The cable company takes an SRS of 250 of the approximately 15,000 households who subscribe to them. They found that 75 percent of the sampled households watch sports on television at least once a month. The company is considering taking more samples like this. Suppose that it is actually 70 percent of their total subscribed households who watch those sports. Let p^ represent the proportion of a sample of 250 households that watch sports on television at least once a month.

What are the mean and standard deviation of the sampling distribution of p^?

Question

Mathematics

Abbie

14 May, 01:34

The cable company takes an SRS of 250 of the approximately 15,000 households who subscribe to them. They found that 75 percent of the sampled households watch sports on television at least once a month. The company is considering taking more samples like this. Suppose that it is actually 70 percent of their total subscribed households who watch those sports. Let p^ represent the proportion of a sample of 250 households that watch sports on television at least once a month.

What are the mean and standard deviation of the sampling distribution of p^?

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Answers (1)

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Giovanni Gallagher · Answer 1

Answer; Mean = p = 0.75

Standard deviation = 0.0274

Step-by-step explanation:

Mean = p = 0.75

Standard deviation = √ [ p (1 - p) / n ]

= √ [ 0.75 * (1 - 0.75) / 250]

= 0.0274