This problem can be solved manually or using Excel\'s Test Statistics or Estimat

Question

This problem can be solved manually or using Excel's Test Statistics or Estimators workbooks. a. A random sample of 11 observations was taken from a normal population. The sample mean and standard deviation are x = 74.5 and s = 9. Can we infer at the 5% significance level that the population mean is greater than 70? b. Repeat Part (a) assuming that you know that the population standard deviation is sigma = 90. Can we infer at the 5% significance level that the population mean is greater than 70? c. Explain why the conclusions produced in Parts (a) and (b) differ. The Student t distribution is the standard normal.

Explanation / Answer

A. ho:null hypothesis : u<=70

Ha:u>70

we need one tail test

t-stat=X-u/SE SE=SD/SQRT(N) =(74.5-70)/(9/SQRT(11)) =1.66

P(X<1.66)=0.95 WHICH is more than significance level we cnt reject null hypothesis

b. sd=90 t-stat=(4.5)/90/sqrt(11)=0.165

P(X<0.16)=0.56 WHICH is more than significance level we cant reject null hypothesis

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