Question

Consider the following regression results based on 20 observations. [You may find it useful to reference the t table.]

	Coefficients	Standard Error	t Stat	p-value
Intercept	31.4171	4.4496	7.061	0.000
x1	0.1629	0.1944	0.838	0.413

a-1. Choose the hypotheses to determine if the intercept differs from zero.

• H₀: β₀ ≥ 0; H_A: β₀ < 0

• H₀: β₀ = 0; H_A: β₀ ≠ 0

• H₀: β₀ ≤ 0; H_A: β₀ > 0

a-2. At the 5% significance level, what is the conclusion to the hypothesis test? Does the intercept differ from zero?

• Reject H₀; the intercept is greater than zero.

• Reject H₀; the intercept differs from zero.

• Do not reject H₀; the intercept is greater than zero.

• Do not reject H₀; the intercept differs from zero.

b-1. Construct the 95% confidence interval for the slope coefficient. (Negative values should be indicated by a minus sign. Round "t_α/2,df" value to 3 decimal places and final answers to 2 decimal places.)

Confidence interval _____ to ______?

b-2. At the 5% significance level, can we conclude the slope differs from zero?

• Yes, since the interval contains zero.

• Yes, since the interval does not contain zero.

• No, since the interval contains zero.

• No, since the interval does not contain zero.

Answer 1

a-1. Null and alternative hypothesis:

H₀: β₀ = 0; H_A: β₀ ≠ 0

a-2. p-value = 0.000

Reject H₀; the intercept differs from zero.

b-1. 95% confidence interval for the slope coefficient.

Critical value, t_c = T.INV.2T(0.05, 18) = 2.1009

95% Confidence interval for slope:

Lower limit = b1 - tc*se(b1) = 0.1629 - 2.1009*0.1944 = -0.25

Upper limit = b1 + tc*se(b1) = 0.1629 + 2.1009*0.1944 = 0.57

b-2. No, since the interval contains zero.