Question

A random sample of 100100 observations from a population with standard deviation 10.7610.76 yielded a sample mean of 91.891.8.

1. Given that the null hypothesis is μ=90μ=90 and the
alternative hypothesis is μ>90μ>90 using α=.05α=.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=90μ=90 and the
alternative hypothesis is μ≠90μ≠90 using α=.05α=.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

Answer #1

Here population standard deviation is known so we will use z statistics

1. a. Test statistics is

b. P value is

c. As P value is less than alpha we reject the null hypothesis

Hence answer here is

**B.** Reject the null hypothesis

2. a. Test statistics is

b. P value is

c. As P value is greater than alpha=0.05, we fail to reject the null hypothesis

So answer here is **A.** There is insufficient
evidence to reject the null hypothesis

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