b. The hypothesis test is Select an answer c. Determine the test statistic. Round to two decimal places. z = d. Find the p-value. Round to four decimal places. p-value = e. Make a decision. Reject the null hypothesis. Fail to reject the null hypothesis. f. Write the conclusion.

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**Title: Gender Differences in Sexting Among Adolescents**

A research study was conducted to explore gender differences in sexting, specifically the sending of sexually explicit messages or images via cell phone. A researcher hypothesizes that the proportion of girls engaging in sexting is less than that of boys. To test this hypothesis, data was collected in the spring of 2010 from a random sample of middle and high school students in a large school district in the southern United States.

The researcher discovered that out of 2,169 girls surveyed, 156 were sexting. Similarly, out of 2,231 boys surveyed, 183 were sexting. The critical question is whether there is substantial evidence to support the hypothesis that the proportion of girls sexting is lower than that of boys, using a 5% significance level.

**Preliminary Assessment:**

a. The first step is to determine if it is safe to assume that:
   - The number of girls sexting is ≤ 5% of all girls in middle and high school students in the district.
   - The number of boys sexting is ≤ 5% of all boys in middle and high school students in the district.
   - Options: Yes / No

b. Verify the assumptions with the formula \( np(1 - \hat{p}) \geq 10 \). Round answers to one decimal place.
   - For girls: \( n_{\text{girls}}\hat{p}(1 - \hat{p}) = \_\_\_\_\_\_\_\_\_\_\_\_ \)
   - For boys: \( n_{\text{boys}}\hat{p}(1 - \hat{p}) = \_\_\_\_\_\_\_\_\_\_\_\_ \)

**Testing the Claim:**

a. Formulate the null and alternative hypotheses:
   - Null Hypothesis (\( H_0 \)): \( p_{\text{girls}} \) ? \(  p_{\text{boys}} \)
   - Alternative Hypothesis (\( H_a \)): \(  p_{\text{girls}} \) ? \(  p_{\text{boys}} \)

b. Select the type of hypothesis test: [Select an answer]

c. Calculate the test statistic. Round to two decimal places.
   - \( z = \_\_\_\_\_\_\_\_\_ \)

d. Determine the p-value. Round to four decimal places.
   - p-value =
Transcribed Image Text:**Title: Gender Differences in Sexting Among Adolescents** A research study was conducted to explore gender differences in sexting, specifically the sending of sexually explicit messages or images via cell phone. A researcher hypothesizes that the proportion of girls engaging in sexting is less than that of boys. To test this hypothesis, data was collected in the spring of 2010 from a random sample of middle and high school students in a large school district in the southern United States. The researcher discovered that out of 2,169 girls surveyed, 156 were sexting. Similarly, out of 2,231 boys surveyed, 183 were sexting. The critical question is whether there is substantial evidence to support the hypothesis that the proportion of girls sexting is lower than that of boys, using a 5% significance level. **Preliminary Assessment:** a. The first step is to determine if it is safe to assume that: - The number of girls sexting is ≤ 5% of all girls in middle and high school students in the district. - The number of boys sexting is ≤ 5% of all boys in middle and high school students in the district. - Options: Yes / No b. Verify the assumptions with the formula \( np(1 - \hat{p}) \geq 10 \). Round answers to one decimal place. - For girls: \( n_{\text{girls}}\hat{p}(1 - \hat{p}) = \_\_\_\_\_\_\_\_\_\_\_\_ \) - For boys: \( n_{\text{boys}}\hat{p}(1 - \hat{p}) = \_\_\_\_\_\_\_\_\_\_\_\_ \) **Testing the Claim:** a. Formulate the null and alternative hypotheses: - Null Hypothesis (\( H_0 \)): \( p_{\text{girls}} \) ? \( p_{\text{boys}} \) - Alternative Hypothesis (\( H_a \)): \( p_{\text{girls}} \) ? \( p_{\text{boys}} \) b. Select the type of hypothesis test: [Select an answer] c. Calculate the test statistic. Round to two decimal places. - \( z = \_\_\_\_\_\_\_\_\_ \) d. Determine the p-value. Round to four decimal places. - p-value =
**Transcription for Educational Website**

**Date:** 11/15/2020  
**Platform:** MyOpenMath

**Statement Evaluations:**

1. There is sufficient evidence to support the researcher’s belief that the proportion of girls sexting is less than boys.

2. There is not sufficient evidence to support the claim that the proportion of girls sexting is less than boys.

*Note: There are no graphs or diagrams associated with this text.*
Transcribed Image Text:**Transcription for Educational Website** **Date:** 11/15/2020 **Platform:** MyOpenMath **Statement Evaluations:** 1. There is sufficient evidence to support the researcher’s belief that the proportion of girls sexting is less than boys. 2. There is not sufficient evidence to support the claim that the proportion of girls sexting is less than boys. *Note: There are no graphs or diagrams associated with this text.*
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