A research study was conducted about gender differences in...

A research study was conducted about gender differences in "sexting." The researcher believed that the proportion of girls involved in "sexting" is less than the proportion of boys involved. The data collected in the spring of 2010 among a random sample of middle and high school students in a large school district in the southern United States is out of 2231 males, 183 particpated in sexting. Out of 2169, 156 particpated. Is the proportion of girls sending sexts less than the proportion of boys "sexting?" Test at a 1% level of significance. a) If we use B to denote the boys and G to denote the girls, identify the correct alternative hypothesis. $H_1: p_B > p_G$ $H_1: p_B eq p_G$ $H_1: p_B < p_G$ b) Determine the test statistic. Round to two decimals. z = c) Find the p-value and round to 4 decimals. p = d) Make a decision. Fail to reject the null hypothesis Reject the null hypothesis

Transcript

00:01 A research study was conducted about gender differences in sexting.

00:04 The researcher believed that the proportion of girls involved in sexting is less than the proportion of boys involved in sexting.

00:11 So the data collected in the spring of 2010 among a random sample of middle and high school students in the large school districts in the southern united states is out of 2 ,231 participated in sexton and out of 269, 156 participated in 16.

00:29 Participated in sexting so so our question says is the proportion of girls sending sex less than proportion of boys sexting so test at 1 % level of significance so the first step is to go into our worksheet and extract all of our details so let's have for girls over here and let us have for meals over here so the data sets for girls i call that sample one and the data set for males i call that sample too so for girls we have a total of n1 is across to 2 ,169 and the proportion of girls that sex text we have that to be 156 and our p1 cap is going to be close to 156 divided by 2169 and if we do the mat we have that to be 0 .072 and for the second for the samples of males we have our n2 should be equals to 20231 and our x2 we have this to be equals to 183 so the proportion of males that sex text, we have that to be 183 divided by soto 31 and that is 0 .082.

01:42 So in this case of r's, our non -hypotesis is that p1 is equal to p2 and the alternative hypothesis is that p1 is lesser than p2.

01:51 That is the p of girls is actually less than the p of what the proportion of girls that sex text is less than the proportion of boys that sex text.

02:01 So the answer to our question is going to be option c so for question one the answer to our question is option c so question two says that our determined test statistics round to do a test our test statistics is a z test given to us as z is equals to p1 cap minus p2 cap divided by the square root of p1 cap q1c divided by n1 plus p2 cap q2 cap divided by n1 plus p2 cap by n2 so p1 cap is a 0 .072 minus 0 .082 divided by the square root of 0 .072 times so 1 minus 0 .072 that gives us 0 .928 divided by 2 ,169 the 0 .082 times so 1 minus 0 .082 that 0 .9 that's 0 .982 that 0 .9 .9 divided by 2 ,2131...

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