A statewide census examined the number of beds in households andreported a mean (μ) of 2.25 beds and standard deviation (σ) of 1.9beds per household. But, since I live in a neighborhood with largerfamilies, I have a hunch that the average number of beds inhouseholds will be higher in my neighborhood. To test this idea, Irandomly picked 25 families in my neighborhood and surveyed them onthe number of beds in their home. I would like to perform a Z testto see if the average number of beds in households in myneighborhood is significantly higher than the statewide average.The significance level for my Z test was set at α = .10.
Household # | # of beds |
1 | 3 |
2 | 2 |
3 | 3 |
4 | 2 |
5 | 1 |
6 | 3 |
7 | 2 |
8 | 3 |
9 | 2 |
10 | 4 |
11 | 2 |
12 | 4 |
13 | 3 |
14 | 4 |
15 | 1 |
16 | 2 |
17 | 3 |
18 | 6 |
19 | 3 |
20 | 2 |
21 | 3 |
22 | 4 |
23 | 3 |
24 | 2 |
25 | 4 |
a) What is the dependent variable in this study? b) What shouldbe my null and alternative hypotheses? State each hypothesis usingboth words and statistical notation. Hint: I am interested in theidea of my neighbors having more beds per household than the stateaverage, so the hypotheses would be directional. c) Calculate thesample mean. d) Calculate standard error (SE, which is the standarddeviation of the sampling distribution) e) Calculate the Zstatistic (which indicates where our sample mean is located on thesampling distribution) f) Specify whether the hypothesis testshould be a two-tailed or a one-tailed test, and explain therationale for the choice. g) Determine the critical value for Z h)Compare obtained Z and critical Z and then make a decision aboutthe result of the hypothesis test: Explicitly state “reject†or“fail to reject†the null hypothesis i) Write a 1-2 sentenceconclusion interpreting the results (you can simply restate theaccepted hypothesis or explain it in another way) j) Calculate theraw and standardized effect sizes k) If the test was done with αlevel of .05, using the same directional hypotheses, what would bethe critical Z value from the Z table? What would be the result ofthe hypothesis test (in terms of rejecting or failing to reject thenull hypothesis)? l) Compare the hypothesis tests result when α =.05 and when α = .10. Were the results the same? Why or whynot?
