In a study of factors affecting soldiers' decisions to reenlist,320 subjects were measured for an index of satisfaction and the sample mean is 28.8 and the sample standard deviation is 7.3.Use the given sample data to construct the 98% confidence interval for the population mean.
A)[27.85 29.75]
B)[27.96 29.64]
C)[11.82 45.78]
D)[28.75 28.85]
E)[28.60 29.00]

Question

Quizplus · Accepted Answer

The correct answer is A because the 98% confidence interval for the population mean is [27.85, 29.75]. This interval was calculated using the formula:CI = x̄ ± z* (s/√n)where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and z* is the critical value from the standard normal distribution corresponding to the desired confidence level. For a 98% confidence level, z* = 2.326. Plugging in the given values, we get:CI = 28.8 ± 2.326 * (7.3/√320)CI = 28.8 ± 2.326 * (7.3/17.89)CI = 28.8 ± 2.326 * 0.41CI = 28.8 ± 0.95CI = [27.85, 29.75]

In a Study of Factors Affecting Soldiers' Decisions to Reenlist,320