Lab #3

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Apr 3, 2024

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Lily Liao Yaxin Fang Dr. Munson Lab 3: One Sample Z and T tests One hundred fifty college students in Indiana participated in a study examining the associations among sleep habits, sleep quality and physical/emotional factors. Participants completed an online survey about sleep habits that included the Pittsburgh Sleep Quality Index (PSQI), the Epworth Sleepiness Scale (ESS), the Horne-Ostberg Morningness Eveningness Scale (MES), the Subjective Units of Distress Scale (SUDS), and questions about academic performance and physical health. 1a. Let’s explore the data and collect some information for the mean GPA. a) (1 point) For the variable GPA, identify the following values: (i) the sample size, (ii) the sample mean, (iii) the sample standard deviation. Round the sample mean and sample standard deviation to 2 decimal places. Provide the table where you found this information in SPSS on your output. Sample Size: 150 Sample Mean: 3.0531 Sample Standard Deviation: 0.38596 Descriptive Statistics N Minimum Maximum Mean Std. Deviation GPA 150 2.17 3.97 3.0531 .38596 Valid N (listwise) 150 b) (1 point) Make a Normal quantile plot of the data. Comment on any important features and on the distribution of the data. Attach your SPSS graph.
According to the Normal QQ plot, the data appears to be normally distributed. The vast majority of the points fall on the 45-degree reference line. I notice that the points that don’t fall on the reference line were either the smaller observed values or the larger observed values. The smaller observed values had an expected normal from – 2 to – 1. The larger observed values had an expected normal from 0 to 2. 2. The researchers are concerned that the mean GPA examined in the study is too different from what has been found in other studies. They expected to see an average GPA of 3.15. Based on our data, is there evidence that the true mean GPA for the population is significantly different than the expected average of 3.15 at a 5% significance level? The population standard deviation is 0.4. a) Perform a hypothesis test BY HAND, completing all the following steps. i. (2 point) State your hypotheses. H0: μ= 3.15 HA: µ≠ 3.15 ii. (2 points) Calculate the test statistic BY HAND. Round to 2 decimal places and show your work. α= 0.05 Sample Mean: 3.0531 Population Deviation: 0.4
Sample Size: 150 Testing 3.03: 3.15 Z= 3.0531-3.15/ 0.4/ √150= -0.0969/ 0.03265986=-2.96694475 iii. (2 points) Write down the probability statement and calculate the p-value. Round to 4 decimal places and show your work. P value=(P>2.97) + (P<-2.97) 2 x P(Z>| -2.97|) = 2 x 0.0015=0.003 b) (3 points) Draw your conclusions from the test. 0.003< 0.05 Reject the null. We have evidence that the true mean GPA for the population is not 3.15. c) (1 point) Based on part b), decide whether the researchers’ concerns are warranted. In other words, given your results above, and that the researchers were expecting the mean GPA to be 3.15, should they be worried? Yes, the researchers were indeed correct. They should be worried that the mean GPA turned out to be different than they expected. 3. We are still interested in testing a similar hypothesis as in problem 2, but we really do not have an accurate knowledge of the population standard deviation. a) (1 point) Based on the information given, answer the following: (i) How does this problem differ from Problem 2? (ii) Based on this difference, will the test statistic be different? State the name of the test statistic. Because in this problem the population standard deviation is unknown, this test statistic will no longer follow the standard normal distribution. Instead, a t statistic will be used. b) Based on the data, conduct a hypothesis test (with a 5% significance level) to see if there is evidence that the population mean GPA is greater than 3.03. USE SPSS to find the test statistic and P-value, and as with all work done in SPSS, include your output in your Brightspace submission. One-Sample Statistics N Mean Std. Deviation Std. Error Mean
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