According to the Centers for Disease Control, the mean number of cigarettes smok

Question

According to the Centers for Disease Control, the mean number of cigarettes smoked per day by individuals who are daily smokers is 18.1. Do retired adults who are daily smokers smoke less than the general population of daily smokers? To answer this question, Sascha obtains a random sample of 40 retired adults who are current daily smokers and record the number of cigarettes smoked on a randomly selected day The data result in a sample mean of 16 8 cigarettes and a SD of 4.7 cigarettes. Is there sufficient evidence at the alpha = 0.01 level of significance to conclude that retired adults who are daily smokers smoke less than the general population of daily smokers?

Explanation / Answer

Solution:-

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: > 18.1

Alternative hypothesis: < 18.1

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected if the sample mean is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.01. The test method is a one-sample t-test.

Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).

SE = s / sqrt(n)

S.E = 0.743

DF = n - 1

D.F = 39

t = (x - ) / SE

t = - 1.75

where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.

The observed sample mean produced a t statistic test statistic of - 1.75. We use the t Distribution Calculator to find P(t < - 1.75) = 0.044.

Thus the P-value in this analysis is 0.044.

Interpret results. Since the P-value (0.044) is greater than the significance level (0.01), we cannot reject the null hypothesis.

From the above test we have sufficient evidence in the favor of the claim that retired adults who are daily smokers smoke less than the general population of daily smokers.

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