For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random

Question

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding. In a random sample of 63 professional actors, it was found that 38 were extroverts. A button hyperlink to the SALT program that reads: Use SALT. (a) Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.) Incorrect: Your answer is incorrect. (b) Find a 95% confidence interval for p. (Round your answers to two decimal places.) lower limit Incorrect: Your answer is incorrect. upper limit Incorrect: Your answer is incorrect.

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Adela 5 months 2021-08-21T22:49:41+00:00 1 Answers 10 views 0

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    2021-08-21T22:51:32+00:00

    Answer:

    a) 0.6032

    b)

    Lower limit: 0.48

    Upper limit: 0.72

    Step-by-step explanation:

    In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

    \pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

    In which

    z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

    Question a:

    In a random sample of 63 professional actors, it was found that 38 were extroverts.

    We use this to find the sample proportion, which is the point estimate for p. So

    \pi = \frac{38}{63} = 0.6032

    Question b:

    Sample of 63 means that n = 63

    95% confidence level

    So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

    The lower limit of this interval is:

    \pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6032 - 1.96\sqrt{\frac{0.6032*0.3968}{63}} = 0.4824

    The upper limit of this interval is:

    \pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.6032 + 1.96\sqrt{\frac{0.6032*0.3968}{63}} = 0.724

    Rounding to two decimal places:

    Lower limit: 0.48

    Upper limit: 0.72

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