Question

In exercise #36 ,test the claim about the population mean  μ at the level of significance a. Assume the population is normally distributed. If convenient, use technology.

Exercise #36

Claim:  μ  < 850; a = 0.025. sample statistics: x = 875, s = 25, n = 14

Answer 1

Null hypothesis H0: = 850

Alternative hypothesis Ha: < 850

Standard error of mean = SE = s / = 25 / = 6.68

Since we do not know the population standard deviation, we will conduct one sample t - test.

Test statistic, t = (Observed mean - Hypothesized mean) / SE

= (875 - 850) / 6.68 = 3.74

Degree of freedom = n-1 = 14 - 1 = 13

P-value = P(t < 3.74, df = 13) = 0.9988

Since p-value is greater than the significance level of 0.025, we fail to reject null hypothesis H0 and conclude that there is no significant evidence that < 850.