# To find:Whether the data provide suffcient evidence to conclude that the invervention program reduces mean heart rate of urban bus drivers in Stockholm.

Question
Study design
To find:Whether the data provide suffcient evidence to conclude that the invervention program reduces mean heart rate of urban bus drivers in Stockholm.

2021-01-20

Concept used:
Let $$\mu_{1}$$ be the mean heart rate of intervention drivers and $$\mu_{2}$$ be the mean heart rate of control drivers.
Consider null and Alternative hypothesis.
Null hypothesis, $$H_{0} : \mu_{1} = \mu_{2}$$.
Alternative hypothesis, $$H_{0} : \mu_{1} < \mu_{2}$$
Here, the hypothesis test is left tailed.
Level of significance is 5%.
Determine the test statistics under Null hypothesis as follows.
$$d_{f}=\frac{\left[\left(\frac{x_{1}^{2}}{n_{1}}\right)+\left(\frac{x_{2}^{2}}{n_{2}}\right)\right]^{2}}{\left(\frac{x_{1}^{2}}{n_{1}}\right)^{2}}/n_{1}-1+\frac{\left(\frac{x_{2}^{2}}{n_{2}}\right)^{2}}{n_{2}}-1$$
$$=\frac{\left[\left(\frac{5.49^{2}}{10}\right)+\left(\frac{9.04^{2}}{31}\right)\right]^{2}}{\frac{5.49^{2}}{10^{2}}}/10-1+\frac{\left(\frac{9.04^{2}}{31}\right)^{2}}{31}-1\approx25$$
Referring the table with 25 degree of freedom, to determine the P-value that is P - value > 0.10.
Using technology, P-value is 0.675 .
Since the P-value is 0.675 which is greater than level of significance $$\alpha = 0.05$$. So we are fail to reject our null hypothesis.
Therefore, the given data does not provide sufficient evidence to conclude that the intervention program reduces mean heart rate of urban drivers in Stockholm.

### Relevant Questions

A random sample of $$n_1 = 14$$ winter days in Denver gave a sample mean pollution index $$x_1 = 43$$.
Previous studies show that $$\sigma_1 = 19$$.
For Englewood (a suburb of Denver), a random sample of $$n_2 = 12$$ winter days gave a sample mean pollution index of $$x_2 = 37$$.
Previous studies show that $$\sigma_2 = 13$$.
Assume the pollution index is normally distributed in both Englewood and Denver.
(a) State the null and alternate hypotheses.
$$H_0:\mu_1=\mu_2.\mu_1>\mu_2$$
$$H_0:\mu_1<\mu_2.\mu_1=\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1<\mu_2$$
$$H_0:\mu_1=\mu_2.\mu_1\neq\mu_2$$
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The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations.
The standard normal. We assume that both population distributions are approximately normal with known standard deviations.
The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations.
(c) What is the value of the sample test statistic? Compute the corresponding z or t value as appropriate.
(Test the difference $$\mu_1 - \mu_2$$. Round your answer to two decimal places.) NKS (d) Find (or estimate) the P-value. (Round your answer to four decimal places.)
(e) Based on your answers in parts (i)−(iii), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level \alpha?
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the $$\alpha = 0.01$$ level, we reject the null hypothesis and conclude the data are not statistically significant.
(f) Interpret your conclusion in the context of the application.
Reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is insufficient evidence that there is a difference in mean pollution index for Englewood and Denver.
Fail to reject the null hypothesis, there is sufficient evidence that there is a difference in mean pollution index for Englewood and Denver. (g) Find a 99% confidence interval for
$$\mu_1 - \mu_2$$.
lower limit
upper limit
(h) Explain the meaning of the confidence interval in the context of the problem.
Because the interval contains only positive numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, we can not say that the mean population pollution index for Englewood is different than that of Denver.
Because the interval contains both positive and negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is greater than that of Denver.
Because the interval contains only negative numbers, this indicates that at the 99% confidence level, the mean population pollution index for Englewood is less than that of Denver.
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