Test H 0 : b 3 = 0 against H a : b 3 > 0 at a = 0.10. As part of a study at a la

Question

Test H0: b3 = 0 against Ha: b3 > 0 at a = 0.10.  

As part of a study at a large university (Communication of the ACM, Vol. 27, 1984), data were collected on n= 224 freshmen computer science (CS) majors in a particular year. The researchers were interested in modeling y, a student’s grade point average (GPA) after three semesters, as a function of the following independent variables (recorded at the time the students enrolled in the university):

x1 = average high school grade in mathematics (HSM)

x2 = average high school grade in science (HSS)       

x3 = average high school grade in English (HSE)

x4 = SAT mathematics score (SATM)

x5 = SAT verbal score (SATV)

The first-order model below was fit to data with the following results:

SOURCE

DF

SS

MS

F VALUE

PROB > F

MODEL

5

28.64

5.73

11.69

.0001

ERROR

218

106.82

0.49

TOTAL

223

135.46

ROOT MSE

0.700

R-SQUARE

0.211

DEP MEAN

4.635

ADJ R-SQ

0.193

PARAMETER

STANDARD

T FOR 0:

VARIABLE

ESTIMATE

ERROR

PARAMETER = 0

PROB > |T|

INTERCEPT

2.327

0.039

5.817

0.0001

X1 (HSM)

0.146

0.037

3.718

0.0003

X2 (HSS)

0.036

0.038

0.950

0.3432

X3 (HSE)

0.055

0.040

1.397

0.1637

X4 (SATM)

0.00094

0.00068

1.376

0.1702

X5 (SATV)

-0.00041

0.00059

-0.689

0.4915

SOURCE

DF

SS

MS

F VALUE

PROB > F

MODEL

5

28.64

5.73

11.69

.0001

ERROR

218

106.82

0.49

TOTAL

223

135.46

Explanation / Answer

TS = 1.397

for df = 218

and alpha = 0.10

p-value = P(T > 1.397) = =T.DIST.RT(1.397,218)

since p-value < 0.10

we reject the null hypothesis

=0.081916984

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