Question

The 5 summary statistics for the homework and final scores of 64 randomly selected students from a large Chemistry class of 2000 students are given in the table below. Avg SD Homework 76 15 Final 64 20 r= 0.15 a. Find the slope and y-intercept of the sample regression equation for predicting Finals from Homework. Predicted Final = $* Tries 0/3 x Homework (Round answer to 2 decimal place.) b. The SE for the slope is (round to 2 decimal places) 33$* Tries 0/3 C. Find a 95% confidence interval for the slope of the regression line for all 2000 students using the Normal curve. Round to 2 decimal places. Put the lower number first. A 95% Confidence Interval for the slope - ( 22* Tries 0/3 d. Does the above CI interval include 0? O yes no ** Tries 0/1 no matter what X is. Fill in the blank with a number using the info given in the summary e. The usual null hypothesis Ho: slopepop = 0 is the same as saying the best prediction for Y = statistics. * Tries 0/2 f. Compute the Z statistic to test the null hypothesis, Ho: slopepop = 0 against the alternative Hai slopepop #0 Z = * Tries 0/2

Answer 1

a)
slope =r *sd(y)/sd(x)
= 0.15 * 20/15
= 0.2

intercept = ybar - slope * xbar
= 64 - 0.2* 76
= 48.8

hence
predicted final = 48.8 + 0.2* Homework
b

b)
SE = sd(y)/sd(x) * sqrt((1-r^2)/(n-2))
= 20/15 * sqrt((1-0.15^2)/(64-2))
= 0.1674

c)
t = 1.96 as n >> 30
(0.2 - 1.96 *0.1674 , 0.2 + 1.96 *0.1674)
= (-0.1281 ,0.5281 )

d) yes, 0 is included

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