29. A daily newspaper is considering whether they should begin publishing a Sund

Question

29. A daily newspaper is considering whether they should begin publishing a Sunday edition. A researcher hired by the paper collects data on the daily and Sunday circulations of n = 34 newspapers that publish both editions. The researcher determines the least-squares regression line to be y = 9.60 + 1.34x, where z and y are daily and Sunday circulations in thousands of readers, respectively. If the newspaper who is interested in adding a Sunday edition has a daily circulation of 135 thousand readers, what is a 99% interval for the newspaper's potential Sunday circulation? The standard errors associated with these data are: s-114.0, SE,-0.07, SEA = 29.4, and SE,-117.7. a. (0, 513) b. (0, 502) d. (181, 200)

Explanation / Answer

Solution:

We are given x = 135 and regression equation as

y-hat = 9.60 + 1.34*x

y-hat = 9.60 + 1.34*135 = 190.5

We have to find 99% confidence interval for y-hat.

Confidence level = 99%

Sample size = n = 34

Degrees of freedom = n – 1 = 34 – 1 = 33

Critical value t = 2.733277

(By using t-table or excel)

Standard error of y-hat = SE(y-hat) = 117.7

Confidence interval = y-hat -/+ t*SE(y-hat)

Confidence interval = 190.5 -/+ 2.733277*117.7

Confidence interval = 190.5 -/+ 321.7067

Lower limit = 190.5 - 321.7067 = -131.207

Upper limit = 190.5 + 321.7067 = 512.2067

Negative value of lower limit is not possible, because number of newspapers would be zero or more but not negative, so we take it as zero. Upper limit will be rounded to next integer, because newspaper could not be fractional. So,

Confidence interval = (0, 513)

Correct answer = a. (0, 513)

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