Question

A family-owned candy company recently hired many new staff members to deal with an increase in demand. They have a day shift (Team A) and a night shift (Team B). Although they are quite happy with their new employees they suspect that some of them may be eating chocolates when they are not looking.

Their signature box weighs 1.87 kgs.
They randomly sampled 9 boxes from Team B and found that on average they weighed 1.37 kgs.
Using the data they collected, the family would like to test whether μ, the mean weight of chocolate per box, is less than their original signature box. Suppose that the weight of chocolate per box is normally distributed with a standard deviation σ= 0.75kg. The p-value associated of the test is .0228.

Which of the following is the appropriate conclusion at the 5% significance level?

a) The data provide evidence to reject H0 and conclude that that the mean weight of each chocalate box is not the required 1.87 kgs.
b) The data provide evidence to reject H0 and conclude that the mean weight of each chocolate box is the required 1.87 kgs.
c) We cannot reject H0. The data do not provide evidence to conclude that the mean weight of each chocalate box is not the required 1.87 kgs.
d) We cannot reject H0. The data do provide enough evidence to conclude that the mean weight of each chocolate box is not the required 1.87 kgs.

Answer 1

A) The data provide evidence to reject H0 and conclude that that the mean weight of each chocalate box is not the required 1.87 kgs.

Explanation:

Given:

Mean, u = 1.87

Sample size, n = 9

Sample mean X' = 1.37

standard deviation, σ= 0.75

P-value = 0.0228

Significance level = 5%

The null and alternative hypotheses:

H0 : u = 1.87

H1 : u < 1.87

Decision rule:

Reject H0, if p-value(0.0228) < significance level (0.05)

Since, we are given a significance level of 5%, and the p-value associated with the test is 0.0228, we can say the data provide evidence to reject H0 and conclude that that the mean weight of each chocalate box is not the required 1.87 kgs, because p-value, 0.0228 is less than level of significance, 0.05