Question

A budget is an expression of management's expectations and goals concerning future revenues and costs. To increase their effectiveness, many budgets are flexible, including allowances for the effect of variation in uncontrolled variables. For example, the costs and revenues of many production plants are greatly affected by the number of units produced by the plant during the budget period, and this may be beyond a plant manager's control. Standard cost-accounting procedures can be used to adjust the direct-cost parts of the budget for the level of production, but it is often more difficult to handle overhead. In many cases, statistical methods are used to estimate the relationship between overhead (y) and the level of production (x) using historical data. As a simple example, consider the historical data for a certain plant. Enter the data into EXCEL and analyze it to answer the following items.

Production (in 10,000) units:	5	6	7	8	9	10	11
Overhead costs (in $1000):	13	11.4	14	15	15.6	15.2	17.6

(a) Test the hypotheses H₀: β₁ = 0 versus  H_a: β₁ ≠ 0 at the 5% level of significance.

State the decision rule. (Which Option below should we use)

1. Reject H₀ if p value > 0.025.
2. Do not reject H₀ if p value ≤ 0.025.Reject H₀ if p value > 0.05.
3. Do not reject H₀ if p value ≤ 0.05.    Reject H₀ if p value < 0.025.
4. Do not reject H₀ if p value ≥ 0.025.Reject H₀ if p value < 0.05.
5. Do not reject H₀ if p value ≥ 0.05.

State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated p-value (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places, and the p-value to four decimal places).

(Choose: (x, ,z p, t, G)) ( _______  ) = ___________  , p (Choose: (≥, >, <, ≤, = )) ___________

State your decision. Are production and overhead costs linearly related?

1.) Reject the null hypothesis: Yes, production and overhead costs appear to be linearly related

2.) Reject the null hypothesis: No, production and overhead costs do not appear to be linearly related.

3.) Do not reject the null hypothesis: Yes, production and overhead costs appear to be linearly related.

4.) Do not reject the null hypothesis: No, production and overhead costs do not appear to be linearly related.

(b) Test the hypotheses  H₀: β₁ = 1 versus  H_a: β₁ ≠ 1 at the 5% level of significance.

State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated p-value (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places, and the p-value to four decimal places).

(Choose: (x, t, p, G, z)) (________  ) = __________ , p (Choose:(= ≥ > ≤ < )) _____________

State your decision. Choose one of the following:

1.) Do not reject the null hypothesis: The slope of the line representing the relationship between overhead costs and production is not significantly different from 1.

2.) Do not reject the null hypothesis: The slope of the line representing the relationship between overhead costs and production is significantly different from 1.

3.) Reject the null hypothesis: The slope of the line representing the relationship between overhead costs and production is not significantly different from 1.

4.) Reject the null hypothesis: The slope of the line representing the relationship between overhead costs and production is significantly different from 1.

Answer 1

Finding the regression equation
Step 1 : Put the data in excel as shown.

Step 2 : Go to Data -> Data Analysis -> Regression

Step 3 : Input the values as shown.

Step 4 : The output will be generated as follows.

State the decision rule. (Which Option below should we use)
Do not reject H0 if p value ≥ 0.05.

State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated p-value (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places, and the p-value to four decimal places).

t = 4.45281
pvalue = 0.006685
pvalue < 0.05

State your decision. Are production and overhead costs linearly related?

1.) Reject the null hypothesis: Yes, production and overhead costs appear to be linearly related