An associate at a large home improvement store claims that she can build a composite 12 × 20 ft deck for an average cost of $7200.We sample eight decks built by this associate and find that the average cost was $8215.22 with a standard deviation of $711.16.Does it appear from this sample that the claim of $7200 is not accurate (either too high or too low)? State the critical value (CV), test statistic (TS), and decision from the test.(Use α = 0.05.)
A) CV = 2.3646; TS = 1.43; fail to reject her claim
B) CV = 1.8946; TS = 1.43; fail to reject her claim
C) CV = 1.8946; TS = 4.04; reject her claim
D) CV = 2.3646; TS = 4.04; reject her claim

Question

Quizplus · Accepted Answer

We will use a one-sample t-test with the null hypothesis being that the true average cost of building a composite deck is $7200 and the alternative hypothesis being that it is not $7200. We will use a significance level of 0.05.

The formula for the t-test statistic is:
TS = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(sample size))

Plugging in the values, we get:
TS = (8215.22 - 7200) / (711.16 / sqrt(8)) = 4.04

The critical value for a two-tailed t-test with 7 degrees of freedom (n-1) and a significance level of 0.05 is 2.3646. Since the calculated TS (4.04) is greater than the critical value (2.3646), we reject the null hypothesis and conclude that the claim of $7200 is not accurate (either too high or too low). Therefore, the best choice is D.

An Associate at a Large Home Improvement Store Claims That