Question

With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.7 minutes. After switching to a single waiting line, he finds that for a random sample of A customers, the waiting times have a standard deviation of B minutes.
a) Use a 0.025 significance level to test the claim that with a single line, waiting times vary less than with individual lines.

Answer 1

Answer:

Step-by-step explanation:

Complete Question

With individual lines at the checkouts, a store manager finds that the standard deviation for the waiting times on Monday mornings is 5.7 minutes. After switching to a single waiting line, he finds that for a random sample of A customers, the waiting times have a standard deviation of B minutes.

a) Use a 0.025 significance level to test the claim that with a single line, waiting times vary less than with individual lines.

If we let italic sigma be the population standard deviation of waiting times for a single line, what are the hypotheses for this test?

Use the traditional method to test the claim. Assume the population of waiting times is normally distributed.

Calculate the test statistic for this test, italic chi to the power of 2 . Round your answer to three digits to the right of the decimal point.

What is the critical value for this left-tailed test? Round your answer to three digits to the right of the decimal point.

Based on the critical value and test statistic, should the null hypothesis be rejected?

Since the claim is the alternative hypothesis, what final conclusion can you draw from this test?

1) Null and Alternative hypothesis

Null hypothesis: H₀ = 5.7

and Alternative hypothesis: H₁ < 5.7

2) Test Statistic

$x^2=\frac{(n-1)s^2}{\sigma^2}$

where s is the standard deviation = 4.9

n sample size = 29

$=\frac{28 \times 4.9^2}{5.7^2} \\\\=20.692$

complete solution is detailed in the image