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.

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:

In which X is the sample mean, 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

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

This means that . So

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

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: