Question

The Central Company manufactures a certain specialty item once a month in a batch production run. The number of items produced in each run varies from month to month as demand fluctuates. The company is interested in the relationship between the size of the production run (x) and the number of hours of labor (v) required for the run. The company has collected the following data for the ten most recent runs. 80 Number of items: 40 30 70 90 50 60 70 40 70 Labor (hours) 84 60 138 180 97 118 140 76 159 146 (a) Test the hypotheses Ho: B1 - 0 versus Ho: Bio at the 5% level of significance. State the decision rule. Reject Ho if p > 0.025 Do not reject Ho if P S 0.025. Reject Ho if p > 0.05 Do not reject Ho if p s 0.05. Reject Ho if p < 0.025. Do not reject Ho if p 2 0.025. Reject Ho if p < 0.05. Do not reject Ho if p 2 0.05.

please use excel if possible to show regression model and answer

Answer 1

Excel output:

Regression Statistics
Multiple R	0.99539833
R Square	0.99081784
Adjusted R Square	0.98967007
Standard Error	4.01586926
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	13921.8824	13921.8824	863.254457	1.9509E-09
Residual	8	129.017647	16.1272059
Total	9	14050.9
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	-1.3117647	4.32302968	-0.3034364	0.76929869	-11.280689	8.65715962
X	2.02352941	0.06887159	29.3811922	1.9509E-09	1.86471124	2.18234758

a.

Decision rule:

Reject H₀ if p < 0.05

Do not reject H₀ if p $\small \geq$ 0.05

b.

Test statistic = t

Degrees of freedom = 8

Test statistic value = 29.381

p-value = 0.0000 < 0.05

Reject the null hypothesis, yes hours of lobor and number of items produced appear to be linearly related.

c.

Test statistic = t

Degrees of freedom = 8

Test statistic,

$\small \\ t = \frac{\hat{\beta_1 } - \beta_1 }{S.E(\hat{\beta_1})} \\ \\ \\ t = \frac{2.024 - 2}{0.069} \\\\ t = 0.348$  

p-value = 0.7368

It is obtained using function =TDIST(0.348,8,2)

p-value > 0.05

Do not reject null hypothesis. The slope of the line representing the relationship between the size of the production run and the number of hours of labor may not be significantly different from 2.