Question

Eliminate one magazine type that you now feel has a mean length different from the others. Redo the hypothesis test, testing that the remaining three means are statistically the same. Use a new solution sheet. Based on this test, are the mean lengths for the remaining three magazines statistically the same?

Short answer

We accept the null hypothesis.

Step-by-step solution

Given Information

Explanation

Consider the null hypothesis that there is no significance difference between the lengths of three magazine types. For this, use Ti-83 calculator. For this, click on STAT $\to$press $1\to$EDIT, then put the above given weights of different groups data into the list $L1,L2andL3$. The screenshot is given as below:

Explanation

Now Again press STAT $\to$arrow over the TESTS $\to$arrow down to ANOVA $\to$Press var then select $1$, press var then select $2$, and press var then select $3$to fill the values of $L1,L2andL3$. The screen shot is given as below:

Explanation

Press ENTER. The screenshot of the obtained output of is given as below:

Explanation

Use the above results to solve the below given subparts.

a. The null hypothesis that three mean commuting mileages are same is given as below:

$H_0:{\mu }_1={\mu }_2={\mu }_3$

b. The alternate hypothesis will be at least any two of the means are different.

c. The degree of freedom in the numerator is $2$, and the degree of freedom in the denominator is $12$

d. The $F$distribution is used for the test of three different means.

e. The value of the test statistic is $2.12$.

Explanation

f. The $P$-value for the test is $\mathbf{0}\mathbf{.}\mathbf{162}$.

g). The graph of the distribution is given as below:

Explanation

h.

a. Level of significance $\alpha$is $0.05$.

b. Decision: Null hypothesis will be accepted.

c. Reason for decision: $P$-value is $0.16$, which is greater than the $0.05$level of significance.

d. The lengths of three magazine types (News, Health and Computer) are same.

Explanation

We accept the null hypothesis.