be percentage 00:05:11.599 --> 00:05:17.099 because as we're presented this hypothesis test, we're comparing the percentage today 00:05:17.099 --> 00:05:20.490 to a percentage that was presented back in 2017. 00:05:20.490 --> 00:05:24.180 Now that we know we're working with percentage, which is the same as proportion, 00:05:24.180 --> 00:05:27.460 we can see our null hypothesis, and that would be P equal to. 00:05:27.460 --> 00:05:30.969 And typically, when we get to the math of things, we work with proportions 00:05:30.969 --> 00:05:34.030 or comparing the old value that would be a status quo, 00:05:34.030 --> 00:05:38.349 and that would be that 42% presented into 2017. 00:05:38.349 --> 00:05:39.349 Continuing on. 00:05:39.349 --> 00:05:42.810 Since the researcher believes that the percentage is greater today, 00:05:42.810 --> 00:05:45.979 the alternative hypothesis is a right-tailed hypothesis. 00:05:45.979 --> 00:05:50.499 Again, the keyword being greater there, leading us to the right-tailed test. 00:05:50.499 --> 00:05:55.169 And that means the alternative hypothesis would be a P greater than a 0.42. 00:05:55.169 --> 00:06:00.009 Well then, heading over to the second example, according to the study published in March 00:06:00.009 --> 00:06:05.909 of 2016, the mean number of text messages sent by millennials was 227 per day. 00:06:05.909 --> 00:06:08.990 A researcher believes that the mean has changed since then. 00:06:08.990 --> 00:06:13.870 Well, like we did before, our research is on the mean of these text messages. 00:06:13.870 --> 00:06:16.639 So we have a hypothesis test about the mean. 00:06:16.639 --> 00:06:22.030 And working on our null hypothesis, the mean number in the past, March of 2016, 00:06:22.030 --> 00:06:25.319 was 227 per day, a mu equal to the 227. 00:06:25.319 --> 00:06:29.240 Now, working on the alternative hypothesis, the researcher believes 00:06:29.240 --> 00:06:34.090 that the mean call length has changed since that 2016 result. 00:06:34.090 --> 00:06:37.340 That keyword doesn't give us a specific direction. 00:06:37.340 --> 00:06:39.570 That means we have a two-tailed test, 00:06:39.570 --> 00:06:44.629 and that means our alternative hypothesis would be a mu not equal to that 227. 00:06:44.629 --> 00:06:47.610 Again, just to reiterate, we have a two-tailed test. 00:06:47.610 --> 00:06:51.889 We are not equal to sign here in our alternative hypothesis. 00:06:51.889 --> 00:06:55.610 The keyword change didn't send us in a specific direction. 00:06:55.610 --> 00:07:00.379 All we're saying at this point is that we think it's something different than the 227, 00:07:00.379 --> 00:07:03.830 which it was back in March of '16. 00:07:03.830 --> 00:07:07.349 And if that's okay, we'll go ahead and roll over to our next example. 00:07:07.349 --> 00:07:11.990 We're told, using an old basket-weaving process, the standard deviation of the amount 00:07:11.990 --> 00:07:17.029 of wicker used to make baskets under water was 0.83 feet. 00:07:17.029 --> 00:07:18.750 Now with new full-faced snorkels, 00:07:18.750 --> 00:07:22.990 a quality control manager believes the standard deviation has decreased. 00:07:22.990 --> 00:07:28.840 Well, first, we see now that the manager is concerned about the standard deviation, 00:07:28.840 --> 00:07:30.840 so the parameter we're working with would be sigma, 00:07:30.840 --> 00:07:33.099 and that means our null hypothesis would be 00:07:33.099 --> 00:07:37.169 that sigma equal to that 0.83 feet presented 00:07:37.169 --> 00:07:40.069 by the problem using the old basket-weaving process. 00:07:40.069 --> 00:07:43.770 Well, if we're okay with that, the quality control manager believes 00:07:43.770 --> 00:07:46.669 that the standard deviation has decreased, and 00:07:46.669 --> 00:07:48.930 that means we've got ourselves a left-tail test 00:07:48.930 --> 00:07:52.539 because the direction we're being sent would be to the left, again, 00:07:52.539 --> 00:07:55.469 referring to the idea of tying this to a number line. 00:07:55.469 --> 00:07:58.569 And if that's okay, we end up with an alternative hypothesis 00:07:58.569 --> 00:08:02.960 of a sigma being less than that 0.83 feet. 00:08:02.960 --> 00:08:06.819 And we're all set with our examples dealing with one population. 00:08:06.819 --> 00:08:11.129 Heading into our next set of examples here, we want to be able to identify the null 00:08:11.129 --> 00:08:14.069 and alternative hypotheses, but now with two populations. 00:08:14.069 --> 00:08:16.419 We're taking a look at our example. 00:08:16.419 --> 00:08:21.059 We're told a grounded teenager want to determine whether teenagers spend more time on Instagram 00:08:21.059 --> 00:08:24.680 or parents spend more time on Facebook, because she was grounded for being 00:08:24.680 --> 00:08:27.069 on her phone too much, only to see her mom whip 00:08:27.069 --> 00:08:29.689 out Facebook two minutes after she got in trouble. 00:08:29.689 --> 00:08:33.810 Well, the teenager believes that parents actually spend more time, on average, 00:08:33.810 --> 00:08:37.150 on Facebook than teenagers do on Instagram. 00:08:37.150 --> 00:08:39.090 Working on our null hypothesis, of course, the 00:08:39.090 --> 00:08:40.940 first thing we want to recognize though is, 00:08:40.940 --> 00:08:45.690 and it's a little bit sneaky in this problem, which parameter are we working with. 00:08:45.690 --> 00:08:50.170 They help us out a little bit as they tell us on average in our key sentence 00:08:50.170 --> 00:08:53.480 that she believes parents actually spend more time on average 00:08:53.480 --> 00:08:56.340 on Facebook than teenagers do on Instagram. 00:08:56.340 --> 00:09:01.450 The average tells us that we're working with means even if it didn't say on average though. 00:09:01.450 --> 00:09:02.490 And it skipped that part. 00:09:02.490 --> 00:09:04.440 We'd have to infer that ourselves. 00:09:04.440 --> 00:09:06.310 And that's where it can get a little bit tricky. 00:09:06.310 --> 00:09:08.940 In this case, though, with that on average being 00:09:08.940 --> 00:09:11.910 there for us, we know we're working with means, 00:09:11.910 --> 00:09:15.890 and that means our null hypothesis is just a mu 1 equal to a mu 2. 00:09:15.890 --> 00:09:17.900 Now this is where we have to be a bit careful though. 00:09:17.900 --> 00:09:23.040 We have to make sure we know which population we're calling mu 1 and mu 2. 00:09:23.040 --> 00:09:27.030 Now over here in our key sentence, the parents were mentioned first, so I'm going to call 00:09:27.030 --> 00:09:32.050 that our population number one, and that makes the teenagers our population number 00:09:32.050 --> 00:09:33.050 two. 00:09:33.050 --> 00:09:36.650 Only because we're trying to work on this, let's go and label that over on a side. 00:09:36.650 --> 00:09:40.150 Mu 1 is representing the parents, and mu 2 is representing the teens. 00:09:40.150 --> 00:09:43.490 We highlight this because it can get a little bit messed up when we go to work 00:09:43.490 --> 00:09:46.570 with our calculators, so we need to be a bit careful with it. 00:09:46.570 --> 00:09:49.270 Now to work on our alternative hypothesis, the 00:09:49.270 --> 00:09:51.770 teenager believes that parents spend more time 00:09:51.770 --> 00:09:55.140 on Facebook than teenagers do on Instagram. 00:09:55.140 --> 00:09:58.670 This is where, again, we just need to make sure we're careful with our organization. 00:09:58.670 --> 00:10:03.870 Remember, we said that parents represent our mu 1, and we just used the word more, 00:10:03.870 --> 00:10:07.810 leading us to a right-tail test, and that means we have an alternative hypothesis. 00:10:07.810 --> 00:10:10.820 That would be a mu 1 greater than mu 2. 00:10:10.820 --> 00:10:15.650 Again, being careful with that because we think that parents spend more time 00:10:15.650 --> 00:10:18.540 than teenagers on their respective apps. 00:10:18.540 --> 00:10:22.950 On the other hand, just thinking mathematically, we want to make sure this is clear, 00:10:22.950 --> 00:10:24.930 that we can write this another way. 00:10:24.930 --> 00:10:28.250 We can turn this into a left-tail test by reversing the populations. 00:10:28.250 --> 00:10:33.240 That is, we can write the alternative hypothesis as mu 2 is less than mu 1 00:10:33.240 --> 00:10:35.760 since those two statements are equivalent. 00:10:35.760 --> 00:10:39.130 The point of this would be, make sure we're careful with our organization 00:10:39.130 --> 00:10:41.250 when we're working with two populations. 00:10:41.250 --> 00:10:46.260 Well, if that's okay, heading over to our next example, we have a grandpa and grandson 00:10:46.260 --> 00:10:50.830 who are talking about classic American muscle cars and modern import cars. 00:10:50.830 --> 00:10:53.810 The grandpa believes that people like classic muscle cars just 00:10:53.810 --> 00:10:55.900 as much as the modern import cars. 00:10:55.900 --> 00:10:59.190 However, the grandson wants to conduct some research on the topic 00:10:59.190 --> 00:11:03.610 because he thinks the proportion of people who like muscle cars will be different 00:11:03.610 --> 00:11:07.060 than the proportion of people who like modern import cars. 00:11:07.060 --> 00:11:11.430 Well, the first keyword we want to highlight would be proportion so that we know 00:11:11.430 --> 00:11:13.200 which parameter we're working with. 00:11:13.200 --> 00:11:17.790 And that means our null hypothesis would be a P1 equal to a P2. 00:11:17.790 --> 00:11:20.780 And just like we did before though, now we just need to make sure we're careful 00:11:20.780 --> 00:11:24.630 with which one we're calling the first population and the second population. 00:11:24.630 --> 00:11:26.780 We'll just stay consistent with the problem. 00:11:26.780 --> 00:11:31.310 The muscle car is represented first, so I'm going to call those population number one. 00:11:31.310 --> 00:11:35.180 And the import cars represented second, so there's our population number two. 00:11:35.180 --> 00:11:39.360 Heading over to the work on the alternative hypothesis, the grandson thinks the proportion 00:11:39.360 --> 00:11:43.610 of people who like muscle cars will be different than the proportion 00:11:43.610 --> 00:11:45.930 of people who like the import cars. 00:11:45.930 --> 00:11:47.560 Different being our keyword again. 00:11:47.560 --> 00:11:50.790 No specific direction given for us to commit to. 00:11:50.790 --> 00:11:53.000 That means we're working with a two-tail test, 00:11:53.000 --> 00:11:55.940 and that means the alternative hypothesis is a 00:11:55.940 --> 00:11:59.040 P1 not equal to a P2, which means we're all set 00:11:59.040 --> 00:12:01.770 with our null and alternative hypotheses. 00:12:01.770 --> 00:12:03.870 And as one more little conversation though, 00:12:03.870 --> 00:12:06.830 we showed how we could reverse our one directional test 00:12:06.830 --> 00:12:09.800 on the previous example just speaking mathematically, 00:12:09.800 --> 00:12:12.820 thinking of this in terms of algebra and variables. 00:12:12.820 --> 00:12:18.140 If doesn't cause confusion, I can subtract P2 from both sides of the equation here, 00:12:18.140 --> 00:12:22.370 and that would lead me to a P1 minus P2 not equal to zero. 00:12:22.370 --> 00:12:26.820 And what we're just trying to say is another way to write this hypothesis would be 00:12:26.820 --> 00:12:31.960 as the difference between these two populations would be not equal to zero. 00:12:31.960 --> 00:12:35.350 Now this is less popular way of writing the alternative hypothesis. 00:12:35.350 --> 00:12:38.050 We're just showing you that it's an option. 00:12:38.050 --> 00:12:41.840 Reverting back to the original writing, typically we just write this as a P1 not equal 00:12:41.840 --> 00:12:45.980 to P2, or we're just trying to be as clear as we can. 00:12:45.980 --> 00:13:12.950 Pause the video and try these problems. 00:13:12.950 --> 00:13:16.350 Now we're jumping into our next objective where we want to make sure we know how 00:13:16.350 --> 00:13:19.490 to state conclusions to hypothesis tests. 00:13:19.490 --> 00:13:23.610 Our first conversation though concerns this big technicality that is the conclusion 00:13:23.610 --> 00:13:27.350 of a hypothesis test, so we have to be very careful with the language. 00:13:27.350 --> 00:13:31.610 The first note we want to make is that the null hypothesis is never accepted. 00:13:31.610 --> 00:13:33.460 Absolutely never is. 00:13:33.460 --> 00:13:34.460 We can lean on that. 00:13:34.460 --> 00:13:37.180 We never accept the null hypothesis. 00:13:37.180 --> 00:13:41.090 Instead there are only two possible outcomes to a hypothesis test. 00:13:41.090 --> 00:13:44.510 The null hypothesis is either rejected or not rejected. 00:13:44.510 --> 00:13:47.280 Now, I may mess with your head a little bit. 00:13:47.280 --> 00:13:50.270 The idea of, well, if it's not rejected, that means it's accepted. 00:13:50.270 --> 00:13:53.690 Again, this is language stuff as opposed to just logic. 00:13:53.690 --> 00:13:59.590 Not rejected is very different, technically speaking, than accepting the null hypothesis. 00:13:59.590 --> 00:14:05.030 The logic behind that is since we only have sample data we never truly know the value 00:14:05.030 --> 00:14:06.770 of the parameter in discussion. 00:14:06.770 --> 00:14:11.670 Remember, the parameter would be the true mean or proportion or standard deviation. 00:14:11.670 --> 00:14:16.350 Since we'll never know the true value of that, we can't accept a null hypothesis. 00:14:16.350 --> 00:14:20.540 We can only say that it is or is not enough evidence to reject the null hypothesis. 00:14:20.540 --> 00:14:24.510 But we'll get into that in a minute in case it's still a little bit confusing. 00:14:24.510 --> 00:14:27.350 The analogy we have is just like the court system. 00:14:27.350 --> 00:14:31.320 We never declare a defendant innocent, meaning when a verdict is read, 00:14:31.320 --> 00:14:35.210 we don't hear the word innocence coming out from that jury. 00:14:35.210 --> 00:14:40.410 Instead a defendant is either guilty or not guilty, and those are the only two options. 00:14:40.410 --> 00:14:45.590 This is because the system is designed that the defendant is innocent until proven guilty, 00:14:45.590 --> 00:14:48.820 so the whole case is presented trying to prove guilt. 00:14:48.820 --> 00:14:52.560 If it's not proven, the verdict is simply not guilty, 00:14:52.560 --> 00:14:54.940 and we can't say that a defendant is innocent 00:14:54.940 --> 00:14:58.530 because the system wasn't designed to prove his innocence. 00:14:58.530 --> 00:14:59.530 Hopefully that makes sense. 00:14:59.530 --> 00:15:02.380 We elaborate more with some examples, of course. 00:15:02.380 --> 00:15:06.040 But before we do that, let's discuss the wording of these conclusions 00:15:06.040 --> 00:15:08.610 since those are also quite technical. 00:15:08.610 --> 00:15:11.830 Our first scenario is, let's say we're going to reject the null hypothesis. 00:15:11.830 --> 00:15:16.820 Well, if rejecting the null is the result of the test, then we can say something like, 00:15:16.820 --> 00:15:22.650 there is sufficient, which is a fancy word for enough, evidence to conclude that -- 00:15:22.650 --> 00:15:25.600 and what you see in this generic template here is we just tie 00:15:25.600 --> 00:15:28.900 in the alternative hypothesis in context with the problem. 00:15:28.900 --> 00:15:31.340 Again, we'll elaborate with some examples. 00:15:31.340 --> 00:15:34.650 But that's our key phrase -- there is sufficient evidence to conclude; 00:15:34.650 --> 00:15:39.970 whereas scenario number two, if we don't get to reject the null hypothesis, 00:15:39.970 --> 00:15:43.160 that means there is insufficient evidence to conclude that -- 00:15:43.160 --> 00:15:46.240 and, again, we tie in the alternative hypothesis. 00:15:46.240 --> 00:15:47.350 Trying to sum this up. 00:15:47.350 --> 00:15:50.410 We basically make the same sentence for each problem, 00:15:50.410 --> 00:15:54.170 the only difference being whether we have sufficient or insufficient evidence 00:15:54.170 --> 00:15:57.530 to conclude whatever the alternative hypothesis would be. 00:15:57.530 --> 00:16:02.190 Well, that takes us over to our example, and hopefully this clarifies any confusion. 00:16:02.190 --> 00:16:03.480 Let's jump right into it. 00:16:03.480 --> 00:16:08.580 We're back to 2017 and the 42% of American adults that did not donate 00:16:08.580 --> 00:16:10.910 to charity despite the tax write-off. 00:16:10.910 --> 00:16:15.080 The Chairman of the Senior Citizens Association still thinks that society is going right 00:16:15.080 --> 00:16:17.780 down the tube, and this percentage is greater today. 00:16:17.780 --> 00:16:20.750 Well, now that we're done with the null and alternative hypotheses 00:16:20.750 --> 00:16:23.350 from our previous conversations, let's go ahead 00:16:23.350 --> 00:16:26.020 and suppose that the sample evidence indicates 00:16:26.020 --> 00:16:29.460 that the null hypothesis should be rejected. 00:16:29.460 --> 00:16:31.350 We're told to state the wording of the conclusion. 00:16:31.350 --> 00:16:36.300 Well, if we're rejecting the null hypothesis, then that means there is sufficient evidence 00:16:36.300 --> 00:16:40.680 to conclude, and now we bring in that alternative hypothesis. 00:16:40.680 --> 00:16:45.500 So we have sufficient evidence to conclude that the percentage of American adults 00:16:45.500 --> 00:16:52.680 who do not donate to charity is greater than the originally stated 42% back in 2017. 00:16:52.680 --> 00:16:55.870 And that's what we mean by tying in the alternative hypothesis. 00:16:55.870 --> 00:17:01.470 Now the next part says, suppose the sample evidence indicates the null hypothesis should 00:17:01.470 --> 00:17:02.470 not be rejected. 00:17:02.470 --> 00:17:05.980 Well, now we are not rejecting the null hypothesis, 00:17:05.980 --> 00:17:10.209 and that's because there is insufficient evidence to conclude and notice 00:17:10.209 --> 00:17:12.150 that the sentence is about the same, 00:17:12.150 --> 00:17:15.990 just changing those keywords, sufficient versus insufficient. 00:17:15.990 --> 00:17:19.809 There is insufficient evidence to conclude that the percentage of American adults 00:17:19.809 --> 00:17:23.519 who do not donate to charity is greater than 42%. 00:17:23.519 --> 00:17:26.829 Now notice one more time, the only word that changed was insufficient. 00:17:26.829 --> 00:17:32.780 The alternative hypothesis of being greater than 42% is still the end of our conclusion. 00:17:32.780 --> 00:17:37.370 Well, if that's okay, let's go ahead and jump into our next example. 00:17:37.370 --> 00:17:39.679 We're back to the text messages sent by millennials. 00:17:39.679 --> 00:17:43.280 Remember, according to a study published in March of 2016, 00:17:43.280 --> 00:17:47.820 the mean number of text messages sent by millennials was 227 per day. 00:17:47.820 --> 00:17:50.999 Any researcher believes that the mean has changed since then. 00:17:50.999 --> 00:17:54.909 Well, now we're told suppose the sample evidence indicates 00:17:54.909 --> 00:17:57.340 that the null hypothesis should be rejected. 00:17:57.340 --> 00:18:00.870 And, again, we need to state the wording of our conclusion. 00:18:00.870 --> 00:18:04.669 Well since we have the evidence to reject the null hypothesis, 00:18:04.669 --> 00:18:08.600 that means there is sufficient evidence to conclude that the mean number 00:18:08.600 --> 00:18:14.450 of text messages sent by millennials is different than the 227 per day. 00:18:14.450 --> 00:18:16.380 Now just highlighting those keywords. 00:18:16.380 --> 00:18:18.999 Remember our researcher believed that the mean has changed 00:18:18.999 --> 00:18:21.529 since then, so we had a two-tail test. 00:18:21.529 --> 00:18:26.230 And that means our alternative hypothesis did not send us in a specific direction. 00:18:26.230 --> 00:18:30.030 That's why we're saying in our conclusion that the mean number of text messages sent 00:18:30.030 --> 00:18:34.460 by millennials is different than the 227 per day as opposed to committing 00:18:34.460 --> 00:18:37.759 to something like greater than or less than. 00:18:37.759 --> 00:18:42.440 Heading over to Part B then, now we're told again, suppose the sample evidence indicates 00:18:42.440 --> 00:18:45.549 that the null hypothesis should not be rejected. 00:18:45.549 --> 00:18:47.899 All that means for the wording of our conclusion, 00:18:47.899 --> 00:18:51.740 there is insufficient evidence this time to conclude that the mean number 00:18:51.740 --> 00:18:56.299 of text messages sent by millennials is -- and just like we had before, 00:18:56.299 --> 00:18:58.889 different than the 227 per day telling you that 00:18:58.889 --> 00:19:02.019 alternative hypothesis is on the two-tail test. 00:19:02.019 --> 00:19:03.700 We're hoping that's okay. 00:19:03.700 --> 00:19:05.529 Let's head into one more example. 00:19:05.529 --> 00:19:09.710 Using an old basket-weaving process, the standard deviation of the amount of wicker 00:19:09.710 --> 00:19:10.710 used 00:19:10.710 --> 00:19:15.909 to make baskets under water was 0.83 feet with new full-faced snorkels. 00:19:15.909 --> 00:19:19.509 A quality control manager believes the standard deviation has decreased. 00:19:19.509 --> 00:19:22.660 Well, then, suppose the sample evidence no indicates 00:19:22.660 --> 00:19:25.700 that the null hypothesis should be rejected again. 00:19:25.700 --> 00:19:28.019 Well, hopefully, we're getting it now. 00:19:28.019 --> 00:19:30.820 Trying to emphasize the fact that it doesn't change a whole lot 00:19:30.820 --> 00:19:33.559 since we are rejecting the null hypothesis. 00:19:33.559 --> 00:19:38.039 That means there is sufficient evidence to conclude that the standard deviation is -- 00:19:38.039 --> 00:19:41.049 and tying in our alternative hypothesis. 00:19:41.049 --> 00:19:45.190 Since the Quality Control Manager believed the standard deviation has decreased, 00:19:45.190 --> 00:19:47.580 that means we have sufficient evidence to conclude 00:19:47.580 --> 00:19:52.050 that the standard deviation is less than our 0.83 feet. 00:19:52.050 --> 00:19:57.080 And heading over to Part B, suppose the sample evidence this time, like we've done before, 00:19:57.080 --> 00:20:00.740 indicates that the null hypothesis should not be rejected. 00:20:00.740 --> 00:20:04.950 And that means one more time we have insufficient evidence to conclude 00:20:04.950 --> 00:20:09.519 that the standard deviation is less than the 0.83 feet. 00:20:09.519 --> 00:20:12.130 And just reiterate one more time that less than 00:20:12.130 --> 00:20:15.999 0.83 feet comes from the alternative hypothesis 00:20:15.999 --> 00:20:20.529 where we think that the standard deviation has decreased. 00:20:20.529 --> 00:20:35.960 Pause the video and try these problems. 00:20:35.960 --> 00:20:48.990 Well, that wraps up our conversation. 00:20:48.990 --> 00:20:51.990 Thank you one more time for joining us in our discussion 00:20:51.990 --> 00:20:53.950 of The Language of Hypothesis Testing.