Question

9)Test the claim that σ² < 44.8 if n = 28, s² = 28, and α = 0.10. Assume that the population is normally

distributed. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement on the decision.

10)The heights (in inches) of 20 randomly selected adult males are listed below.  Test the claim that the

variance is less than 6.25. Assume the population is normally distributed. Use α = 0.05. Identify the claim, state the null and alternative hypotheses, find the critical value, find the standardized test statistic, make a decision on the null hypothesis (you may use a P-Value instead of the standardized test statistic), write an interpretation statement on the decision.

70 72 71 70 69 73 69 68 70 71

67 71 70 74 69 68 71 71 71 72

Answer 1

9)

Given : Hypothesized value=

Sample size=n=28

Sample standard variance=s²=28

Significance level=

a) Claim :

b) The null hypothesis is ,  

The alternative hypothesis is ,   

c) Since , the test is left tailed test.

The critical value is ,

; From excel "=CHIINV(0.9,27)"

d) The standardized test statistic is ,

e) Decision : Here ,

Therefore , reject the null hypothesis.

f) Interpretation: Hence , there is sufficient evidence to support the claim that the variance is less than 44.8

10)

Given : Hypothesized value=

Sample size=n=20

From the given sample data , Sample standard variance=s²=

Significance level=

a) Claim :

b) The null hypothesis is ,  

The alternative hypothesis is ,   

c) Since , the test is left tailed test.

The critical value is ,

; From excel "=CHIINV(0.95,19)"

d) The standardized test statistic is ,

e) Decision : Here ,

Therefore , reject the null hypothesis.

f) Interpretation: Hence , there is sufficient evidence to support the claim that the variance is less than 6.25