Interpretation of results of hypothesis testing

Describe the results of the test and explain how the use of this hypothesis testing can be used to evaluate solutions to your research issue.

Steadily rising transportations expend larger portions of the consumer budget. This test is specifically targeting funds spent on public transportation, gasoline, or toll fees. In order ascertain whether the average consumer is maintaining an average weekly transportation cost of $30, sample data was collected. Each author of this paper submitted the amount of money spent on transportation in the last week. The data set is as follows:
$40, 45, 40, 51
? Formulation of the null and the alternative hypotheses

Null Hypothesis
The null hypothesis states that consumers continue to spend $30 a week or less on transportation. Ho: µ < $30.00

Alternative Hypothesis
The alternative hypothesis states that consumers are now spending more than $30 per week on transportation. H1: µ > $30.00

? Specification of the level of significance

We will use a significance level of &#945; = 0.05.

? Calculation of the test statistic

This will be a one-tailed, one-sample t-test. The test statistic is calculated as:

Sx is the sample standard deviation divided by the square root of the number of cases.

For this dataset, the average is x = 44, the standard deviation is s = 5.228, and the sample size is n = 4. Plugging those values into the formula, we get:

t = (44 - 30)/(5.228/2) = 14/2.614 = 5.356

The test statistic is t = 5.356.

? Definition of the region of rejection

We need to find the critical value of t that we will use to make our decision. The critical value for a t-distribution with 3 degrees of freedom (d.f. = n - 1 = 4 - 1 = 3) and a significance level of 0.05 is t = 2.353.

Because we are conducting a one-sided test (specifically a right-sided test), we will reject the null hypothesis if the test statistic is larger than the critical value.

? Selection of the appropriate hypothesis

The test statistic (t = 5.356) is larger than the critical value (2.353). Therefore, we can reject the null hypothesis at the 0.05 levels, and assume the alternative hypothesis: that consumers are now spending more than $30 a week on transportation.

ASSIGNMENT:

Write 350 words describing the results of the test and explain how the use of this hypothesis testing can be used to evaluate solutions to your research issue.