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A research study was conducted about gender differences in “sexting.” The researcher believed that the proportion of girls involved in “sexting” is different from the proportion of boys involved. The data collected in the spring of 2012 among a random sample of middle and high school students in a large school district in Vermont is summarized in the table below.

	Females	Males
Sent "sexts"	82	84
Total number surveyed	420	470

Is the proportion of girls sending sexts different from the proportion of boys “sexting?” Test at a 10% level of significance.

Procedure:

Assumptions: (select everything that applies)

Population standard deviation are unknown
The number of positive and negative responses are both greater than 10 for both samples
Paired samples
Population standard deviations are known
Population standard deviation are unknown but assumed equal
Independent samples
Simple random samples
Sample sizes are both greater than 30
Normal populations

Step 1. Hypotheses Set-Up:

$\displaystyle {H}_{{0}}:$ =	, where the and the units are
$\displaystyle {H}_{{a}}:$	, and the test is

Step 2. The significance level $\displaystyle \alpha=$ %

Step 3. Compute the value of the test statistic: = (Round the answer to 3 decimal places)

Step 4. Testing Procedure: (Round the answers to 3 decimal places)

CVA	PVA
Provide the critical value(s) for the Rejection Region:	Compute the P-value of the test statistic:
left CV is and right CV is	P-value is

Step 5. Decision:

CVA	PVA
Is the test statistic in the rejection region?	Is the P-value less than the significance level?

Conclusion:

Step 6. Interpretation:

At 10% significance level we have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

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