Question

Q6

This is from a dataset of 420 CA school districts.

We estimate the relationship between the student-teacher ratio (X1=STR) and test scores (Y=TestScore), controlling for the percentage of English learners in the classroom (X2=PctEL):

TestScore=686.0-1.10*STR-0.65*PctEL

The standard error of beta0hat is 8.7. The standard error of beta1hat is 0.43. The standard error of beta2hat is 0.31.

Test the statistical significance of STR using alpha=0.05.

What is your p-value? Round to four decimal places.

Answer 1

Y=TestScore

X1=STR=student-teacher ratio

X2=PctEL=percentage of English learners in the classroom

TestScore=686.0-1.10*STR-0.65*PctEL

The standard error of beta0hat is 8.7. The standard error of beta1hat is 0.43. The standard error of beta2hat is 0.31.

Ho: beta1 = 0

Ha: beta1 <> 0

The t-statistic of beta1 of STR = (-1.10-0)/0.43

= -2.55814

The absolute value of t-statistic = 2.55814

The number of observations = n = 420

The degree of freedom = n - 3 = 417

The critical t-statistic at 417 degree of freedom using =tinv() excel function is 1.965669

Thus, since, the actual t-statistic is greater than the critical t-statistic, the STR is statistically significant at alpha=0.05

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The p-value of the actual t-statistic is given by =tdist() excel function

=tdist(2.55814,417,2)

= 0.010876

=0.0109 (round to four decimal places)