Homework: Tests and Single Sample t -tests Assignment Instructions Overview This Homework: Z-Tests & Single Sample T-Tests Assignment is designed to assess your understanding of the concepts and applications

Part I: General Concepts

These questions are based on the concepts covered in this module’s assigned readings and presentations.

Answer the following questions using your own words.

1.

What is the critical value for a one-tailed z test? For a two-tailed z test? Which is more likely to result in a rejection of the null hypothesis? Why?

ANSWER

2.

Why does t_cv. Change when the sample size changes? What must be computed to determine t_cv.?

ANSWER  

3.

Henry performed a two-tailed test for an experiment in which N = 24. He could not find his table of t critical values, but he remembered the t_cv at df = 13. He decided to compare his t_obt with this t_cv. Is he more likely to make a Type I or a type II error in this situation? Briefly discuss why.

ANSWER

Given a population standard deviation of 12, answer the following two questions.

4) Calculate the standard error of the mean (  given the following two sample sizes (show all your work and round to two decimal places):

N₁ = 20

N₂ = 70

WORK:

N₁ =

N₂ =

ANSWER

N₁ =

N₂ =

5) How does the sample size change the standard error of the mean? What does this mean for statistical power?

ANSWER

Calculate the critical degrees of freedom and identify the critical values for the following tests, using p = .05 and the tables in your e-book for all scenarios (do NOT round). Then, state whether the null hypothesis would be rejected or failed to be rejected.

6) Single sample t-test: two-tailed, N = 20,  t  = 2.05

df= ANSWER

critical t = ANSWER

Reject or Fail to Reject H_o:

ANSWER

7)  Single sample t-test: one-tailed, N = 20,  t  = 2.05

df= ANSWER

critical t = ANSWER

Reject or Fail to Reject H_o:

ANSWER

8) Pearson’s r correlation: two-tailed, N = 15, r = 0.47

df= ANSWER

critical r = ANSWER

Reject or Fail to Reject H_o:

ANSWER

9) Pearson’s r correlation: one-tailed, N = 15, r = 0.47

df= ANSWER

critical r = ANSWER

Reject or Fail to Reject H_o:

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 75 employees who logged enough hours was 87. The mean health score for all employees (population) was 85, with a population standard deviation of 6.5.

10) Calculate the standard error of the mean.

ANSWER

11) Conduct the z-test. Show your work (use at least two decimal places throughout).

What is the z_obt score?

ANSWER

12) Write your conclusion using complete sentences in APA format. Don’t forget to include the statistical statement and whether you reject or fail to reject 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

Spatial ability was quantified using a sample of the general population (N=15). Their scores are shown below, where higher scores represent better spatial ability. Enter this data into SPSS to answer the following questions.

13)

Run descriptive statistics for general population data provided above (make sure to include the mean and confidence interval by using the “Explore” option as shown in this module’s presentation).

ANSWER SPSS output of descriptive statistics

14)

You want to compare your sample of the general population to individuals who listen to classical music, but you only know their mean (m = 60). Run a single sample t test. Paste the output below.

ANSWER: SPSS output of the t-Test

15)

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.

A recruiter wants to know if college GPA is truly predictive of one’s grit. He examined this by having 14 job applicants complete a grit inventory using a Likert scale (range 1 -7) where higher numbers indicate more “grit”. GPA was confirmed using college transcripts (scale 0 – 4.0). Enter the data shown below into SPSS to assess whether GPA can predict one’s grit.

Remember – prediction requires a different analysis than mere relationships. Choose the correct test to analyze this question, set up the SPSS file, and run the analysis. Paste the output, appropriate graph, and then report the results using complete sentences in APA style following the example in the lecture presentation for this statistical test.

16) Paste appropriate SPSS output.

ANSWER

17) Paste appropriate SPSS graph.

ANSWER

18) 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 inclue all relevant information.

ANSWER

Done!