Question

A sample mean, sample standard deviation, and sample size are given. Use the one-mean t-test to perform the required hypothesis test about the mean, μ, of the population from which the sample was drawn. Use the critical-value approach.

, , n = 18, H₀: μ = 10, H_a: μ < 10, α = 0.01

Group of answer choices

Test statistic: t = -4.43. Critical value: t = -2.33. Reject H₀. There is sufficient evidence to support the claim that the mean is less than

Test statistic: t = -4.43. Critical value: t = -2.567. Reject H₀. There is sufficient evidence to support the claim that the mean is less than

Test statistic: t = -4.43. Critical value: t = -2.33. Do not reject H₀. There is not sufficient evidence to support the claim that the mean is less than

Test statistic: t = -4.43. Critical value: t = -2.552. Reject H₀. There is sufficient evidence to support the claim that the mean is less than

Answer 1

Solution : -

Given that ,

The null and alternative hypothesis is

H0 : = 10

Ha : < 10

This is the left tailed test .

Test statistic = t = -4.43

n = 18

df = n - 1 = 18 - 1 = 17

= 0.01

t,df = t0.01 , 17 = -2.567

The critical value t = -2.567

-4.43 < -2.567

Test statistic < Critical value   

Reject the null hypothesis .

Answer : - Test statistic: t = -4.43. Critical value: t = -2.567. Reject H0. There is sufficient evidence to support the claim that the mean is less than 10 .