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	?$8.65
Sample standard deviation	?$1.19	?$1.27
Sample size	27	32

a. Perform a hypothesis? test, using alpha=0.05?, 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.

a.1. Determine the null and alternative hypotheses for the test.

a.2. Calculate the appropriate test statistic and interpret the result.

a.3. Calculate the critical value.

Use this information to draw a conclusion about the test.

b. Identify the? p-value from part a and interpret the result.

Answer 1

a.1)

Ho: 1-2 =0.50

Ha: 1-2 >0.50

a-2)

from above test statistic =3.07

a-3) critical value =1.672

as test statisitc is higher than critical value we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that mean 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.

b)

for above test statsitic and 57 degree of freedom p value =0.0016

as p value is less than 0.05 level we reject null hypothesis

we have sufficient evidence at 0.05 level to conclude that mean 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.