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. What symbol represents the random variable for this test

Respuesta :

Answer:

bar x

Step-by-step explanation:

The variable in this test is the mean length of time that the burglars  would spend in . The symbol is x-bar

x-bar = 4

s = 1.4

n= 27

null: u = 2.5

h1; u ≠ 2.5

4-2.5/(1.9/√27)

= 1.5/(1.4/5.196)

= 1.5/0.2694

= 5.57

z critical = 1.6445

z > z critical

we reject the null hypothesis