Question

In: Statistics and Probability

In 1990, the mean height of women 20 years of age or older was 63.7 inches...

In 1990, the mean height of women 20 years of age or older was 63.7 inches based on data obtained from the CDC. Suppose that a random sample of 45 women who are 20 years of age or older in 2015 results in a mean height of 63.9 inches with a standard deviation of 0.5 inch. Does your sample provide sufficient evidence that women today are taller than in 1990? Perform the appropriate test at the 0.05 level of significance.

(a) Give the appropriate hypotheses for this test and define any parameters used.

(b) List and verify conditions for the appropriate hypothesis test.

(c) Give the appropriate test statistic. Show formula, work, and value.

(d) Find the rejection region. Draw an appropriate picture, show work.

(e) What is your decision regarding the null hypothesis?

(f) What are your conclusions about this particular test?

Solutions

Expert Solution

To Test :-

H0 :-  

H1 :-  

Samples taken should be from normal population

Test Statistic :-


t = 2.6833


Test Criteria :-
Reject null hypothesis if

Rejection region  
Result :- Reject null hypothesis


Decision based on P value
P - value = P ( t > 2.6833 ) = 0.0051
Reject null hypothesis if P value < level of significance
P - value = 0.0051 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the claim that today's women re taller than 1990's at 5% level of significance.


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