The National Health Statistics Report a 10-year old were measured Their mean hei

Question

The National Health Statistics Report a 10-year old were measured Their mean height was 54.5 inches with a described study in which a sample of 100 girl standard deviation 2.7 of inches. A pediatrician claimed in 1960 hat the mean height of 10-year old girls was 54 inches. Do the data provide convincing evidence that the mean height of 10-year old girls has increased since 1960? Use 0.05 as your level of significance. You need to do a hypothesis test to answer this question. O A. Yes, reject the null hypothesis O B. No, accept the null hypothesis O c. here is not enough information to answer the question O D. No, do not reject the null hypothesis

Explanation / Answer

(1)

Data:     

n = 100    

= 54    

s = 2.7    

x-bar = 54.5    

Hypotheses:     

Ho: 54    

Ha: > 54    

Decision Rule:     

= 0.05    

Degrees of freedom = 100 - 1 = 99   

Critical t- score = 1.660391157    

Reject Ho if t > 1.660391157    

Test Statistic:     

SE = s/n = 2.7/100 = 0.27   

t = (x-bar - )/SE = (54.5 - 54)/0.27 = 1.851851852   

p- value = 0.033513612    

Decision (in terms of the hypotheses):     

Since 1.851851852 > 1.660391157 we reject Ho and accept Ha

Conclusion (in terms of the problem):

There is sufficient evidence that the mean height has increased.    

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