Question

2. Given the null and alternative hypotheses and the test statistics provided, compute the p-value for each of the following hypothesis testing scenarios. If the tests are conducted at 5% level of significance, what will be your decisions in each case?

a. Ho: µ = 1346 versus Ha: µ ≠ 1346 and test statistic Z* = 2.30

b. Ho: µ ≥ 4000 versus Ha: µ < 4000 and test statistic Z* = -1.80

c. Ho: µ ≤ 24.78 versus Ha: µ > 24.78 and test statistic Z* = 0.84

d. Ho: µ ≥ 200 versus Ha: µ < 200 and test statistic Z* = -2.10

Answer 1

a)

For two tailed test, Critical values at 0.05 level = -1.96 , 1.96

Rejection rule = reject H0 if z < -1.96 or z > 1.96

Since test statistics falls in rejection region, we have sufficient evidence to reject H0.

b)

For left tailed test, Critical value at 0.05 level = -1.645

Rejection rule = reject H0 if z < -1.645

Since test statistics falls in rejection region, we have sufficient evidence to reject H0.

c)

For right tailed test, Critical value at 0.05 level = 1.645

Rejection rule = reject H0 if z > 1.645

Since test statistics falls in non-rejection region, we do not have sufficient evidence to reject H0.

d)

For left tailed test, Critical value at 0.05 level = -1.645

Rejection rule = reject H0 if z < -1.645

Since test statistics falls in rejection region, we have sufficient evidence to reject H0.