Besides their known long-term effects, do cigarettes also cause short-term illnesses such as colds? To help answer this question, a sample of 231 smokers was drawn. Each person was asked to report the average number of cigarettes smoked per day and the number of days absent from work due to colds last year.

The data are stored in Dataset 5 sheet. Using this data set and EXCEL answer the following questions.

(a)Show a numerical summary output for the two variables; cigarettes smoked and days absent, and explain the key numerical descriptive measures.

(b)Comment on the shape of the distribution of the two variables; cigarettes smoked and days absent.

(c)Test the hypothesis that the population mean days absent is less than 14 (hint: use a 5% level of significance and use the 6 steps procedure to perform this test).

(d)If the researcher claims that the population mean days absent is greater than 14, do you agree with that? Explain why.

(e)If the researcher wants to examine the association between cigarettes smoked and days absent, what is the dependent variable and independent variable for this analysis? Why?

(f)Present an appropriate plot to investigate the relationship between cigarettes smoked and days absent. Comment on the relationship between the two variables.

(g)Using an appropriate numerical descriptive measure, comment on the strength and the direction of the linear relationship between cigarettes smoked and days absent.

(h)Estimate the relationship between cigarettes smoked and days absent using a linear regression model and display the regression summary output table. What do the estimated regression coefficients reveal about the relationship between cigarettes smoked and days absent?

(i)Comment on the fitness of the estimated model.

(j)Test whether a linear relationship exists between cigarettes smoked and days absent at the 5% significance level (hint: use a 5% level of significance and use the 6 steps procedure to perform this test).

(k)Based on your answers to (a) to (j) above, try to give a research report for the head of research division of your company,summarizing your findings.

Dataset 5 Cigarettes Days absent 44 18 41 18 17 18 35 15 33 14 44 15 39 18 35 10 43 16 43 14 41 16 47 19 41 13 30 12 15 18 39 18 36 11 41 13 37 10 43 21 32 13 17 13 34 15 32 11 19 10 44 26 30 13 42 25 34 5 36 8 42 15 47 15 55 19 27 15 28 15 45 22 29 10 37 13 52 13 34 16 48 23 40 15 29 16 34 10 35 19 57 23 48 1141 10 40 13 36 13 26 7 29 15 52 16 28 16 35 11 42 15 54 19 56 19 37 9 41 17 32 16 63 20 31 15 36 15 31 12 25 15 40 25 55 16 37 21 28 15 56 21 24 16 61 19 40 16 50 14 52 10 45 14 42 19 47 23 22 0 26 12 38 13 46 13 27 9 45 21 43 15 17 11 45 16 40 15 41 17 37 15 30 10 14 31 9 49 10 44 15 N 1625 30 20 36 11 39 14 49 13 37 19 20 11 48 12 28 5 51 16 36 21 42 6 47 9 17 11 22 16 42 21 32 11 31 7 49 16 30 11 31 11 38 18 44 14 41 17 40 20 32 17 48 15 29 17 40 18 45 18 40 15 35 18 37 17 41 16 25 16 35 19 44 15 58 24 27 13 42 22 26 9 48 15 30 11 36 13 26 8 27 6 39 14 17 17 44 2141 19 26 14 30 14 36 13 31 15 55 17 45 17 27 17 25 9 42 15 18 6 49 15 60 19 40 18 29 15 32 12 35 16 45 15 42 11 52 13 52 16 8 16 36 15 33 12 38 17 38 11 38 14 36 16 44 11 36 14 35 12 30 13 39 21 37 7 26 22 51 18 42 10 44 19 41 15 32 16 56 19 47 22 39 11 18 10 33 12 49 14 16 7 38 9 27 00 26 1527 00 25 15 14 11 38 9 38 13 52 18 47 14 54 9 37 6 40 17 56 17 38 16 53 22 52 19 21 11 34 16 23 5 44 13 36 17 45 14 23 10 26 12 54 20 37 19 56 11 38 14 59 18 39 16 38 21 42 20 44 17 32 17 45 13