Question

The following table shows the average hourly wage rates for​ day-care centers from two locations based on two random samples. Use the table to complete parts a through c. Location 1 Location 2

Sample mean    ​$ 9.64    ​$ 8.55

Sample standard deviation ​ $ 1.31    ​$ 1.13

Sample size 29    31

a. Perform a hypothesis​ test, using α=0.10​, to determine if the average hourly wage for​ day-care workers in Location 1 is​ $0.50 per hour higher than the average hourly wage for​ day-care workers in Location 2. Assume the population variances for wage rates in each location are equal.

Determine the null and alternative hypotheses for the test.

H0: μ1−μ2 ▼ less than < less than or equals ≤ greater than > not equals ≠ equals = greater than or equals ≥ ​$0.50

H1: μ1−μ2 ▼ less than < equals = less than or equals ≤ greater than > not equals ≠ greater than or equals ≥ ​$0.50

Calculate the appropriate test statistic and interpret the result.

The test statistic is ​(Round to two decimal places as​ needed.)

The critical​ value(s) is(are) . ​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

Because the test statistic ▼ is less than the critical value/is greater than the critical value/falls within the critical values/does not fall within the critical values,),(reject/do not reject)the null hypothesis.

b. Identify the​ p-value from part a and interpret the result. The​ p-value is . ​(Round to three decimal places as​ needed.)

Interpret the result. Choose the correct answer below.

A. Since the​ p-value is less than the significance​ level, do not reject do not reject the null hypothesis.

B. Since the​ p-value is not less not less than the significance​ level, do not reject do not reject the null hypothesis.

C. Since the​ p-value is not less not less than the significance​ level, reject the null hypothesis.

D. Since the​ p-value is less than the significance​ level, reject the null hypothesis.

c. What assumptions need to be made in order to perform this​ procedure?

A. Although the sample size in the second sample is large​ enough, it must be assumed that the distribution for the first sample is normally​ distributed, and that the samples are independent.

B. Since the sample sizes are large​ enough, no assumptions are needed.

C. It must be assumed that the distribution for both populations are normally​ distributed, and that the samples are independent.

D. Although the sample size in the first sample is large​ enough, it must be assumed that the distribution for the second population is normally​ distributed, and that the samples are independent.

Answer 1

from above

a)

H0: μ1−μ2 <=0.5

Ha: μ1−μ2 >0.5

The test statistic is=1.87

The critical​ value =1.30

Because the test statistic is greater than the critical value (reject the null hypothesis.

b)

p value =0.033

D. Since the​ p-value is less than the significance​ level, reject the null hypothesis

c)

A. Although the sample size in the second sample is large​ enough, it must be assumed that the distribution for the first sample is normally​ distributed, and that the samples are independent.