Question

a)

In order to estimate if there is astatistical difference between the average hourly wages of employees of two branches of a department store, two independent random samples were selected and the following statistics were calculated. Downtown Store North Mall Store 25 20 Sample size Sample mean Sample standard deviation $9 $8 $2 $1 For alpha= 1, the null hypothesis should be rejected should not be rejected should be revised None of the answers is correct.

b)

Answer 1

Answer: a) In order to estimate if there is astatistical difference between the average hourly wages of employees of two branches of a department store, two independent random samples were selected.

Solution:

The hypothesis test:

Ho: μ1 = μ2

Ha: μ1 ≠ μ

Test statistic t:

t = (x̄1 - x̄2)/√(s1^2/n1 + s2^2/n2)

t = (9 - 8)/√(2^2/25 + 1^2/20)

t = 2.1822

Test statistic t = 2.182

df = [s1^2/n1 + s2^2/n2]^2 / [s1^2/n1]^2/n1-1 + [s2^2/n2]^2/n2-1

df = [2^2/25 + 1^2/20]^2 / [2^2/25]^2/25-1 + [1^2/20]^2/20-1

df = 36

P-value from test statistic and df:

P-value = 0.0357

Since, P-value (0.03) < α (0.10) significance level.

We reject the null hypothesis Ho.

​Therefore, the first option is correct answer.

The null hypothesis should be rejected.

Answer: b) A statistics teacher wants to see if there is any difference in the abilities of students enrolled in statistics today and those enrolled five years ago.

Solution:

The hypothesis test:

Ho: today = 5 years ago.

Ha: today ≠ 5 years ago.

The first option is correct answer.

The null hypothesis is

Ho: today = 5 years ago.