Witte & Witte, 9e Page 1 of 3 Pages
Chapter 10
Chapter 10: Introduction to Hypothesis Testing: The z Test
Exercise 1
Calculate the value of the z test for each of the following situations:
a. = 100; = 16; n = 25; = 94
b. = 100; = 15; n = 9; = 108
c. = 150; = 20; n = 81; = 130
d. = 150; = 20; n = 9; = 130
e. = 10; = 2; n = 25; = 11
Answers:
a. z = -1.25
b. z = 0.60
c. z = -9.00
d. z = -3.00
e. z = 2.5
Exercise 2
The national norms for youth fitness tests are available on a website, http://www.exrx.net/Testing/YouthNorms.html. Let’s say that a physical education teacher wants to test null hypotheses related to these norms. First using words, then symbols, identify the null hypothesis for each of the following.
a. The teacher wants to determine whether the 13-year-old girls in the school district differ, on average, from the girls’ national norm of 1,861 yards for the 12-minute run.
b. The teacher wants to determine whether 13-year-old boys in the school district differ, on average, from the boys’ national norm of 2,592 yards for the 12-minute run.
c. The teacher wants to determine whether the 15-year-old boys in the school district differ, on average, from the boys’ national norm of 23 push ups.
d. The teacher wants to determine whether the 15-year-old girls in the school district differ, on average, from the girls’ national norm of 18 push ups.
e. The teacher wants to determine whether the 16-year-old boys in the school district differ, on average, from the boys’ national norm of 7 pull ups.
f. The teacher wants to determine whether the 16-year-old girls in the school district differ, on average, from the girls’ national norm of 33 sit ups.
g. The teacher wants to determine whether the 16-year-old boys in the school district differ, on average, from the boys’ national norm of a standing long jump of 84 inches.
Answers:
a. The 13-year-old girls in the school district average 1,861 yards in 12 minutes. H0: = 1,861 yards.
b. The 13-year-old boys in the school district average 2,592 yards in 12 minutes. H0: = 2,592 yards.
c. The 15-year-old boys in the school district average 23 push ups. H0: = 23 push ups.
d. The 15-year-old girls in the school district average 18 push ups. H0: = 18 push ups.
e. The 16-year-old boys in the school district average 7 pull ups. H0: = 7 pull ups.
f. The 16-year-old girls in the school district average 33 sit ups. H0: = 33 sit ups.
g. The 16-year-old boys in the school district average distance for a standing long jump is 84 inches. H0: = 84 inches.
Exercise 3
For each of the following situations, indicate whether H0 should be retained or rejected and justify your answer by specifying the precise relationship between observed and critical z scores. Should H0 be retained or rejected, given a hypothesis test with critical z scores of ± 1.96, and
a. z = 1.96
b. z = -1.96
c. z = 0.05
d. z = -0.025
e. z = -1.98
f. z = -2.78
g. z = 3.59
Answers:
a. Reject H0 at the .05 level of significance because z = 1.96 is equal to the critical z score of 1.96.
b. Reject H0 at the .05 level of significance because z = -1.96 is equal to the critical z score of -1.96.
c. Retain H0 at the .05 level of significance because z = 0.05 is less positive than 1.96.
d. Retain H0 at the .05 level of significance because z = -0.025 is less negative than 1.96
e. Reject H0 at the .05 level of significance because z = -1.98 is more negative than 1.96.
f. Reject H0 at the .05 level of significance because z = -2.78 is more negative than 1.96.
g. Reject H0 at the .05 level of significance because z = 3.59 is more positive than 1.96.
Exercise 4
Last year, the average cost for upscale kitchen remodeling in an exclusive suburb of Chicago was $68,900, with a standard deviation of $15,800. A researcher wishes to find out if the $68,900 average also describes the upscale kitchen remodeling jobs completed in an exclusive suburb of Detroit. Modeling cost information is obtained for a random sample of 16 homeowners. The mean cost for the upscale kitchen remodeling jobs in the sample equals $66,500.
a. The researcher wishes to conduct a hypothesis test for what population?
b. What is the null hypothesis, H0?
c. What is the alternative hypothesis, H1?
d. Specify the decision rule, using the .05 level of significance.
e. Calculate the standard error of the mean.
f. Calculate the value of z.
g. What is your decision about H0?
h. Using words, interpret this decision in terms of the original problem.
Answers:
a. The population of interest is the cost of upscale kitchen remodeling jobs in an exclusive suburb of Detroit.
b. The null hypothesis is that the average cost of the remodeling jobs in the Detroit suburb is $68,900. H0: = $68,900
c. The alternative hypothesis is that the average cost of the remodeling jobs in the Detroit suburb is not $68,900. H1: ≠ $68,900.
d. Reject the null hypothesis if the obtained z value ≥1.96 or if the obtained z value ≤ -1.96.
e. = 3,950
f. = -0.61
g. Retain the null hypothesis because z = -0.61 is less negative than -1.96.
h. There is no evidence that the average cost of upscale kitchen remodeling jobs in the Detroit suburb differs from $68,900.
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