Question

a. Obtain individual normal probability plots and the standard deviation of the samples.

b. Perform a residual analysis.

c. Use your results from parts (a) and (b) to decide whether conducting a one-way ANOVA test on the data is reasonable. If so. also do parts (d) and (e).

d. Use a one-way ANOVA test to decide, at the $5\%$significance level, Whether the data provide sufficient evidence to conclude that a difference exists among the means of the populations fewer than the samples were taken.

e. Interpret your results from part (d)

Daily TV Viewing Time. Nielsen Media Research collects information on daily TV viewing time, in hours, and publishes its findings in Time Spent Viewing. The WeissStats site provides data on daily viewing times of independent simple random samples of men, women, teens, and children.

Short answer

(a) The standard deviation of the samples are

Men$=1.486$

Women$=1.69$

Teens $=1.04$

Children $=1.08$

(b) The residual analysis is

(c) Conducting of ANOVA test on given data is reasonable.

(d) An ANOVA test is run on the data.

(e) The statistics give adequate evidence to establish that the four groups' average TV viewing times differ.

Step-by-step solution

Part (a) Step 1: Concept introduction

ANOVA, or non - parametric tests, is a potent quantitative approach for revealing the disparity amongst two or more phenomena or aspects using variable importance. It also illustrates how to determine statistical significance among several demographics.

Part (a) Step 2: Explanation

To plot the normal probability plots and determine their standard deviations, use any software.

Enter the men's data that has been provided.

Men's normal probability plot is shown below.

Enter the given data of women.

The normal probability plot of women is given below.

Enter the given data of teens.

The normal probability plot of teens is given below.

Enter the given data of children.

The normal probability plot of children is given below.

The standard deviations are

Men$=1.486$

Women$=1.69$

Teens$=1.04$

Children$=1.08$

Part (b) Step 1: Concept introduction

ANOVA, or non - parametric tests, is a potent quantitative approach for revealing the disparity between two or more phenomena or aspects using variable importance. It also illustrates how to determine statistical significance among several demographics.

Part (b) Step 2: Explanation

To perform residual analysis, you can use any software.

Fill in the time and group information.

Draw the residual probability distribution.

Draw the plot of residual verses fits.

Part (c) Step 1: Concept introduction

ANOVA, or non - parametric tests, is a potent quantitative approach for revealing the disparity amongst two or more phenomena or aspects using variable importance. It also illustrates how to determine statistical significance among several demographics.

Part (c) Step 2: Explanation

From parts a and b

The ratio of largest to smallest standard deviations is

$=\frac{1.695}{1.04}$

$=1.63<2$

The ratio must not exceed two.

It shows that the equal standard deviation assumption is not broken.

As a result, the assumptions of normal populations and equal standard deviations in the population are met.

As a result, performing an ANOVA test on the data is plausible.

Part (d) Step 1: Concept introduction

ANOVA, or non - parametric tests, is a potent quantitative approach for revealing the disparity amongst two or more phenomena or aspects using variable importance. It also illustrates how to determine statistical significance among several demographics.

Part (d) Step 2: Explanation

The level of significance is $\alpha =0.05$

Let us see the below test hypothesis

Null hypothesis

$H_0$: There is no difference exist in the mean TV viewing times of the four groups.

Alternative hypothesis

$H_a$: There is difference exist in the mean TV viewing times of the four groups.

To determine the test statistic, run the ANOVA test using any software.

After entering the given information, we receive F-static width="59">=37.65and $p-$value$=0$ .

As a result, an ANOVA test is run on the data.

Part (e) Step 1: Concept introduction

ANOVA, or non - parametric tests, is a potent quantitative approach for revealing the disparity amongst two or more phenomena or aspects using variable importance. It also illustrates how to determine statistical significance among several demographics.

Part (e) Step 2: Explanation

From part d

The $p-$value is $0$

The rejection rule

$p-value\le \alpha$, the null hypothesis is rejected

The level of significance, $\alpha =0.05$

$p-value(0.0)<\alpha (0.05)$

As a result, the null hypothesis is rejected at a significant level of $5\%$.

As a result, the results are statistically significant at the $5\%$level.

As a result, the statistics give adequate evidence to establish that the four groups' average TV viewing times differ.