Question

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 1

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

Explanation:

Our test statistic is:

In which X is the sample mean,
`\mu` 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
`\mu = 50`

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

This means that
`X = 56, s = 25, n = 100`. So

`t = (6)/(2.5)`

`t = 2.4`

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