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? What is the value of the t-statistic for this test (three decimal places)?

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

Let [tex]\mu[/tex] = overall mean purchase amount

SO, Null Hypothesis, [tex]H_0[/tex] : [tex]\mu[/tex] [tex]\geq[/tex] $40 {means that the overall mean purchase amount is at least $40}

Alternate Hypothesis, [tex]H_A[/tex] : [tex]\mu[/tex] < $40 {means that the overall mean purchase amount is less than $40}

The test statistics that will be used here is One-sample t test statistics because we don't know about the population standard deviation;

T.S. = [tex]\frac{\bar X -\mu}{{\frac{s}{\sqrt{n} } } }[/tex] ~ [tex]t_n_-_1[/tex]

where, [tex]\bar X[/tex] = sample mean sale = $45.26

s = sample standard deviation = $20.67

n = sample of purchases = 20

So, test statistics = [tex]\frac{45.26-40}{{\frac{20.67}{\sqrt{20} } } }[/tex] ~ [tex]t_1_9[/tex]

= 1.138

Hence, the value of the t-statistic for this test is 1.138.