An article reported that 55% of people participating in a survey of social network users said it was not OK for someone to "friend" his or her boss. Let pp denote the proportion of all social network users who feel this way and suppose that p=0.55p=0.55 . (a) Would p^p^ based on a random sample of 50 social network users have a sampling distribution that is approximately normal? Read and complete the following statement. Select Yes No . The sampling distribution of p^p^ based on a random sample of 50 social network users Select would be would not be approximately normal. This is because npnp is Select less than at least 10 and n(1−p)n(1−p) is Select less than at least 10. (b) What are the mean and standard deviation of the sampling distribution of p^p^ if the sample size is 100? (Round your standard deviation to four decimal places.) Enter a number.meanEnter a number.standard deviation
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- Given \( p = 0.55 \) and \( n = 50 \). - Calculate \( np = 50 \times 0.55 = 27.5 \). - Calculate \( n(1-p) = 50 \times (1 - 0.55) = 50 \times 0.45 = 22.5 \). Since both \( np = 27.5 \) and \( n(1-p) = 22.5 \) are greater than 10, the sampling distribution of Show more…
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An article reported that 54% of people participating in a survey of social network users said it was not OK for someone to "friend" his or her boss. Let p denote the proportion of all social network users who feel this way and suppose that p = 0.54. (a) Would p based on a random sample of 50 social network users have a sampling distribution that is approximately normal? Yes, the sampling distribution of p based on a random sample of 50 social network users is approximately normal because np is less than 10 and n(1-p) is less than 10. (b) What are the mean and standard deviation of the sampling distribution of p if the sample size is 100? (Round your standard deviation to four decimal places) mean: standard deviation:
Ana Carolina D.
The article referenced in the previous exercise also reported that $38 \%$ of the 1200 social network users surveyed said it was OK to ignore a coworker's friend request. If $\hat{p}=0.38$ is used as an estimate of the proportion of all social network users who believe this, is it likely that this estimate is within 0.05 of the actual population proportion? Use what you know about the sampling distribution of $\hat{p}$ to support your answer.
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