Question

The table below lists measured amounts (mg) of tar, carbon monoxide (CO), and nicotine in king size cigarettes of different brands. Tar 25 27 20 24 20 20 21 24 CO 18 16 16 16 16 16 14 17 Nicotine 1.5 1.7 1.1 1.6 1.1 1.0 1.2 1.4 Use the amounts of nicotine and carbon monoxide (CO).

1.Find the value of the linear correlation coefficient between amounts of nicotine and carbon monoxide.

2.Use the data and determine whether there is sufficient evidence to support a claim of a linear correlation between amounts of nicotine and carbon monoxide. Find the P-value.

3.Based on the P-value, is there a linear correlation between the amounts of nicotine and carbon monoxide?

4.Using the data, and letting y represent the amount of carbon monoxide and letting x represent the amount of nicotine, find the regression equation.

5.Referring to the data in Question 16, The Raleigh brand king size cigarette is not included in the table, and it has 1.3 mg of nicotine. What is the best predicted amount of carbon monoxide?

Answer 1

• Excel output for correalation and regression equation

• No	x=Nicotine	y=co	(x-xbar)^2	(y-ybar)^2	(x-xbar)*(y-ybar)
  1	1.5	18	0.030625	3.515625	0.328125
  2	1.7	16	0.140625	0.015625	-0.046875
  3	1.1	16	0.050625	0.015625	0.028125
  4	1.6	16	0.075625	0.015625	-0.034375
  5	1.1	16	0.050625	0.015625	0.028125
  6	1	16	0.105625	0.015625	0.040625
  7	1.2	14	0.015625	4.515625	0.265625
  8	1.4	17	0.005625	0.765625	0.065625
  sum	10.6	129	0.475	8.875	0.675
  mean	1.325	16.125	sxx	syy	sxy

• Below calculated slope,intercept and correalation coiefficient

slope=b1=sxy/sxx	1.421052632
intercept=b0=ybar-(slope*xbar)	14.24210526
SST	SYY	8.875
SSR	sxy^2/sxx	0.9592105
SSE	syy-sxy^2/sxx	7.9157895
r^2	SSR/SST	0.1080801
r	sxy/sqrt(sxx*syy)	0.3287553

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• 1)

r=sxy/sqrt(sxx*syy) =0.3287

applying the above values in the formula of r gives r=0.328. i have atached the calculations below.

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2.Use the data and determine whether there is sufficient evidence to support a claim of a linear correlation between amounts of nicotine and carbon monoxide. Find the P-value.

• Step 1:

  H0: Null Hypothesis: =0

  HA: Alternative Hypothesis: 0

  Step 2:

  r = 0.328

  n = 8

  =0.01

  df = 8 - 2 = 6

  Test Statistic is given by:

• t=r*sqrt((n-2)/(1-r^2))

  t=0.328*sqrt(6/(1-0.328*0.328))

  t=0.8505

  Step 3:

  Corresponding to t score = 0.8505, df = and Two Tail Test, By Technology,

  p - value = 0.6152

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3.)

Based on the P-value, is there a linear correlation between the amounts of nicotine and carbon monoxide?

Step 4:

Since p - value = 0.6152 is greater than = 0.01, the difference is not significant. Fail to reject null hypothesis.

A,the correlation coefficient is 0.328 which indicate a weak correlation. That is there is no sufficient evidence to support the claim that there is a linear correlation between amounts of noictotine and carbon monoxide.

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4.Using the data, and letting y represent the amount of carbon monoxide and letting x represent the amount of nicotine, find the regression equation.

slope=b1=sxy/sxx	1.421052632
intercept=b0=ybar-(slope*xbar)	14.24210526

• B,The required regression equation is

  the linear regression line of y on x takes the form

  

  

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5.Referring to the data in Question 16, The Raleigh brand king size cigarette is not included in the table, and it has 1.3 mg of nicotine. What is the best predicted amount of carbon monoxide?

c,considering x as 1.3 in the regression equation obtained in B, the predicted value is 16.086. the predicted value is much higher than the actual value 15.

best predicted amount of carbon monoxide =16.086

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