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[\ I\: \’\\\ Stony Brook University “ Name: \PxO For the sole use of students at Stony Brook University. Copyright © 2019 (Copyright Dr. Brenda J Anderson) All Rights Reserved Chapter 9 PRACTICE PROBLEM 1: Fifteen years ago, the average weight of a select subset of the US population between the ages of 30 and 50 was 166 |b. (p=166). A researcher would like to determine whether there has been any change in this figure during the past 15 years. A sample of n = 100 people within the same subset and between 30 and 50 years old was randomly chosen. The average weight for the sample was 173 Ib with a standard deviation of 23. Can the researcher conclude that there is a significant change in weight? Use a two tailed test with alpha =.05 1.1a State the Null Hypothesis in words: M€ b N0 dnong( e (] T p ‘ 1.1b State the Null Hypothesis in mathematical terms: ) My 1.2a What is your alpha level? O5 df? 1o \ 1.2b What is your criterion t value? _= ) \) Calculate your sample statistic: Under these conditions, we use the t-test. The strategy for testing our hypothesis with a z-score or t-score is the same. And that similarity is very evident in this chapter, where we assume we still know the . We can use the same numerator, M -y, but we have to replace g, as the denominator. Just as M estimates |, we'll calculate the sample standard deviation, s, to estimate. 0. We'll use s to calculate Sm_to replace o, as the denominator. 13 | : [ oD £ 1 I \“ \ 1.4a How would you describe this to your aunt? 1.4b How would you report this in a research paper? »

g b | Name: A S . ! For the sole use of students at Stony Brook University. Copyright © 2019 (Copyright Dr. Brenda J Anderson) All Rights Reserved \V Stony Brook University | [t(23)= >, p 05; __ vt the Null Hypothesis]. Is this a “statistically significant difference”? PRACTICE PROBLEM 2: Same idea but starting with the raw data for the sample. “A major corporation in the Northeast noted its employees averaged 5.8 absences during the winter season (December to February) last year (u = 5.8). The distribution is normal. In an attempt to reduce absences, the company offered free flu shots to a small random sample of employees. For a sample of 16 people who took flu shots, the number of absences can be seen in the box below. Use a 1-tailed test and alpha .05, 2.1a State the alternative hypothesis: i Pl shy 2.1b State the Null Hypothesis in words: The A v Y redwu S 2.1c State the Null Hypothesis in mathematical terms: _ |4, 2 M, = Au- 2.2 aWhat is your alpha level? . 05 df?_Lb -1 =15 2.2 b What is your criterion t value? (the direction/sign is determined by the alternative hypothesis) — 1. 157 (note that in the t-table, like the unit normal table, only positive values are provided. However, the t-distribution, like the normal distribution has negative values. When conducting a one-tailed test, you must decide whether the criterion t-score should be positive or negative. Like before, draw the distribution. Place the alpha in the side stated by the alternative hypothesis). If you aren’t sure, see the help item (page 2) in the chapter folder. Calculate your sample statistic: Under these conditions, we use the t-test. The strategy for testing our hypothesis with a z-score or t-score is the same. And that similarity is very evident in this chapter, where we assume we still know the u We can use the same numerator, M -, but we have to replace a,, as the denominator. Just as M estimates u, we'll calculate the sample standard deviation, s, to estimate o. We'll use s to calculate sy to replace @, as the denominator.

4] W\ . e E\‘[\\\ Stony Brook University Name: For the sole use of students at Stony Brook University. Copyringr. Brenda J Anderson) All Rights Reserved 2.4a Draw a conclusions and report the statistics by stating a conclusion about the effect and then reporting the statistics between brackets following the sentence as shown here tC)=_p< .05; Reject/Fail to Reject the Null Hypothesis]. To start you off, make a statement that answers the following question: Did flu shots reduce absences? 2.4b Why do you think it is important to list the df? Will t-scores have the same probability when df changes? 11 2.5a What is the estimated effect size? Use Cohen’s d (covered in video 3 and slides 79-82) 2.5b What is the effect size? Use r? 3a In both examples, we had to estimate the standard error of the mean, because we didn’t have the population standard deviation. What did we substitute in the formula to obtain this estimate? S When we knew the population standard deviation (chapters 7 & 8), we could calculate the Oy. That told us with some certainty the distance between the typical sample mean and the population mean. Now, we have to estimate the @, which leaves us less certain about distance between sample means and the population mean. In other words, we don’t know the width of our distribution of means. 4 3b To be cautious, we judge samples means against a distribution that is broader than the normal distribution. This distribution is called __ 4 -l )b uih O 3¢ This type of distribution gets wider when we have Lowe 11, and narrow when we have 3d One way to compare the normal distribution and the new distribution is to look at the difference in criterion scores. In chapter 8, an alpha = .05 and a 2-tailed test gave us a criterion z-score of A , regardless of sample size.

Ffl‘:\x Stony Brook University d Name: For the sole use of students at Stony Brook University. Copyright © 2019 (Copyright Dr. Brenda J Anderson) All Rights Reserved 3e When working with t-distributions, how many subjects would we need to have a t- criterion score of +1.96? (@2 3f If we had only 20 subjects in our sample, our criterion t-score would be 2 : That is nearer/farther lcircle one) from the center of the distribution than the criterion score for an infinite number of sample subjects. 4. 1magine we have a sample mean of 24 with a standard deviation of 10 and a sample size of 25. The population has a mean of 20)The population is normally distributed. We don’t know the population standard deviation so we have to estimate the standard error of the mean (sw). This produces a t-score because it belongs to a wider distribution called the t-distribution. Would you reject or fail to reject the null hypothesis? Assume you are using a 2-tailed test and alpha .05. 4.1a What is your criterion t-score? 2 : 4.1b What is your sample t-score? 4.1c Would you reject the null hypothesis? _\Q LV Now imagine that you found the population standard deviation. It was also 10. Since this allows us to calculate the true @,,, we can calculate the z-score instead of the t-scores. Z-scores are normally distributed, and therefore you can use the unit normal table. In this case, would you reject or fail to reject the null hypothesis? 4.2a What is your criterion z-score? -\ O\.s A 4.2b What is your sample z-score? VL e 3 T L 4.2¢ Would you reject the null hypothesis? A = \J 4.3 The two conditions above differed. In the first, we didn’t know o, and in the second, we did. If your rejection of the null was different for the two conditions, explain why. Use your own words. You may use figures. (if you have trouble, refer back to video 2, and slides 37-75). 0 AU AN