Question

We are testing H0: µ ≤ 42; versus HA: µ > 42. When Picture = 45, s = 1.2, and n = 15, at α = .01 we do not reject the null hypothesis. (Assume that the population from which the sample is selected is normally distributed.)

True

False

Answer 1

False

Explanation:

H0: µ ≤ 42

HA: µ > 42

S represents the sample standard deviation, then we must use the t-student test.

t-statistic formula:

t= (xbar-m)/(S/(sqrt(n)))

xbar: sample mean

m: hypothesized value

S: sample standard deviation

n: number of observations

t=(45-42)/(1.2/sqrt(15))

t-statistic= 9.682

The critical value from the t-student distribution with, 15-1 degrees of freedom and 1% significance level , is 2.6245

Because the t-statistic is greater than the critical value, we must reject the null hypothesis.