Questions: Do married and unmarried women spend the same amount of time per week using Facebook? A random sample of 45 married women who use Facebook spent an average of 4.0 hours per week on this social media website. A random sample of 39 unmarried women who regularly use Facebook spent an average of 4.4 hours per week. Assume that the weekly Facebook time for married women has a population standard deviation of 1.2 hours, and the population standard deviation for unmarried, regular Facebook users is 1.1 hours per week. Using the 0.05 significance level, do married and unmarried women differ in the amount of time per week spent on Facebook? Required: a. State the decision rule for 0.05 significance level: H0: μmarried women =μunmarried women: H2: μmarried women ≠μunmarried womenNote: Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. Reject H0 if 2< or 2>

Do married and unmarried women spend the same amount of time per week using Facebook? A random sample of 45 married women who use Facebook spent an average of 4.0 hours per week on this social media website. A random sample of 39 unmarried women who regularly use Facebook spent an average of 4.4 hours per week. Assume that the weekly Facebook time for married women has a population standard deviation of 1.2 hours, and the population standard deviation for unmarried, regular Facebook users is 1.1 hours per week. Using the 0.05 significance level, do married and unmarried women differ in the amount of time per week spent on Facebook?

Required:
a. State the decision rule for 0.05 significance level: H0: μmarried women =μunmarried women: H2: μmarried women ≠μunmarried womenNote: Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.

Reject H0 if 2< or 2>

Transcript text: Do married and unmarried women spend the same amount of time per week using Facebook? A random sample of 45 married women who use Facebook spent an average of 4.0 hours per week on this social media website. A random sample of 39 unmarried women who regularly use Facebook spent an average of 4.4 hours per week. Assume that the weekly Facebook time for married women has a population standard deviation of 1.2 hours, and the population standard deviation for unmarried, regular Facebook users is 1.1 hours per week. Using the 0.05 significance level, do married and unmarried women differ in the amount of time per week spent on Facebook? Required: a. State the decision rule for 0.05 significance level: $H_{0}: \mu_{\text {married women }}=\mu_{\text {unmarried women: }} H_{2}: \mu_{\text {married women }} \neq \mu_{\text {unmarried }}$ womenNote: Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places. Reject $H_{0}$ if $2<$ or $2>$

Solution

Solution Steps

Step 1: State the Hypotheses

We want to test whether there is a significant difference in the amount of time spent on Facebook between married and unmarried women. The hypotheses are stated as follows:

Null Hypothesis $H_0$: $\mu_{\text{married}} = \mu_{\text{unmarried}}$
Alternative Hypothesis $H_1$: $\mu_{\text{married}} \neq \mu_{\text{unmarried}}$

Step 2: Calculate the Standard Error

The standard error $SE$ is calculated using the formula:

\[ SE = \sqrt{\frac{\sigma_1^2}{n_1} + \frac{\sigma_2^2}{n_2}} = \sqrt{\frac{1.44}{45} + \frac{1.21}{39}} \approx 0.251 \]

Step 3: Calculate the Test Statistic

The test statistic $z$ is calculated using the formula:

\[ z = \frac{\bar{x}_1 - \bar{x}_2}{SE} = \frac{4.0 - 4.4}{0.251} \approx -1.5933 \]

Step 4: Calculate the P-value

The P-value is calculated as follows:

\[ P = 2 \times (1 - Z(|z|)) \approx 0.1111 \]

Step 5: Determine the Critical Value

For a two-tailed test at a significance level of $\alpha = 0.05$, the critical value is determined using:

\[ Z = \Phi^{-1}(1 - \frac{\alpha}{2}) \approx \pm 1.96 \]