A random sample of 60 women was collected and the sample mean height for the wom

Question

A random sample of 60 women was collected and the sample mean height for the women was 64.20 inches with a standard deviation of 1.33 inches. Use a 0.05 significance level to test the claim that the mean height for all women from this population that the sample came from is more than 63.8 inches.

a. Write down the null and alternative hypotheses.

b. Determine the test statistic.

c. Determine the range of values for the P-value.

d. Write the decision about the null hypothesis and explain how you reached it. This problem is continued on the next page. 4 Problem 2 continued.

e. Write the conclusion that addresses the original claim.

f. Determine the type of error that could have made, (Type I or Type II), explain why, and what it means in terms of your decision.

Explanation / Answer

a) null hypothesis: mean 63.8

alternate hypothesis: mean>63.8

b) std error =std deviaiton/(n)1/.2 =0.1717

hence test stat t=(X-mean)/std error =(64.20-63.8)/0.1717=2.3296

c) for above at 59 degree of freedom ; p value =0.0116

d) as p value is less then 0.05 level we can reject null hypothesis

e) we have sufficient evidence to conclude that mean height for all women from this population that the sample came from is more than 63.8 inches.

f) this can be type I error as we have rejected null hypothesis. Type I error means rejecting that women height from this population is 63.8 while it is true.

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