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

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

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.  = $\frac{\bar X -\mu}{{\frac{s}{\sqrt{n} } } }$  ~ $t_n_-_1$

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

              s = sample standard deviation = $20.67

              n = sample of purchases = 20

So, test statistics  =  $\frac{45.26-40}{{\frac{20.67}{\sqrt{20} } } }$  ~ $t_1_9$

                               =  1.138

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