Question

Psychologists at an university compared the levels of alcohol consumption of male and female freshman students. Each student was asked to estimate the amount of alcohol (beer, wine, or liquor) they consume in a typical week. Summary statistics for 126 males and 184 females are provided in the accompanying table Click here to view the table a. For each gender, find a 95% confidence interval for mean weekly alcohol consumption For males, the 95% confidence interval is ( (Round to the nearest hundredth as needed.) For females, the 95% confidence interval is ( Round to the nearest hundredth as needed.) b. Prior to sampling, what is the probability that at least one of the two confidence intervals will not contain the population mean it estimates. Assume that the two intervals are independent. OD The probability is(Round to four decimal places as needed) c. Based on the two confidence intervals, what inference can you make about which gender consumes the most alcohol, on average, per week? 0 A. The females consume the most alcohol, on average, per week. B. The males consume the most alcohol, on average, per week. O C. There is not enough information to answer this question Data Table Sample size, n Mean (ounces), x Standard deviation Males 126 16.75 13.53 Females 184 10.75 11.52 Print Done Click to select your answer(s)

Answer 1

(a)

For male:

Answer: (14.37, 19.14)

For female:

Answer: (9.07, 12.43)

(B)

The probability that 95% confidence interval does not contain true population mean is 1 - 0.95 = 0.05

Since both intervals are independent so the probability that both intervals does not contain true parameter is 0.05*0.05 = 0.0025

Answer: 0.0025

(C)

The confidence interval for male has all values above the confidence interval of female. That is lower limit for confidence interval of male is above the upper limit of confidence interval of female. So we can say that males consume more alcohol per week in comparison to female.

Correct option is B.