A company’s management thinks that monthly sells have increased, and now average over £50 per month.

Question

The distribution is known to be normal.

We assume \sigmaσ = 10 is known.

N = 49

sample mean = 53.1

Test the claim at the 10% significance (\alpha = .10)(α=.10). (first question)

A random sample is obtained from a population with a variance of σ^2 = 200σ
2
=200, and the sample mean is computed to be x̅ c=60.

Test if the mean value is μ=40μ=40.

Test the claim at the 10% significance (\alpha = .10)(α=.10).

Consider the null hypothesis H_0:μ=40H
0
​
:μ=40 versus the alternative hypothesis H_1 μ≠ 40H
1
​
μ

​
=40

The distribution of the mean is normal

N = 100. (second question)

Answer 1

For the first question, the test statistic is z = (53.1 - 50)/(10/√49) = 2.10.

The critical value for a two-tailed test at the 10% significance level is 1.645.

Since the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the mean monthly sales is greater than £50.

For the second question, the test statistic is z = (60 - 40)/(√200/√100) = 4.

The critical value for a two-tailed test at the 10% significance level is 1.645.

Since the test statistic is greater than the critical value, we reject the null hypothesis and conclude that the mean value is not equal to 40.