The accompanying data gives the results of a survey on the number of hours spent online per week on a certain social networking website. Determine if the mean number of hours spent online per week is the same for males as it is for females. Assume that the population variances are unequal. E Click the icon to view the social media survey data. .... Is there sufficient evidence at the 0.05 level of significance that the mean number of hours spent online per week is the same for males as it is for females? Determine the null hypothesis, H2, and the alternative hypothesis, H,. Let females be population 1 and males be population 2. Họ H,: (Type integers or decimals. Do not round.) Compute the test statistic. (Round to two decimal places as needed.) Find the p-value for the test. |(Round to three decimal places as needed.) State the conclusion. The p-value is V the chosen value of a, so V the null hypothesis. There is evidence to conclude that the mean number of hours spent online per week for males is different than for females.

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# Analysis of Online Hours Based on Gender

## Introduction

This study investigates whether there is significant evidence at the 0.05 level of significance that the mean number of hours spent online per week is the same for both males and females on a specific social networking platform. It assumes unequal population variances between male and female groups.

## Hypothesis Testing

### Null Hypothesis (H₀)
The mean number of hours spent online per week is the same for both males and females.
\[ H_0: \mu_1 = \mu_2 \]

### Alternative Hypothesis (H₁)
The mean number of hours spent online per week is different for males and females.
\[ H_1: \mu_1 \neq \mu_2 \]

Here, population 1 refers to females and population 2 refers to males.

## Steps to Compute

1. **Compute the Test Statistic:**
   - Round to two decimal places.

2. **Find the p-value:**
   - Round to three decimal places.

3. **State the Conclusion:**
   - Compare the p-value to the chosen level of significance \(\alpha\) = 0.05.
   - Determine whether to reject or fail to reject the null hypothesis.
   - Assess if there is evidence to conclude a difference in online hours between males and females.

## Survey Data

The survey data table includes the gender and the number of hours spent online per week for each participant.

| Gender | Hours Online/Week | Gender | Hours Online/Week |
|--------|-------------------|--------|-------------------|
| Female | 4                 | Male   | 7                 |
| Female | 9                 | Male   | 15                |
| Female | 10                | Male   | 6                 |
| Female | 5                 | Male   | 4                 |
| Female | 7                 | Male   | 6                 |
| Female | 13                | Male   | 3                 |
| Female | 2                 | Male   | 9                 |
| Female | 6                 | Male   | 4                 |
| Female | 3                 | Male   | 6                 |
| Female | 5                 | Male   | 8                 |
| Female | 7                 | Male   | 5                 |
| Female | 4                 | Male   | 4                 |
| Female | 3                 |
Transcribed Image Text:# Analysis of Online Hours Based on Gender ## Introduction This study investigates whether there is significant evidence at the 0.05 level of significance that the mean number of hours spent online per week is the same for both males and females on a specific social networking platform. It assumes unequal population variances between male and female groups. ## Hypothesis Testing ### Null Hypothesis (H₀) The mean number of hours spent online per week is the same for both males and females. \[ H_0: \mu_1 = \mu_2 \] ### Alternative Hypothesis (H₁) The mean number of hours spent online per week is different for males and females. \[ H_1: \mu_1 \neq \mu_2 \] Here, population 1 refers to females and population 2 refers to males. ## Steps to Compute 1. **Compute the Test Statistic:** - Round to two decimal places. 2. **Find the p-value:** - Round to three decimal places. 3. **State the Conclusion:** - Compare the p-value to the chosen level of significance \(\alpha\) = 0.05. - Determine whether to reject or fail to reject the null hypothesis. - Assess if there is evidence to conclude a difference in online hours between males and females. ## Survey Data The survey data table includes the gender and the number of hours spent online per week for each participant. | Gender | Hours Online/Week | Gender | Hours Online/Week | |--------|-------------------|--------|-------------------| | Female | 4 | Male | 7 | | Female | 9 | Male | 15 | | Female | 10 | Male | 6 | | Female | 5 | Male | 4 | | Female | 7 | Male | 6 | | Female | 13 | Male | 3 | | Female | 2 | Male | 9 | | Female | 6 | Male | 4 | | Female | 3 | Male | 6 | | Female | 5 | Male | 8 | | Female | 7 | Male | 5 | | Female | 4 | Male | 4 | | Female | 3 |
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