In: Statistics and Probability
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)_____
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.