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)?

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 = overall mean purchase amount

SO, Null Hypothesis, : $40   {means that the overall mean purchase amount is at least $40}

Alternate Hypothesis, : < $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.  =  ~

where,   = sample mean sale = $45.26

              s = sample standard deviation = $20.67

              n = sample of purchases = 20

So, test statistics  =    ~

                               =  1.138

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

20%

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a

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