Question

please answer question 7 (confidence interval).

(14 points) Birth weight and gestational age. The Child Health and Development Studies considered pregnancies among women in the San Francisco East Bay area. Researchers took a random sample of 50 pregnancies and used statistical software to construct a linear regression model to predict a baby's birth weight in ounces using the gestation age (the number of days the mother was pregnant). A portion of the computer output and the scatter plot is shown below. Round all calculated results to four decimal places. Coefficients Intercept gestation Estimate 0.8118 0.4223 Std. Errort value Pr>It!) 45.2807 0.0179 0.9858 0.1644 2.5685 0.0134 Residual standard error: 16.4399 on 48 degrees of freedom Multiple R-squared: 0.1208, Adjusted R-squared: 0.1025 160 140 Birthweight in ounces 120 100 240 260 280 300 320 Gestation age

Answer 1

Q7:

df = 48

Significance level, α = 1-0.90 = 0.10

Critical value, t_c = T.INV.2T(0.10, 48) = 1.6772

90% Confidence interval for slope:

Lower limit = b1 - tc*se(b1) = 0.4223 - 1.6772*0.1644 = 0.1466

Upper limit = b1 + tc*se(b1) = 0.4223 + 1.6772*0.1644 = 0.6980