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 P-value approach. Also, assess the strength of the evidence against the null hypothesis.

sample mean = 24.4, s = 9.2, n=25, H0: μ = 26, Ha : μ , 26, α = 0.05

Options:

A: Test statistic: t = -0.87. P-value = 0.1922. Do not reject H₀. There is not sufficient evidence to conclude that the mean is less than 26. The evidence against the null hypothesis is strong.

B: Test statistic: t = -0.87. P-value = 0.8034. Do not reject H₀. There is not sufficient evidence to conclude that the mean is less than 26. The evidence against the null hypothesis is weak or none.

C: Test statistic: t = -0.87. P-value = 0.1966. Do not reject H₀. There is not sufficient evidence to conclude that the mean is less than 26. The evidence against the null hypothesis is weak or none.

D: Test statistic: t = -0.87. P-value = 0.8078. Do not reject H₀. There is not sufficient evidence to conclude that the mean is less than 26. The evidence against the null hypothesis is strong.

Answer 1

Ans:

Test statistic:

t=(24.4-26)/(9.2/SQRT(25))

t=-0.87

df=25-1=24

p-value=TDIST(0.87,24,1)=0.1966

As,p-value>0.05,so we fail to reject H0.

Option C is correct.

Test statistic: t = -0.87. P-value = 0.1966. Do not reject H0. There is not sufficient evidence to conclude that the mean is less than 26. The evidence against the null hypothesis is weak or none.