# HOMEWORK 6 z tests and single sample t-tests

HOMEWORK 6 z tests and single sample t-tests

Homework 6

z tests and single sample t-tests

When submitting this file, be sure the filename includes your full name, course and section. Example:  HW6_JohnDoe_510B01

Be sure you have reviewed this module/week’s lesson and presentations along with the practice data analysis before proceeding to the homework exercises. Complete all analyses in SPSS, then copy and paste your output and graphs into your homework document file. Answer any written questions (such as the text-based questions or the APA Participants section) in the appropriate place within the same file.

Every question is worth 2 points.

 Part I: General Concepts These questions are based on the concepts covered in this week’s assigned readings and presentations.

 Fill in the highlighted blanks with the best word or words. 1) For single-sample statistical tests, you choose a (answer here) test if the population variance is known, and a (answer here) test if the population variance is unknown. 2) The critical value for a one-tailed one sample z- test is +/-: (answer here) 3) If the z–score for a sample mean is 1.75, and it was a one-tailed z-test, we  (answer here) the null hypothesis. 4) A researcher reports the results of a single-sample t-test as t(28) = 1.80. The degrees of freedom for this t-test are (answer here), which means there were (answer here) total participants in the researcher’s sample. 5) Based on the information in question #4 above and knowing it is a two-tailed test, the critical t value is: (answer here)

 Given a population standard deviation of 40, calculate the standard deviation of the mean ( given the following sample sizes (show all your work): 6) N = 25 Answer: 7) N = 60 Answer:

 If you know the sample mean for worker satisfaction is 77.3, and the estimated standard error of the mean is 11.7, and the sample size is 30, calculate the 95% confidence interval for a non-directional test (show all your work): 8) Confidence Interval (lower and upper limits): Answer: 9) Written statement: Answer:

 Calculate the critical degrees of freedom and identify the critical t value for a single-sample t test in each of the following situations, using p=.05 for all scenarios. Then, state whether the null hypothesis would be accepted or rejected: 10) Two-tailed test, N = 10, t  = 2.35 df= (answer) critical t = (answer) Reject or Fail to Reject Ho: (answer) 11)  One-tailed test, N = 15, t  = 1.85 df= (answer) critical t = (answer) Reject or Fail to Reject Ho: (answer)

 A company decides to offer a monetary incentive for employees who log a specified number of hours spent exercising in an attempt to improve employee health. The average health score (higher = better) of the 45 employees who logged enough hours was 89. The mean health score for all employees was 85, with a standard deviation of 3.1. 12) What is the alternative hypothesis? Answer: 13) Is this one or two-tailed? Answer: 14) Conduct the z-test. Show your work (use at least two decimal places throughout). What is the zobt score? Answer: 15) What is the z critical value (zcv)? Answer: 16) Write your conclusion in APA format. Don’t forget to include the statistical statement and a decision about the null hypothesis. Answer:

 Part II: SPSS Application These questions require the use of SPSS. Remember you must submit all of your work within this word document. You will need to take a screen shot of your data view if necessary, or copy and paste your output into the spaces below. Remember to report the exact p value provided by SPSS output – simply reporting p<.05 or p>.05 is not acceptable (unless SPSS output states p=.000 – in that case you can report p<.001).

Exercise 1

Create a data file in SPSS using the following memory scores for this sample of 15 fictional patients with dementia:

 8 3 11 7 6 5 4 8 9 8 7 9 5 4 10

Higher memory number indicates better memory performance. Use this information to complete the following in SPSS.

17) Run descriptive statistics on the dementia patients’ memory scores (make sure to include the mean and confidence interval by using the “Explore” option as shown in this week’s presentation).
Answer: SPSS output of descriptive statistics

18) You want to compare your sample dementia patients with a population of age matched controls, and you only know their mean (μ = 13.1). Run a single sample t test. Paste the output below. 2pts
Answer: SPSS output of the t-Test

19) Write a results section in current APA style describing the outcome.

All homework results sections must follow the example given in the SPSS presentation and in the textbook. Results sections are multiple sentences (a single paragraph) and must include the APA-formatted statistical statement and a decision about the null hypothesis.

Answer:

20)  You want to compare your sample dementia patients with a population of patients with TBI and you only know their mean (μ = 8.5). Run a single sample t test. Paste the output below. 2pts
Answer: SPSS output of the t-Test

21) Write a results section in current APA style describing the outcome.

All homework results sections must follow the example given in the SPSS presentation and in the textbook. Results sections are multiple sentences (a single paragraph) and must include the APA-formatted statistical statement and a decision about the null hypothesis.

Answer:

 Part III: Cumulative These questions can be related to anything covered thus far in the course.

Answer the following questions about measures of central tendency and variability using the 6 datum provided in the box. Do not round when calculating these answers.

 11 13 15 17 15 19

22) Which measure of central tendency is most if the data are not skewed, do not contain any outliers, and are interval/ratio? Answer:
23) Calculate the measure of central tendency in the previous answer. Show your work (if applicable) in the “work” section and make sure your final answer is displayed in the “Answer” section. Do not round.
Answer: Work:
24) Which measure of central tendency would be most appropriate if the data were nominal? Answer:
25) Calculate the measure of central tendency in the previous answer. Show your work (if applicable) in the “work” section and make sure your final answer is displayed in the “Answer” section.
Answer: Work:
26) What is the range of the data?
Answer: Work:
27) Calculate the Standard Deviation (Note: Compute by hand using the formula from Module 4 and do not round until the end – when you can report two decimal places. Programs like SPSS or Excel use a slightly different formula that we won’t use until later and will give you the wrong answer for this section.)
Answer:

Work:

A counselor wants to study the relationship between use of social media and number of friends one talks to on a daily basis face-to-face. He collects scores from a sample of 15 patients on two measures: one is a a self-report use of social medial on which higher scores indicate more use of social media (possible range of scores = 0- 30), and the other was a single question – “On average, how many different people do you talk to face-to-face that you consider a friend per week?”.

Is there a significant relationship between these variables? Choose the correct test to analyze this question, set up the SPSS file, and run the analysis. Paste the output, the correct graph to display this relationship, and using complete sentences, report the results in APA style.

 Social media Friends 20 12 27 12 13 5 4 1 8 3 21 4 13 7 25 11 9 15 15 11 23 10 19 9 28 14 15 7 22 6
28) Paste appropriate SPSS output.

Answer:

29) Paste appropriate SPSS graph.
Answer:

30) Write a Results section in current APA style describing the outcome using complete sentences. Make sure you report the statistical notation in APA format, and explicitly make a decision about the null hypothesis.
Answer:

Submit Homework 6 by 11:59 p.m. (ET) on Sunday of Module/Week 6. Remember to name file appropriately.

 Done!

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