Answer:
We conclude that less than or equal to 90% of all orders are mailed within 72 hours after they are received which means the company's claim is not true.
Step-by-step explanation:
We are given that the company claims that more than 90% of all orders are mailed within 72 hours after they are received. The quality control department at the company often takes samples to check if this claim is valid.
A recently taken sample of 175 orders showed that 161 of them were mailed within 72 hours.
<u><em>Let p = percentage of all orders that are mailed within 72 hours.</em></u>
SO, Null Hypothesis, : p
90% {means that less than or equal to 90% of all orders are mailed within 72 hours after they are received}
Alternate Hypothesis, : p > 90% {means that more than 90% of all orders are mailed within 72 hours after they are received}
The test statistics that will be used here is <u>One-sample z proportion</u> <u>statistics</u>;
T.S. = ~ N(0,1)
where, = proportion of orders that were mailed within 72 hours in a sample of 175 =
= 92%
n = sample of orders = 175
So, <u><em>test statistics</em></u> =
= 0.975
The value of the test statistics is 0.975.
<em>Now at 1% significance level, the z table gives critical value of 2.3263 for right-tailed test. Since our test statistics is less than the critical value of z as 0.975 < 2.3263, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which </em><em><u>we fail to reject our null hypothesis</u></em><em>.</em>
Therefore, we conclude that less than or equal to 90% of all orders are mailed within 72 hours after they are received which means the company's claim is not true.