In a study of factors affecting whether soldiers decide to reenlist,320 subjects were measured for an index of satisfaction.The sample mean is 28.8 and the sample standard deviation is 7.3.Use the given sample data to construct the 98 percent 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 z-score corresponding to the desired confidence level. In this case, x̄ = 28.8, s = 7.3, n = 320, and z = 2.326 (for a 98% confidence level). Plugging these values into the formula gives:CI = 28.8 ± 2.326 * (7.3/√320)= 28.8 ± 2.326 * (7.3/17.89)= 28.8 ± 2.326 * 0.41= 28.8 ± 0.95= [27.85, 29.75]

In a Study of Factors Affecting Whether Soldiers Decide to Reenlist,320