Question

A carpet company advertises that it will deliver your carpet within 6 days of purchase. A sample of 46 past customers is taken. The average delivery time in the sample was 6.8 days. The population standard deviation is known to be 2.7 days.

Test to determine if their advertisement is legitimate at a  significance level 0.01. (Show all steps)

Answer 1

Solution:
Given in the question
Number of samples (n) = 46
Population standard deviation() = 2.7
Sample mean (Xbar) = 6.8
To test the claim whether the company will deliver the carpet within 6 days of purchase
So null and alternate hypothesis can be written as
Null hypothesis H0: <= 6 days
Alternate hypothesis Ha: >6 days
here we will use the Z test as the sample size is large enough and population standard deviation is known so Z test statistic can be calculated as
Z test stat = (Xbar - )//sqrt(n) = (6.8-6)/2.7/sqrt(46) = 2.01
As this is the right-tailed test, so p-value from the Z table is
P-value = 0.0223
So at alpha = 0.01, we are failed to reject the null hypothesis as the p-value is greater than the alpha value (0.0222>0.01), So we don't have significant evidence to support the alternative hypothesis.