Lab 3-One Sample Z and T test_student

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Name: Connor Wood T.A. name: Ziyi Wang Lecturer: Christina Munson Lab 3: One Sample Z and T tests NOTE: SPSS outputs are necessary to show full completion of the lab. Please paste all SPSS outputs into your lab report and submit the completed reports including all requested tables and graphs via Brightspace (under the "Lab" folder) by 11:50 pm Friday. Two points will be deducted for each SPSS requested output that is not included in the submitted lab document. Also, 30% points will be deducted for late submission, up to 24 hours. Dataset : This lab uses the dataset ( SleepPatterns ), located on Brightspace under Lab in the Datasets submodule. Instructions for opening the dataset in SPSS are found as follows.  SPSS installed on a computer: Reference page 4 of the SPSS Instruction Manual  SPSS running remotely: Reference the slide “Opening your Dataset Remotely in SPSS via Go Remote” in the document “SPSS using Citrix access guidelines” on Brightspace. Two 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. 1. 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. i. 250 ii. Sample Mean: 2.98 iii. Standard Deviation: 0.38 Descriptive Statistics N Minimum Maximum Mean Std. Deviation GPA 250 2.10 3.98 2.9816 .38393 Valid N (listwise) 250 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.

The data is mostly Normal with a few values that could be outliers. 2. Previous studies claim that the population mean GPA is 3.0 , with a population standard deviation of 0.4. Therefore, we have knowledge of the population standard deviation. Based on the data, conduct a hypothesis test BY HAND (with a 1% significance level ) to see if there is evidence that the population mean GPA is less than 3.0. a) (1 point) Write down your null and alternative hypotheses. Be sure to use appropriate notation. H o : μ = 3.0 H a : μ < 3.0 b) (2 points) Calculate the test statistic BY HAND. Begin by writing down the formula and be sure to use appropriate notation. Round to 2 decimal places and show your work.

c) (2 points) Give the probability statement for the test statistic and the p-value. Report the p- values to 4 decimal places. P (Z < -0.79) = 0.2148 d) (2 points) State your conclusion in terms of the story . Make sure to specify whether your conclusion refers to the population or the sample . We fail to reject the null hypothesis because there is insufficient evidence to support the alternative hypothesis that the population mean for GPA is less than 3.0. 3. We are still interested in testing the same 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. i. This problem is different from Problem 2 because the population standard deviation is unknown. ii. The test statistic will be different because it will require the t-value since the population standard deviation is unknown. 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 less than 3.0 . 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. i. (1 point) State your null and alternative hypotheses. Be sure to use appropriate notation. H o : μ = 3.0 H a : μ < 3.0 ii. (2 points) Give the value of the test statistic ( USE SPSS, you should NOT calculate this by hand).

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t = -0.759 One-Sample Test Test Value = 3.0 t df Significance Mean Difference 95% Confidence Interval of the Difference One-Sided p Two-Sided p Lower Upper GPA -.759 249 .224 .448 -.01844 -.0663 .0294 iii. (2 points) Write down the probability statement and the p-value ( USE SPSS for the p-value ). Round your answer to 4 decimal places and show your work . P (T<-0.759) = 0.244 iv. (1 point) State your conclusion in terms of the story . Make sure to specify whether your conclusion refers to the population or the sample . We fail to reject the null hypothesis because there is insufficient evidence to support the alternative hypothesis that the sample mean for GPA is less than 3.0. c) (2 points) What is the 95% confidence interval for the population mean GPA ? Keep in mind we still don’t know the true population standard deviation. You should use the SPSS output from (b) and if you are confused, refer to page 11 in the SPSS Instruction Manual. Round your answer to 2 decimal places and show your work. 95% confidence interval for the population mean GPA: (-0.07,0.03) 4. (2 points) Consider the restrictions for using the t test procedures (robustness guidelines), for this sample size. a) What do we need our data to look like for the t procedures to be appropriate? Data with a size of 40 or greater is appropriate for using the t procedures. t test procedures are usually used when the data isn’t normally distributed. Which usually means the data has outliers. b) Is it appropriate to use the t procedures for this data? (Consider using a plot to determine if it is appropriate, but please include it in your Brightspace submission.) It is not appropriate to use the t procedures for this data because the data does not have outliers and is normally distributed. This is demonstrated by the boxplot which shows there are no outliers.

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