Question

Now suppose that the actual mean and standard
deviation of PH measurement are unknown. A researcher would like to test that claim that the
exceeds 8. She collected a random sample of 4 specimens and derived sample mean and standard
deviations as 9.25 and 0.96.

1) find P-value and critical value.

Answer 1

This is the right tailed test .

The null and alternative hypothesis is

H₀ : = 8

H_a : > 8

Test statistic = t

= ( - ) / s / n

= (9.25 - 8) / 0.96 / 4

Test statistic = 2.6042

df = 3

P-value = 0.04

Critical value = 2.353