Question

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study was then done to see if the mean time has increased in the new century. A random sample of 27 first-time convicted burglars in a recent year was picked. The mean length of time in jail from the survey was four years with a standard deviation of 1.9 years. Suppose that it is somehow known that the population standard deviation is 1.4. Conduct a hypothesis test to determine if the mean length of jail time has increased. Assume the distribution of the jail times is approximately normal. Calculate the following. (Enter exact numbers as integers, fractions, or decimals.) (a) x Incorrect: Your answer is incorrect. (b) σ Incorrect: Your answer is incorrect. (c) sx Incorrect: Your answer is incorrect. (d) n

Answer 1

a)
x = 4

b)
sigma = 1.4

c)

std.dev x = 1.9

std.error = 1.4/sqrt(27) = 0.2694

d)

n = 27