Answer:
We conclude that the population mean waiting for time to check out is less than 4 minutes.
Step-by-step explanation:
We are given that the population mean waiting time to check out of a supermarket has been 4 minutes.
A sample of 100 customers was selected, and their mean waiting time to check out was 3.10 minutes, with a sample standard deviation of 2.5 minutes.
Let = <em><u>population mean waiting for time to check out</u></em>.
So, Null Hypothesis, : 4 minutes {means that the population mean waiting for time to check out is more than or equal to 4 minutes}
Alternate Hypothesis, : < 4 minutes {means that the population mean waiting for time to check out is less than 4 minutes}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean waiting time to check out = 3.10 minutes
= sample standard deviation = 2.5 minutes
n = sample of customers = 100
So, <u><em>the test statistics</em></u> = ~
= -3.6
The value of t test statistics is -3.6.
<u>Now, at 0.10 significance level the t table gives critical value of -1.291 at 99 degree of freedom for left-tailed test.</u>
Since our test statistic is less than the critical value of t as -3.6 < -1.291, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.
Therefore, we conclude that the population mean waiting for time to check out is less than 4 minutes.