Question

3. A medical researcher wishes to see whether the pulse rates of smokers are higher than the pulse rate for non-smokers. Random samples of 65 smokers and 74 non-smokers are selected, and the pulse rate results are shown below. Test the researchers claim at a 0.01. Assume the d.f. = 137 Nonsmokers Smokers Sample Mean Sample Standard Deviation Sample Size 90 88 6.3 74 5.2 65

Answer 1

Solution:

The null and alternative hypotheses are:

$H_{0}:\mu_{smokers}=\mu_{non-smokers}$

$H_{a}:\mu_{smokers}>\mu_{non-smokers}$

Under the null hypothesis, the test statistic is:

$\large t=\frac{\bar{x}_{1}-\bar{x}_{2}}{\sqrt{\frac{s_{1}^{2}}{n_{1}}+\frac{s_{2}^{2}}{n_{2}}}}$

$\large =\frac{90-88}{\sqrt{\frac{5.2^{2}}{65}+\frac{6.3^{2}}{74}}}$

  $\large =2.049$

Now we have to find the t-critical value at 0.01 for df=137. Using the t-distribution table, we have:

$\large t_{critical}=2.354$

Conclusion:

Since the t-statistic is less than the t-critical value, we, therefore, fail to reject the null hypothesis and there is not sufficient evidence to support the researcher's claim that the pulse rate of smokers is higher than the pulse rate of non-smokers.