A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample variance, 52, is determined to be 12.9. Complete parts (a) through (c). (a) Construct a 90% condence interval for oz if the sample size. n, is 20. The lower bound is . (Round to two decimal places as needed.) The upper bound is _ (Round to two decimal places as needed.) (b) Construct a 90% condence interval for 52 if the sample size. n, is 30. The lower bound is . (Round to two decimal places as needed.) The upper bound is D. (Round to two decimal places as needed.) How does increasing the sample size affect the width of the interval? O The width does not change 0 The width decreases O The width increases (c) Construct a 98% condence interval for 52 if the sample size, n, is 20. The lower bound is . (Round to two decimal places as needed.) The upper bound is _ (Round to two decimal places as needed.) Compare the results with those obtained in part (a). How does increasing the level of condence affect the condence interval? 0 The width does not change 0 The width decreases O The width increases In a study, researchers wanted to measure the effect of alcohol on the hippocampal region, the portion of the brain responsible for long-term memory storage, in adolescents. The researchers randomly selected 14 adolescents with alcohol use disorders to determine whether the hippocampal volumes in the alcoholic adolescents were less than the normal volume of 9.02 cm" . An analysis of the sample data revealed that the hippocampal volume is approximately normal with no outliers and x = 8.02 cm" and s = 0.8 cm . Conduct the appropriate test at the a = 0.01 level of significance. C. . State the null and alternative hypotheses. Ho: H Hy: H (Type integers or decimals. Do not round.) Identify the t-statistic. to =(Round to two decimal places as needed.) Identify the P-value. P-value = (Round to three decimal places as needed.) Make a conclusion regarding the hypothesis. the null hypothesis. There sufficient evidence to claim that the mean hippocampal volume is cm 3A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 3 points with 99% confidence assuming s = 10.9 based on earlier studies? Suppose the doctor would be content with 90% confidence. How does the decrease in confidence affect the sample size required? Click the icon to view a partial table of critical values. A 99% confidence level requires subjects. (Round up to the nearest subject.) A 90% confidence level requires subjects. (Round up to the nearest subject.) How does the decrease in confidence affect the sample size required? O A. The sample size is the same for all levels of confidence. O B. Decreasing the confidence level increases the sample size needed. O C. Decreasing the confidence level decreases the sample size needed