Question

A study was conducted to determine whether the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance. The researchers hypothesized the linear model y=β0+β1xy=β0+β1x, where xx is the score on the verbal ability test and yy is the final grade in the psychology course. The verbal scores and final grades for students are shown in the table below.

Student	1	2	3	4	5	6	7	8
Verbal Score xx	73	39	71	72	65	76	47	35
Final Grade yy	77	67	63	94	97	82	96	64

Find the following:

(a) The least squares regression line: ŷ =y^=

(b) State the null and alternative hypotheses:
(Note: Type b_1 for the symbol β1β1 for the slope of the regression line.
Enter: b_1not=0b_1not=0 for "there is a linear relationship"
b_1>0b_1>0 for "there is a positive relationship"
b_1<0b_1<0 for "there is a negative relationship" )
H0H0:
HAHA:

(c) Give the test statistic for the test:

(d) Using α=0.1α=0.1, the test shows:

A. There is not sufficient evidence to reject H0H0.
B. There is sufficient evidence to reject H0H0.

Answer 1