132 a research study was conducted to examine the...

13.2. A research study was conducted to examine the differences between older and younger adults on perceived life satisfaction. Ten older adults (over the age of 70) and ten younger adults (between 20 and 30) were give a life satisfaction test. Scores on the measure range from 0 to 60 with high scores indicative of high life satisfaction; low scores indicative of low life satisfaction. The data are presented below. \begin{tabular}{c|cccccccccc} older adults & 45 & 38 & 52 & 48 & 25 & 39 & 51 & 46 & 55 & 46 \\ \hline younger adults & 34 & 22 & 15 & 27 & 37 & 41 & 24 & 19 & 26 & 36 \end{tabular} We will perform a t-test on those data. 1. (1) Define the null-hypothesis and the alternative. 2. (1) Is a 5% level reasonable? Motivate your answer. 3. (1) Compute the t statistic of the data. (Show all passages) 4. (1) How many degrees of freedom n does the reference t distribution have? Motivate your answer. The quantile is \(t_{n, 975}=2.1\). 5. (1) Is there a significant difference between the two groups? 6. (1) If you have made an error, would it be a Type I or a Type II error?

Transcript

00:01 Once again, welcome to a new problem.

00:04 This time we're dealing with hypothesis testing.

00:09 We're dealing with hypothesis testing.

00:13 And when it comes to hypothesis testing, we have hypothesis testing for means.

00:20 And a perfect example for testing hypothesis for means is the independent samples.

00:35 T test, independent sample t test, where the test statistic, where the test statistic is t equals to x -bar -1 minus x -bar -2, minus mu -2, all over square root of the variance of the first group plus the variance, plus the variance that's the standard error.

01:12 The denominator represents the standard error.

01:15 So this is the variance of the second group and the sample size of the second group.

01:21 The denominator represents the standard error.

01:29 X by 1 is the sample 1 mean and x by 2 is sample 2 mean.

01:46 Also, we have two types of error.

01:50 Type 1, error is rejecting a true now hypothesis.

02:03 So rejecting a true now hypothesis.

02:06 And of course, type 2 error happens to be failing to reject a false false.

02:24 Now a hypothesis.

02:32 So those are the numbers and if you think about it, if you think about it, you have two samples that you want to compare and then these two samples you subtract them from each other and then once you subtract them from each other, you you get the the differences between those two samples.

03:13 We have a new problem and in this particular problem we have specific requirements.

03:23 We want to find the differences, we want to find the differences between older versus young adults when it comes to life satisfaction.

03:37 Each group has 10 different subgroups.

03:43 So each group happens to have 10 different subjects.

03:47 The scores for life satisfaction go from 0 to 60.

03:53 And we want to see, for example, if you look at all the adults, it just so happens that the difference scores include 45, 38, 52, 48, 25, 25, 39, 51, 46 55 46 that's older adults and then we're also thinking about younger adults so we have 34 we have 22 we have 15 we have 27 we have 47 we have 41 we have 24 and besides 24 so these are just the numbers will looking at older and younger adults, we have 19, we have 26, and then finally we have 36.

04:56 So the first thing we want to do is we want to determine the now and alternative hypothesis for this test on life satisfaction.

05:05 So the now hypothesis is that the two groups have similar average in terms of life satisfaction...

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