Question

3. A quality control manager at an amusement park feels that the amount of time that peopled if effective in reducing wait time, he measure the amount of time people wait in line on and then measures the amount of time after he implements the new system below. To make sure the test is fair, he measure the wait times at the same time during the 7 period and twice on Saturday and Sunday f a new loading procedure The data is given is too long. 7 days day The data is recorded in the table below. A normal probability plot for the data and a boxplot indicate that the differences are approximately normally distributed and there are no outliers. Day and time Wait time before 11.6 25.9 20.0 38.2 57.3 32.1 818 57.1 62.8 Wait time after Wednesday (2 pm) Thursday (2 pm) Friday (2 pm) Saturday (11 am) Saturday (4pm) Sunday (12 noon) 10.7 28.3 19.2 35.9 59.2 31.8 75.3 54.9 62.0 Test the hypothesis that the quality control specialist had that his new system decreases wait time a. What type of test will you use? b. State Ho and H c. State the p-value- d. Conclusion: 4. Do business travelers walk at a different pace than leisure travelers? Researchers measured the walking speed of the different travelers at the San Francisco and Cleveland airports. The findings are summarized in the table below. A normal probability plot for the data and a boxplot indicate that the differences are approximately normally distributed and there are no outliers. Business Leisure 20 20 Mean speed (in feet 272261 per minute) Standard deviation 43 (in feet per minute) Test the hypothesis that business travelers walk faster than leisure travelers a. What type of test will you use? b. State Ho and H c. State the p-value- d. Conclusion

Answer 1

Solution:

3. a. What type of test will you use?

Answer: Paired t-test.

b.State H₀ and H₁.

Answer:

$H_{0}:\mu_{d}\leq 0$$\mu_{d}=before - after$

$H_{1}:\mu_{d}> 0$

c. State the p-value

Answer: $\boldsymbol{p-value =0.1286 }$

d. Conclusion

Answer: Since the p-value is greater than the significance level, we, therefore, fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that the quality control specialist had his new system decreases wait time.

4. a. What type of test will you use?

Answer: Two sample independent t-test (pooled)

b.State H₀ and H₁.

Answer:

$H_{0}:\mu_{1}-\mu_{2}\leq 0$

$H_{1}:\mu_{1}-\mu_{2}> 0$

c. State the p-value

Answer: $\boldsymbol{p-value =0.2224}$

d. Conclusion

Answer: Since the p-value is greater than the significance level, we, therefore, fail to reject the null hypothesis and conclude that there is not sufficient evidence to support the claim that the business travelers walk faster than leisure travelers.