Please help me out with these problems. A teacher asked her 8 introductory stati
ID: 3255336 • Letter: P
Question
Please help me out with these problems.
A teacher asked her 8 introductory statistics students to record the total amount of time they spent studying for a particular test. The amounts of study time x (in hours) and the resulting test grades y are given below.
x 2 1 1.5 0.5 1 3 0 2
y 92 81 84 68 85 96 48 74
6. The standard error of the slope SEb is defined as SEb= s/squareroot of E(x-xhat)2
Calculate SEb. (3 points)
7. Suppose we want to find out if the number of hours studied helps predict grade awarded on this statistics test. Formulate null and alternative hypotheses about the slope of the true regression line. State a two-sided alternative. ( 2 points)
8. Determine the test statistic, the degrees of freedom, and the P-value of t against the alternative. (3 points)
9. Would you reject the null hypothesis at the 1% significance level? Explain briefly. (2 points)
10. Write your conclusions in plain language. (2 points)
11. Compute a 95% confidence interval for the slope ß of the true regression line. (2 points)
Explanation / Answer
Solution:-
6) the standard error of the slop SEb is defined as s/(x-xbar)^2
I got .1423
Correct answer is 3.827499196
7) Ho: b = 0
Ha: b not equal 0
8) t-statistic = b/SEb = 12.94117647 / 3.827499196 = 3.381104948
d.f. = n-2 = 8-2 = 6
P-value from t-table = 0.014837548
9) Do NOT reject. P > 0.01
10) At the 1% level of significance, there is no supporting evidence
11) CI = mean +/-(t*)(standard error)
CI = 12.94117647 +/-(2.4469)(3.827499196)
CI = 12.94117647 +/- 9.36550778
C.I. = 3.575623345 to 22.3067296