Question

A company has two locations that provide technical support to cell phone costumers, office A and Office B. An analyast suspects that the variance of the time it takes to resolve costumer issues is higher at office A than office B. The analyast takes a random sample of 16 issues at office A and measures time to resolution and finds a variance of 102. A random sample of 21 issues at office B has a variance of 64.3.

The analyast performs a hypothesis that at the a=.05 sig level to determine if the variance of issue resolution times at office A is higher than the variance issue times at office B.

A) what is the hypothesis?

B) what is the test statistic?

C) what is the numerator degrees of freedom, df1?

D) recall that a=.05 the critical value is:

E) should he bull be rejected?

F) at the a=.05 sig level the analyast a)can b) can not conclude that office a has a)higher b) lower A)variance b) mean of resolution timesbthan office B

Answer 1

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H₀: ?_A²< ?_B²

Alternative hypothesis H_A: ?_A² > ?_B²

Formulate an analysis plan. For this analysis, the significance level is 0.05.

Analyze sample data. Using sample data, the degrees of freedom (DF), and the test statistic (F).

DF₁ = n₁ - 1 = 16 -1

D.F₁ = 15

DF₂ = n₂ - 1 = 21 -1

D.F₂ = 20

Test statistics:-

F = 1.59

F_critical = 2.203.

Since the first sample had the larger standard deviation, this is a right-tailed test.

p value for the F distribution = 0.165

Interpret results. Since the P-value (0.165) is greater than the significance level (0.05), we have to accept the null hypothesis.

From the above test there is insufficient evidence to conclude that the variance of issue resolution times at office A is higher than the variance issue times at office B.

E) Do not reject null hypothesis.

F) At the a=.05 sig level the analyast can not conclude that office a has higher variance mean of resolution timesbthan office B.