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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

Respuesta :

Using Z- distribution it is found that the mean length of jail time has increased because the test statistics is greater than the critical value.

Z- distribution: It is a special normal distribution where the mean is 0 and standard deviation is 01.

                             z = (x -μ) / σ

At the Null hypothesis, it is tested if the mean length of jail time is still of 2.5 years.,          

            i.e.,  H₀ :μ = 2.5

Null hypothesis : It refers to a hypothesis that states that there is no relationship between two population parameters.

At the alternative hypothesis, it is tested if it has increased

                 i.e., H₁ :μ>2.5

Alternative Hypothesis:   The alternative hypothesis states the research prediction of an effect or relationship.

we have the standard deviation for population thus the z- distribution is used.  The test statistics is :

                 z= ⁻ₓ -μ /σ /√n

where, x is the sample mean

           μ is the value tested at the null hypothesis.

           σ is the standard deviation of sample.

           n is the sample size.

For this problem the values of parameter are:

         x= 5 ,σ =1.4 ,μ = 2.5 and n = 27

hence the value is :

              z= ⁻ₓ -μ /σ /√n

                 = 5 - 2.5 / 1.4 ÷ √27

                 = 2.5 × √27 /1.4

                 = 9.27

The critical value for a right tailed test as we are testing if the mean is greater than a value with a significance level of 0.05 is of 2*= 1.645.

since, the test statistics is greater than the critical value, it can be concluded that the mean length of jail time has increased.

Learn more about Standard Deviation :

https://brainly.com/question/14747159

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