2. A regression line relating y lours of sleep the previous day to -liours studi

Question

2. A regression line relating y lours of sleep the previous day to -liours studied the previous day is estimated using data from n 10 students. The estimated slope 31 0.30. The standard error of the slope is 0.20. a) What is the value of the test statistic for the following hypothesis test about, the population slope B1-0 0.30-0 Solution 1.5 t SE 0.20 B1 (b) At the a 0.10 level, would you reject the null hypothesis? State your conclusion in terms of the problem. Solution: d.f. n -(k 1) -s 1.833 We fail to reject the null hypothesis and conclude the alternative is not true. There is not a linear relationship between hours studied the previous day, and the hours of sleep the previous day (c) What is a 90% confidence interval for B1, the population slope? Interpret the confidence interval you calculate Solution C.I. (-0.67, 0.07) We are 90% confident that a one hour increase in hours studied the previous day is associated with somewhere between 0.67 decrease and 0.07 increase in hours of sleep the previous day

Explanation / Answer

Here k represents the no of independent variable, here no of independent variable is only 1 so k = 1 which gives

df = n -(k+1) = 10-(1+1) = 8

If the no of independent variable is 2 then k = 2

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