Question

We would like to conduct a hypothesis test at the 2% level of significance to determine whether the true mean pH level in a lake differs from 7.0. Lake pH levels are known to follow a normal distribution. We take 10 water samples from random locations in the lake. For these samples, the mean pH level is 7.3 and the standard deviation is 0.37. Using the critical value approach, the decision rule would be to reject H₀ if the test statistic is:

Question 12 options:

	A) less than -2.326 or greater than 2.326
	B) less than -2.398 or greater than 2.398
	C) less than -2.564 or greater than 2.564
	D) less than -2.764 or greater than 2.764
	E) less than -2.821 or greater than 2.821

Answer 1

Given that, sample size (n) = 10

sample mean = 7.3 and sample standard deviation = 0.37

The null and alternative hypotheses are,

H0 : p = 7.0

Ha : p ≠ 7.0

This test is two-tailed.

Degrees of freedom = 10 - 1 = 9

t-critical values at significance level of 0.02 with 9 degrees of freedom are, t^* = ± 2.821

Excel Command : =TINV(0.02, 9) = 2.821

Therefore, using the critical value approach, the decision rule would be to reject H0 if the test statistic is : less than -2.821 or greater than 2.821

Answer : E)