Answer:
D) Fail to reject the null hypothesis. There is insufficient evidence to conclude that the mean is greater than $100.
Step-by-step explanation:
We are given that the owner of a shoe store randomly selected 10 receipts and identified the total spent by each customer. The totals (rounded to the nearest dollar) are given below;
X: 125, 99, 219, 65, 109, 89, 79, 119, 95, 135.
Let = <u><em>average customer bought worth of shoes</em></u>.
So, Null Hypothesis, :
$100 {means that the mean is smaller than or equal to $100}
Alternate Hypothesis, :
> $100 {means that the mean is greater than $100}
The test statistics that will be used here is <u>One-sample t-test statistics</u> because we don't know about population standard deviation;
T.S. = ~
where, = sample mean =
= $113.4
s = sample standard deviation = = $42.78
n = sample of receipts = 10
So, <u><em>the test statistics</em></u> = ~
= 0.991
The value of t-test statistics is 0.991.
Now, at a 0.05 level of significance, the t table gives a critical value of 1.833 at 9 degrees of freedom for the right-tailed test.
Since the value of our test statistics is less than the critical value of t as 0.991 < 1.833, so <u><em>we have insufficient evidence to reject our null hypothesis</em></u> as it will not fall in the rejection region.
Therefore, we conclude that the mean is smaller than or equal to $100.