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The random sample shown below was selected from a normal distribution. 4,5,8,8, 7,4 O Complete parts a and b. a. Construct a 90% confidence interval for the population mean p. ( , ) (Round to two decimal places as needed.) b. Assume that sample mean x and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n =25 observations. Repeat part a. What is the effect of increasing the sample size on the width of the confidence intervals? The confidence interval is ( ) . (Round to two decimal places as needed.) What is the effect of the sample size on the width of the confidence interval? () A. As the sample size increases, the width increases. () B. As the sample size increases, the width stays the same. (1) C. As the sample size increases, the width decreases. In a psychology journal, researchers reported that a chief executive officer's facial structure can be used to predict a firm's financial performance. The study involved measuring the facial width-to-height ratio (WHR) for each in a sample of 45 CEQOs at publicly traded Fortune 500 firms. These WHR values (determined by computer analyzing a photo of the CEO's face) had a mean of x=1.83 and a standard deviation of s =0.14. Use this information to complete parts a and b below. a. Find and interpret a 99% confidence interval for pu, the mean facial WHR for all CEOs at publicly traded Fortune 500 firms. (Round to three decimal places as needed.) () A. The 99% confidence interval for mean facial WHR indicates that the true mean facial WHR for the CEOs in the sample is between and with 99% confidence. () B. The 99% confidence interval for mean facial WHR indicates that 99% of all CEOs at publicly traded Fortune 500 firms have a WHR between and () . The 99% confidence interval for mean facial WHR indicates that the true mean facial WHR for all CEOs at publicly traded Fortune 500 firms is between and with 99% O D. The 99% confidence interval for mean facial WHR score indicates that 99% of CEOs in the sample have a WHR between andb. The researchers found that CEOs with wider faces (relative to height) tended to be associated with firms that had greater financial performance. They based their inference on an equation that uses facial WHR to predict financial performance. Suppose an analyst wants to predict the financial performance of a Fortune 500 firm based on the value of the true mean facial WHR of CEOs. The analyst wants to use the value of p=1.6. Do you recommend the use this value? () A. No, since the suggested value of p does not lie within the confidence interval from part a, it is not reasonable to assume that it is the true mean facial WHR of CEOs. () B. Yes, since the suggested value of p would be a usual value to obtain in a sample of 45 CEQOs, it is reasonable to assume that it is the true mean facial WHR of CEOs. No, since the suggested value of p would be a usual value to obtain in a sample of 45 CEQOs, it is not reasonable to assume that it is the true mean facial WHR of CEOs. . Yes, since the suggested value of p lies within the confidence interval from part a, it is reasonable to assume that it is the true mean facial WHR of CEOs. For the binomial sample information summarized below, indicate whether the sample size is large enough to use the large sample approximation to construct a confidence interval for p. n = 200, p = 0.30 Is the sample size large enough? A O A. Yes, because np 2 15 and nq 2 15. O B. No, because np