Question

Let x be a random variable that represents the percentage of successful free throws a professional basketball player makes in a season. Let y be a random variable that represents the percentage of successful field goals a professional basketball player makes in a season. A random sample of n = 6 professional basketball players gave the following information.

x	67	64	75	86	73	73
y	44	39	48	51	44	51

(e) Find a 90% confidence interval for y when x = 70. (Round your answers to one decimal place.)

lower limit	64.73  %
upper limit	%

(f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)

t =
critical t =

Answer 1

using excel>addin>phstat>Regression

we have

Regression Analysis
Regression Statistics
Multiple R	0.8032085
R Square	0.645143894
Adjusted R Square	0.556429868
Standard Error	3.135677162
Observations	6
ANOVA
	df	SS	MS	F	Significance F
Regression	1	71.50344828	71.50344828	7.27217465	0.05427978
Residual	4	39.32988506	9.832471264
Total	5	110.8333333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	9.918390805	13.50255091	0.734556816	0.50334796	-27.57070057	47.40748217
x	0.496551724	0.184133303	2.696696989	0.05427978	-0.014684284	1.007787732

Confidence Interval Estimate
Data
X Value	70
Confidence Level	90%
Intermediate Calculations
Sample Size	6
Degrees of Freedom	4
t Value	2.131847
XBar, Sample Mean of X	73
Sum of Squared Differences from XBar	290
Standard Error of the Estimate	3.135677
h Statistic	0.197701
Predicted Y (YHat)	44.67701
For Average Y
Interval Half Width	2.972295
Confidence Interval Lower Limit	41.70472
Confidence Interval Upper Limit	47.64931
For Individual Response Y
Interval Half Width	7.315796
Prediction Interval Lower Limit	37.36122
Prediction Interval Upper Limit	51.99281

(e) Find a 90% confidence interval for y when x = 70. (Round your answers to one decimal place.)

lower limit	41.7
upper limit	47.7

(f) Use a 5% level of significance to test the claim that β > 0. (Round your answers to two decimal places.)

t =	2.69
critical t =	2.13