Question

The CEO of the Jen and Benny's ice cream company is concerned about the net weight of ice cream in their 50 ounce ice cream tubs. He decides that he wants to be fairly sure that the mean weight of these ice cream tubs (μ) is greater than 53 ounces. A hypothesis test is conducted with the following hypotheses:

H0: μ = 53

Ha: μ > 53

The level of significance used in this test is α = 0.05. A random sample of 26 ice cream tubs are collected and weighed. The sample mean weight is calculated to be x = 55.75 and the sample standard deviation is s = 8.77.

a)Calculate the test statistic (t) for this test. Give your answer to 4 decimal places.

t =

b)The result of this test is that the null hypothesis rejected.

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :   = 53

H_a : > 53

= 55.75

= 53

s = 8.77

n = 26

df = n - 1 = 26 - 1 = 25

Test statistic = t

= ( - ) / s / n

= (55.75 - 53) / 8.77 / 26

= 1.5989

Test statistic = 1.5989

P-value = 0.0612

= 0.05

P-value >

Fail to reject the null hypothesis .