Question

Here’s some information for 7 different firms in different locations, regarding the price of a popular item they sell, and the quantity they make available for purchase of that item (quantity supplied) in a given week.

Firm	Quantity Supplied (y)	Price (x)
A	500	$7.00
B	700	7.50
C	750	9.00
D	590	6.50
E	540	7.50
F	650	7.00
G	480	4.50

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A. Perform a t test to see if price and quantity supplied are related. Complete this test using the p-value method. Let α = .01.

2. Perform an F test to see if price and quantity supplied are related. Complete this test using the critical value method. Let α = .01.
3. Develop a 90% confidence interval to estimate the average quantity supplied for a group of firms, if the price is $8.00

d. Develop a 90% prediction interval to estimate the quantity supplied of a specific firm that charges a price of $8.00.

Answer 1

Result:

A. Perform a t test to see if price and quantity supplied are related. Complete this test using the p-value method. Let α = .01.

 H0: β = 0   

 H1: β ≠ 0   

 calculated t =  2.538, P=0.0520 which is > 0.01 level of significance.

The null hypothesis is not rejected. we conclude that price and quantity supplied are not related.

Perform an F test to see if price and quantity supplied are related. Complete this test using the critical value method. Let α = .01.

H0:  The regression model is not significant

H1: The regression model is significant

 calculated F =6.44

 critical F(1,5) at 0.01 level of significance = 16.26

 calculated F =6.44 < critical F value 16.26.

The null hypothesis is not rejected. we conclude that price and quantity supplied are not related.

Develop a 90% confidence interval to estimate the average quantity supplied for a group of firms, if the price is $8.00

90% confidence interval = (585.90, 730.60)

Develop a 90% prediction interval to estimate the quantity supplied of a specific firm that charges a price of $8.00.

90% prediction interval =(492.03, 824.46).

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis

Regression Analysis
	r²	0.563	n	7
	r	0.750	k	1
	Std. Error of Estimate	74.262	Dep. Var.	Quantity Supplied (y)
Regression output					confidence interval
variables		coefficients	std. error	t (df=5)	p-value	90% lower	90% upper
Intercept	a =	203.701	159.230	1.279	.2569	-117.154	524.557
Price (x)	b =	56.818	22.391	2.538	.0520	11.699	101.937
ANOVA table
Source	SS	df	MS	F	p-value
Regression	35,511.364	1	35,511.364	6.44	.0520
Residual	27,574.351	5	5,514.870
Total	63,085.714	6
Predicted values for: Quantity Supplied (y)
		90% Confidence Interval	90% Prediction Interval
Price (x)	Predicted	lower	upper	lower	upper	Leverage
8	658.25	585.90	730.60	492.03	824.46	0.234