The following table shows the average hourly wage rates for day-care centers fro

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. a. Perform a hypothesis test, using a = 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 Calculate the appropriate test statistic and interpret the result H_0: mu_1 - mu_2 lessthanorequalto $0.50 H_1: mu_1 - mu_2 > $0.50 The test statistic is 1.79. (Round to two decimal places as needed) The critical value(s) is(are) 1.30 (Round to two decimal places as needed Use a comma to separate answers as needed.) Because the test statistic is greater than the critical value, reject the null hypothesis. b. Identify the p-value from part a and interpret the result The p-value is 0.039

Explanation / Answer

a)

Hypothesis;

Null hypothesis: 1 - 2 <= 0.50
Alternative hypothesis: 1 - 2 > 0.50

Test statistic:

SE = sqrt [(s12/n1) + (s22/n2)]
SE = sqrt[(1.28^2/ 22) + (1.23^2 /35)

= 0.34

t = [ (x1 - x2) - d ] / SE

= [ (9.63 - 8.52) - 0.50 ] / 0.34

= 1.79

The critical value for 0.10 with df = 55 = 3.4764

Here, critical value is greater than test statistic so we fail to reject the null hypothesis

P value = 0.039

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