Please complete the problem below, in addition to the book review problems poste

Question

Please complete the problem below, in addition to the book review problems posted to Blackboard Is the use of social media associated with higher rates of depression? You are about to administer I. Suppose that 62% of Twitter's 300 million users are women. Before looking at depression rates, (a) To predict the number of women in our simple random sample, we can use a box model a survey to a simple random sample of 400 Twitter users to determine their depression rates we'll predict how many women will be in the sample Randomly choosing people for our sample is like randomly drawing tickets from a box The sum of the draws should represent the total number of women. Sketch the box. How many draws will we make from the box? (b) Fill in the blanks and show your work: We expect that there will be -wornen In our sample, give or take (c) Fill in the blanks and show your work We expect that our sample will have percent. (The number in the sccond blank is an estimate for women, give or take the size of the chance error in the percentage (d) what is the chance that we'll see 60% or more women in our simple random sample of 400 users?

Explanation / Answer

Number of twitter users in sample = 400

(1) Pr(Women) = 0.62

Here we will assign woman as 1 and man as 0. So, we will assign tickets to women numbered 1 and men as 0.

Now we will add all the total numbers of tickets in the box. We will draw 400 deaws from the box.

(b) We expect that there will be (400 * 0.62 = 248) women in our sample, give or take sqrt(0.62 * 0.38 * 400) = 9.71

(c) We expect that our sample will have 62 percent women, give or take sqrt(0.62 * 0.38/400) = 2.43%.

(d) Here we have to find that 60% or more women in our sample of 400 users

Pr(p > 0.60 ; 0.62 0.0243) = 1- Pr(p < 0.60 ; 0.62 ; 0.0243)

Z = (0.60 - 0.62)/ 0.0243 = -0.823

Pr(p > 0.60 ; 0.62 0.0243) = 1- Pr(p < 0.60 ; 0.62 ; 0.0243) = 1 - Pr(Z < -0.823) = 1 - 0.2053 = 0.7947

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