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In a study of the effect of cigarette smoking on the carbon monoxide diffusing capacity (DL) of the lung, researchers found that current smokers had DL readings significantly lower than those of either ex-smokers or nonsmokers. The carbon monoxide diffusing capacities for a random sample of n =20 current smokers are listed here:

103.768 88.602 73.003 123.086 91.052
92.295 61.675 90.677 84.023 76.014
100.615 88.017 71.210 82.115 89.222
102.754 108.579 73.154 106.755 90.479

Required:
a. Do these data that the mean DL reading for current smokers is significantly lower than 100 DL, the average for nonsmokers? Use αα=.01.
b. Find a 99% upper one-sided confidence bound for the mean DL reading for current smokers. Does this bound confirm your conclusions in part a?

Sagot :

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Answer:

we conclude that mean DL reading for current smokers is significantly lower than 100 DL

μ ≤ 98.32

Step-by-step explanation:

Given :

H0 : μ = 100

H1 : μ < 100

Given the sample data:

103.768 88.602 73.003 123.086 91.052

92.295 61.675 90.677 84.023 76.014

100.615 88.017 71.210 82.115 89.222

102.754 108.579 73.154 106.755 90.479

Sample mean, xbar = 89.855

Sample standard deviation, s = 14.904

Test statistic :

(Xbar - μ) ÷ (s/√n)

(89.855 - 100) /(14.904/√20)

-10.145 / 3.3326357

Test statistic = - 3.044

Pvalue : using the Pvalue from T score calculator :

Pvalue = 0.00333

Pvalue < α ; Reject H0

Hence, we conclude that mean DL reading for current smokers is significantly lower than 100 DL.

b. Find a 99% upper one-sided confidence bound for the mean DL reading for current smokers. Does this bound confirm your conclusions in part a?

Tcritical at 99% (one sided) = 2.54

Upper confidence interval :

Xbar ± standard Error

Standard Error = Tcritical * s/√n

Standard Error = 2.54 * 14.904/√20 = 8.465

Upper boundary:

Xbar + standard error

89.855 + 8.465 = 98.32

μ ≤ 98.32

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