Question

In: Statistics and Probability

A.   We are concerned about the cost of a surgical procedure in two different cities.  We took...

A.  

We are concerned about the cost of a surgical procedure in two different cities.  We took a random sample of patients who underwent that procedure in each city and ascertained their cost, and the following data was obtained:

City A: sample mean = $8500, sample size = 30, population standard deviation = $400

City B: sample mean = $8100, sample size = 40, population standard deviation = $500

Our hypothesis are

H0: muA - muB = 0, H1: muA - muB is not zero.

Find the value of the test statistic. (Provide two decimal values)

B.

We are studying the cost of a surgical procedure in two different cities.  We took a random sample of patients who underwent that procedure in each city and ascertained their cost, and the following data was obtained:

City A: sample mean = $8400, sample size = 30, population standard deviation = $300

City B: sample mean = $8200, sample size = 40, population standard deviation = $400

Our hypothesis are

H0: muA - muB = 0, H1: muA - muB is not zero.

To test this at a 1% significance level, what is the critical value for the test statistic?

Give only the positive value (i.e. if the critical values are -2.5 and +2.5, give your answer as 2.5)

(Provide two decimal values)_____

Solutions

Expert Solution

Here ,

Que 1) in this Question it is given that the sample,

City A: sample mean = $8500, sample size = 30, population standard deviation = $400

City B: sample mean = $8100, sample size = 40, population standard deviation = $500

Our hypothesis :

H0: muA - muB = 0 vs H1: muA - muB is not zero.

To test this hypothesis we have to use two sample z test because here the population standard deviations is known.

Using the two sample z test the test Statistic is,

The calculated z Statistic is z cal = 3.72. ( Rounded to two decimal places).

Que 2) In this scenario it is given that the sample information,

City A: sample mean = $8400, sample size = 30, population standard deviation = $300

City B: sample mean = $8200, sample size = 40, population standard deviation = $400

Our hypothesis are

H0: muA - muB = 0, H1: muA - muB is not zero.

To test this hypothesis at a 1% significance level, we have to use again two sample z test because here the population standard deviations is known.

Further the test is performed at 0.01 level of significance as below,

Here the z critical value is calculated using Standerd normal z-table. At two tailed z,0.005 = -+2.58

The critical value for the test statistic is 2.58.

thank you.


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