Question

A random sample of 25 values is drawn from a mound_shaped symmetric distribution. The sample mean is 10 and the sample standard deviation is 2.

Use α = 0.05 to test the claim that the population mean is different from 9.5.

A) Check the requirements.

B) Set up the hypothesis.   

C) Compute the test statistic.

D) Find the p-value.

E) Do we reject or do not reject Ho?

Answer 1

Given,

X_bar = 10

s= 2

n=25

a) Hypothesis :

H₀ : =9.5

H₁ : 9.5

b) test statistic

t = (x_bar - ​​​​​​)/(s/n)

= (10-9.5)/(2/25)

t = 1.25

3) Df = n-1 = 25-1 = 24

p value for t test statistic with 24 degree of freedom is 0.2234.

P value = 0.2234

4) conclusion:

P value (0.2234) is greater than 0.05, hence do not reject null hypothesis.