Question 22 Solve the problem. After obtaining a regression line y = Po + interv

Question

Question 22 Solve the problem. After obtaining a regression line y = Po + interval for the mean of all values y for whi obtained as follows: |x, a confidence ch x = xo can y-E.y+E) 1 n (x0-x) |n. n572. where E-(tar) is found from the t-table using n-2 The critical value ta/2 is found from the t-table using n 2 degrees of freedom. Use the data below to obtain a 95% confidence interval estimate of the mean test score of all students who study 10.5 hours. Note that the equation of the regression line is y- 52 8804 3 405x and that se 6 8359 x (hours studied)|2.5 4.5 5.1 7.9 116 y (score on test) 66 70 60 83 93 (80.48, 96.78) (72 49, 104.78) (61.55, 115.71) (77.11. 100.15)

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: y
Independent Variable: x
y = 52.880405 + 3.4049992 x
Sample size: 5
R (correlation coefficient) = 0.89695771
R-sq = 0.80453313
Estimate of error standard deviation: 6.8359061

Parameter estimates:

Analysis of variance table for regression model:

Predicted values:

Hence,

95% confidence interval for x = 10.5 is:

(72.49, 104.78)

Option B is correct.

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 52.880405 6.8446912 0 3 7.7257547 0.0045 Slope 3.4049992 0.96899379 0 3 3.5139536 0.0391

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