Question

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)?

Answer 1

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

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

Let
`\mu` = overall mean purchase amount

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

Alternate Hypothesis,
`H_A` :
`\mu` < $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. =
`\frac{\bar X -\mu}{{(s)/(√(n) ) } }` ~
`t_n_-_1`

where,
`\bar X` = sample mean sale = $45.26

s = sample standard deviation = $20.67

n = sample of purchases = 20

So, test statistics =
`\frac{45.26-40}{{(20.67)/(√(20) ) } }` ~
`t_1_9`

= 1.138

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