Question

The manufacturer of an airport baggage scanning machine claims it can handle an average of 530 bags per hour. (a) At α=.05 in a left-tailed test, would a sample of 16 randomly chosen hours with mean of 510 and a standard deviation of 50 indicate that the manufacturer's claim is overstated? (b) Why might the assubption of a normal population be doubtful?

Answer 1

Answer:

(a) The manufacturer's claim is NOT overstated.

(b) The assumption of a normal population might be doubtful because the hourly distribution might vary during the day.

Step-by-step explanation:

(a) Let's use one-tailed Hypothesis Testing with:

$H_{0}$: the population average is 530

α = 0.05

sample number n = 16

population average $\overline{x}$ = 530

sample average μ = 510

sample standard deviation σ = 50

If z < 1.645 then the hypothesis $H_{0}$ is valid.

Let's calculate z = $\frac{\overline{x}-\mu}{\sigma/\sqrt{n}}\sqrt{x}$ = $\frac{530-510}{50(4} = 8/5 = 1.6$

Given that 1.6 < 1.645 then the hypothesis is valid.

Thus the manufacturer's claim is NOT overstated

(b) The hourly distribution might vary along the day. This is why the population might be not necessarily normal.