Answer:
The value of the t-statistic for this test is 1.138.
Step-by-step explanation:
We are given that a new manager of a small convenience store randomly samples 20 purchases from yesterday’s sales. The mean was $45.26 and the standard deviation was $20.67.
We wish to test for evidence that the overall mean purchase amount is at least $40
<u />
<u><em>Let </em></u><u><em> = overall mean purchase amount</em></u>
SO, <u>Null Hypothesis</u>, : $40 {means that the overall mean purchase amount is at least $40}
<u>Alternate Hypothesis</u>, : < $40 {means that the overall mean purchase amount is less than $40}
The test statistics that will be used here is <u>One-sample t test statistics</u> because we don't know about the population standard deviation;
T.S. = ~
where, = sample mean sale = $45.26
s = sample standard deviation = $20.67
n = sample of purchases = 20
So, <u><em>test statistics</em></u> = ~
= 1.138
<em>Hence, the value of the t-statistic for this test is 1.138.</em>