### Estimating the Size of Personal Networks in Older AdultsA research program used a representative random sample of men and women to gauge the size of the personal network of older adults. Each adult in the sample was asked to "please name the people you have frequent contact with and who are also important to you." The responses of 2,822 adults in this sample yielded statistics on network size, that is, the mean number of people named per person was \( \bar{x} = 14.3 \), with a standard deviation of \( s = 9.8 \). Complete parts a through d.#### a. Give a point estimate for \( \mu \).\[\boxed{\text{(Type an integer or a decimal.)}}\]#### b. Give an interval estimate for \( \mu \). Use a confidence coefficient of 0.95.\[\left( \boxed{\phantom{00}}, \boxed{\phantom{00}} \right) \quad \text{(Round to two decimal places as needed.)}\]#### c. Comment on the validity of the following statement: "95% of the time, the true mean number of people named per person will fall in the interval computed in part b." Choose the correct answer below.- ⃝ **A.** The statement is correct. 95% of the time, the true mean number of people named per person will fall within an interval computed with a confidence coefficient of 0.95.- ⃝ **B.** The statement is incorrect. A correct statement would be "One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b."- ⃝ **C.** The statement is incorrect. A correct statement would be "95% of the time, the true mean number of people named per person will fall outside the interval computed in part b."- ⃝ **D.** The statement is incorrect. A correct statement would be "One can be 95% confident that the true mean number of people named per person will fall outside the interval computed in part b."#### d. It is unlikely that the personal network sizes of adults are normally distributed. In fact, it is likely that the distribution is highly skewed. If so, what impact, if any, does this have on the validity of inferences derived from the confidence interval?-

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A research program used a representative random sample of men and women to gauge the size of the personal network of older adults. Each adult in the sample was asked to "please name the people you have frequent contact with and who are also important to you." The responses of 2,822 adults in this sample yielded statistics on network size, that is, the mean number of people named per person was x = 14.3, with a standard deviation of s = 9.8. Complete parts a through d. a. Give a point estimate for µ. |(Type an integer or a decimal.) b. Give an interval estimate for u. Use a confidence coefficient of 0.95. ( ) (Round to two decimal places as needed.) c. Comment on the validity of the following statement: "95% of the time, the true mean number of people named per person will fall in the interval computed in part b." Choose the correct answer below. O A. The statement is correct. 95% of the time, the true mean number of people named per person will fall within an interval computed with a confidence coefficient of 0.95. B. The statement is incorrect. A correct statement would be "One can be 95% confident that the true mean number of people named per person will fall in the interval computed in part b." C. The statement is incorrect. A correct statement would be "95% of the time, the true mean number of people named per person will fall outside the interval computed in part b." D. The statement is incorrect. A correct statement would be "One can be 95% confident that the true mean number of people named per person will fall outside the interval computed in part b." d. It is unlikely that the personal network sizes of adults are normally distributed. In fact, it is likely that the distribution is highly skewed. If so, what impact, if any, does this have on the validity of inferences derived from the confidence interval? O A. It does not impact the validity of the interpretation because the sampling space of the sample mean is approximately normal according to the Central Limit Theorem. B. It does impact the validity of the interpretation because the interpretation was based upon a sample instead of the entire population. C. It does not impact the validity of the interpretation because the interpretation is based on highly skewed results. O D. It does impact the validity of the interpretation because the interpretation is based on highly skewed results.