According to a 2017 opinion poll by FB Public Affairs, 75% of American teens hav

Question

According to a 2017 opinion poll by FB Public Affairs, 75% of American teens have a Twitter page. It also found that 30% of girls and 24% of boys admitted to accessing their Twitter page continuoulsy throughout the day; they are termed :”super users”. The results were based on a survey of randomly selected 501 girls and 508 boys interviewed on the FB. Online Teen omnibus. Find 95% confidence interval for the difference of proportions of super users of girls and super users of boys Should we conclude that girls are more likely than boys to be super users of Twitter?

Explanation / Answer

The pooled sample proportion(P) = (p1 * n1 + p2 * n2)/(n1 + n2)

                                                     = (0.3 * 501 + 0.24 * 508)/(501 + 508)

                                                    = 0.27

SE = sqrt(P * (1 - P) * (1/n1 + 1/n2))

      = sqrt(0.27 * 0.73 * (1/501 + 1/508))

     = 0.028

At 95% confidence interval the critivcal value is z0.025 = 1.96

The 95% confidence interval is

p1 - p2 +/- z0.025 * SE

= (0.3 - 0.24) +/- 1.96 * 0.028

= 0.06 +/- 0.055

= 0.005, 0.115

As the confidence interval doesn't cointain the hypothised value 0, so the null hypothesis is rejected.

So We can conclude that girls are more likely tan boys to be super users of twitter.

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