Question

The following data give the number of hours 55 students spent studying and their corresponding grades on their midterm exams.

Hours Studying	00	22	22	33	55
Midterm Grades	7878	8787	8888	9393	9797

Table

Construct the 90% confidence interval for the slope. Round your answers to three decimal places.

Construct the 90% confidence interval for the slope. Round your answers to three decimal places.

Construct the 95% confidence interval for the slope. Round your answers to three decimal places.

Construct the 99% confidence interval for the slope. Round your answers to three decimal places.

Construct the 80% confidence interval for the slope. Round your answers to three decimal places.

Construct the 85% confidence interval for the slope. Round your answers to three decimal places.

Answer 1

	Hour Study X	Midnight Grades Y	Sxx =Σ (Xi - X̅ )	Syy = Σ( Yi - Y̅ )	Sxy = Σ (Xi - X̅ ) * (Yi - Y̅)	X2
	0	7878	696.96	1146184.36	28263.84	0
	22	8787	19.36	26114.56	711.04	484
	22	8888	19.36	3672.36	266.64	484
	33	9393	43.56	197491.36	2933.04	1089
	55	9797	817.96	719782.56	24264.24	3025
Total	132	44743	1597.2	2093245.2	56438.8	5082

Equation of regression line is Ŷ = a + bX
b = ( n Σ(XY) - (ΣX* ΣY) ) / ( n Σ X2 - (ΣX)2 )
b = ( 5 * 1237654 - 132 * 44743 ) / ( 5 * 5082 - ( 132 )^{2})
b = 35.3361

a =( ΣY - ( b * ΣX ) ) / n
a =( 44743 - ( 35.3361 * 132 ) ) / 5
a = 8015.7273
Equation of regression line becomes Ŷ = 8015.7273 + 35.3361 X

X̅ = Σ (Xi / n ) = 132/5 = 26.4
Y̅ = Σ (Yi / n ) = 44743/5 = 8948.6

S² = ( 2093245.2 - 35.3361 * 56438.8 ) / 5 - 2
S² = 32972.7064
S = 181.5839

Confidence Interval



90% confidence interval is

Part 2)

Confidence Interval



95% confidence interval is

Part 3)

Confidence Interval



99% confidence interval is

Part 4)

Confidence Interval



80% confidence interval is

Part 5)

Confidence Interval



85% confidence interval is