This exercise refers to the following Minitab output, relating y = son's height to x = father's height for a sample of n = 76 college males.

Question

This exercise refers to the following Minitab output, relating y = son's height to x = father's height for a sample of n = 76 college males.

The regression equation is

Height = 30.0 + 0.576 dadheight

76 cases used 3 cases contain missing values

Predictor Coef SE Coef T P

Constant 29.981 5.129 5.85 0.000

dadheight 0.57568 0.07445 7.73 0.000

S = 2.657, R - Sq = 44.7%

Predicted Values [for dad's heights of 65, 70, and 74]

Fit SE Fit 95.0% CI 95.0% PI

67.400 0.415 (66.574, 68.226) (62.041, 72.759)

70.279 0.318 (69.645, 70.913) (64.946, 75.612)

75.581 0.494 (71.596, 73.566) (67.195, 77.967)

(a) What is the equation for the regression line? (Round all answers to the nearest thousandth.)

 = _____ +  0.576x

(b) Identify the value of the t-statistic for testing whether or not the slope is 0. Verify that the value is correct using the formula for the t-statistic and the information provided by Minitab for the parts that go into the formula. (Round the answer to two decimal places.)

State and test the hypotheses about whether or not the population slope is 0. Use relevant information provided in the output. Complete the following sentence.

H₀: 𝛽₁  = 

H_a: 𝛽₁ ≠

The p-value given is 0.000 (associated with t = 7.73) so we can reject the null hypotheses and conclude that the relationship is statistically significant.

(d) Compute a 95% confidence interval for 𝛽₁, the slope of the relationship in the population. (Round the answer to three decimal places.)

 _____________to __________

(e) Complete a sentence that interprets this interval.

For the population of male college students, we can say with 95% confidence that for each 1-inch increase in father's height the mean increase in son's height is between _____  and ____ inches.

Answer 1

a) 29.981

b) T = 7.73

c) H₀: ß₁=0, H₁: ß₁≠0

d) (0,572, 0.650)

e) between 0.572 inches and 0.650 inches.