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)____________

C.  

A study is done to compare the wages of day care workers in two states. The wages are Normally distributed. The following data is available:

= 25,     = 12.7,   = 1.8

= 20,     = 10.6,   = 1.6

We are testing the null hypothesis that the population means are equal.

We cannot assume that the variances are equal. We have computed the degrees of freedom to be 42.

Find the test statistic. (Provide two decimal places)_________________

Solutions

Expert Solution

A)

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

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

Hypothesis are,

Difference =
Estimate for difference: 400
Test statistic is,

B)

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

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

Hypothesis are,

Critical value,

C)

Sample size (n1) = 25, Sample mean = 12.7, standard deviation = 1.8

Sample size (n2) = 20, Sample mean = 10.6, standard deviation = 1.6

The hypothesis are,

The test statistic is given by,

degrees of freedom,

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