Question

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

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

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

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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