Question

The manufacturer of an airport baggage scanning machine claims it can handle an average of 530 bags per hour.

(a-1) At α = .05 in a left-tailed test, would a sample of 16 randomly chosen hours with a mean of 510 and a standard deviation of 50 indicate that the manufacturer’s claim is overstated? Choose the appropriate hypothesis.(Multiple Choice)

a. H1: μ < 530. Reject H1 if tcalc > –1.753

b. H0: μ < 530. Reject H0 if tcalc > –1.753

c. H1: μ ≥ 530. Reject H1 if tcalc < –1.753

d. H0: μ ≥ 530. Reject H0 if tcalc < –1.753

(a-2) State the conclusion. (Multiple Choice)

a. tcalc = –1.6. There is not enough evidence to reject the manufacturer’s claim.

b. tcalc = –1.6. There is significant evidence to reject the manufacturer’s claim.

Answer 1

(a-1) Answer: Option (D): H0: μ ≥ 530. Reject H0 if tcalc < –1.753

> Null hypothesis, H0: μ ≥ 530

Alternative hypothesis, H1: μ < 530

Degrees of freedom = 16 - 1 = 15; Significance level = 0.05

So, t-critical = - 1.753 (left-tailed); So we reject H0 if tcalc < - 1.753

(a-2) Answer: Option (A)

tcalc = (510 - 530)/(50÷√16) = -1.6

As tcalc is not less than -1.753, we fail to reject the null hypothesis and conclude that there is not enough evidence to reject the manufacturer's claim.