Question

A random sample of 100 observations from a population with standard deviation 14.29 yielded a sample mean of 92.7.

1. Given that the null hypothesis is μ=90 and the alternative hypothesis is μ>90 using α=.05, find the following:

(a) Test statistic =

(b) P - value:

(c) The conclusion for this test is:

A. There is insufficient evidence to reject the null hypothesis

B. Reject the null hypothesis

C. None of the above

2. Given that the null hypothesis is μ=90 and the alternative hypothesis is μ≠90 using α=.05, find the following:

(a) Test statistic =

(b) P - value:

(c) The conclusion for this test is:

A. Reject the null hypothesis

B. There is insufficient evidence to reject the null hypothesis

C. None of the above

Answer 1

given data are:-

sample mean () = 92.7

population sd () = 14.29

sample size (n) = 100

1).hypothesis:-

a).test statistic :-

b).p value:-

[ using standard normal table]

c).The conclusion for this test is:-

Reject the null hypothesis (B)

[ p value =0.0294 <0.05 (alpha).]

2).hypothesis:-

a).test statistic :-

b).p value:-

[ using standard normal table]

c).The conclusion for this test is:-

There is insufficient evidence to Reject the null hypothesis (B)

[ p value =0.0588 > 0.05 (alpha).]

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