The National Health Statistics Reports described a study in which a sample of 10

Question

The National Health Statistics Reports described a study in which a sample of 100 10-year old girls were measured. Their mean height was 54 5 inches with a standard deviation of 2.7 inches A pediatrician claimed in 1960 that 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 A. No, accept the null hypothesis B. There is not enough information to answer the question. C. Yes. reject the null hypothesis D. No, do not reject the null hypothesis

Explanation / Answer

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):

Yes, reject Ho. There is sufficient evidence that the mean height has increased.     

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