A store manager designs a new accounting system that will be cost effective if the mean monthly charge account balance is more than $50. A sample of 100 accounts is randomly selected. The sample mean balance is $56 and the sample standard deviation is $25.a.Find the t-statistic for a hypothesis test that is designed to answer the question.

Answer:

The t-statistic for a hypothesis test that is designed to answer the question is 2.4.

Step-by-step explanation:

Our test statistic is:

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]

In which X is the sample mean, [tex]\mu[/tex] is the value tested at the null hypothesis, s is the standard deviation of the saple and n is the size of the sample.

A store manager designs a new accounting system that will be cost effective if the mean monthly charge account balance is more than $50.

This means that [tex]\mu = 50[/tex]

A sample of 100 accounts is randomly selected. The sample mean balance is $56 and the sample standard deviation is $25.

This means that [tex]X = 56, s = 25, n = 100[/tex]. So

[tex]t = \frac{X - \mu}{\frac{s}{\sqrt{n}}[/tex]

[tex]t = \frac{56 - 50}{\frac{25}{\sqrt{10}}[/tex]

[tex]t = \frac{6}{2.5}[/tex]

[tex]t = 2.4[/tex]

The t-statistic for a hypothesis test that is designed to answer the question is 2.4.

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