Question

JR Carpetech, Inc. Claims that the average cost of carpet installation and repairs is Php19760. A sample of 60 repairs has an average of Php17880. The standard deviation of the sample is Php1000. At α=0.05, is there enough evidence to reject the company’s claim? What should be the null hypothesis? What should be your alternative hypothesis? What is the level of significance? What is the test statistic? What type of test of significance should be used? What is the decision rule? What should be the decision?

Answer 1

Null hypothesis (Ho):

Alternative hypothesis (Ha):

Level of significance = α = 0.05

Test statistic

t = -14.56

t test for single mean should be used because we do not know the population standard deviation.

Decision rule: Degrees of freedom = n - 1 = 60 - 1 = 59

For 59 degrees of freedom, two tailed test and 0.05 level of significance, Critical values = -2.001, 2.001

Hence,

Decision rule: Reject Ho if t < -2.001 or t > 2.001

Decision: Since the test statistic lie in the rejection region, we reject the null hypothesis.

We have sufficient evidence to reject the company's claim that the average cost of carpet installation and repairs is Php19760.