1) A company wants to implement a flextime schedule so that workers can schedule their own work hours, but it needs a mean of working hours no less than 7.5 hours per day per assembly worker to operate effectively. A random sample of 61 workers was asked to submit a tentative flextime schedule. If the mean number of hours per day for Monday was 7.32 hours and the standard deviation was 0.75 hours, do the data provide sufficient evidence to indicate that the mean number of hours worked per day on Mondays, for all of the company's assemblers, will be less than the expected at =0.04 level? (Round your answer at the nearest 4^th decimal place, if necessary.) What are the hypotheses of the test?

2) Olestra is a fat substitute approved by the FDA for use in snack foods. Because there have been anecdotal reports of gastrointestinal problems associated with olestra consumption, a randomized, double-blind, placebo-controlled experiment was carried out to compare olestra potato chips to regular potato chips with respect to GI symptoms. Among 520 individuals in the TG control group (noted as "C"), 93 experienced an adverse GI event, whereas among the 560 individuals in the olestra treatment group (noted as "T"), 75 experienced such an event. Carry out a test of hypotheses at =0.05 significance level to decide whether the incidence rate of GI problems for those who consume olestra chips according to the experimental regimen differs from the incidence rate for the TG control treatment.

What is the critical value of the test?

3) Some sports that involve a significant amount of running, jumping, or hopping put participants at risk for Achilles tendon injuries. A study in The American Journal of Sports Medicine looked at the diameter (in mm) of the injured tendons for patients who participated in these types of sports activities. Suppose that the Achilles tendon diameters in the general population are normally distributed with a mean of 5.92mm. When the diameters of the injured tendon were measured for a random sample of 18 patients, the average diameter was 7.12mm with a standard deviation of 1.98mm. Is there sufficient evidence to indicate that the average diameter of the tendon for patients with Achilles tendon injuries is longer than of the general population at the 0.01 level of significance. (Round your answer at the nearest 4th decimal place, if necessary.) What is the test statistic?

4) Olestra is a fat substitute approved by the FDA for use in snack foods. Because there have been anecdotal reports of gastrointestinal problems associated with olestra consumption, a randomized, double-blind, placebo-controlled experiment was carried out to compare olestra potato chips to regular potato chips with respect to GI symptoms. Among 520 individuals in the TG control group (noted as "C"), 93 experienced an adverse GI event, whereas among the 560 individuals in the olestra treatment group (noted as "T"), 76 experienced such an event. Carry out a test of hypotheses at =0.04 significance level to decide whether the incidence rate of GI problems for those who consume olestra chips according to the experimental regimen differs from the incidence rate for the TG control treatment.As a difference in proportion, what is the upper boundary of the confidence interval?

5)Of those women who are diagnosed to have early-stage breast cancer, 30% eventually die of the disease. Suppose a screening program for the early detection of breast cancer was started in order to increase the survival rate of those diagnosed to have the disease. A random sample of 300 women was selected from among those who were screened by the program and who were diagnosed to have the disease. If 230 women in the sample did survive the disease, can you conclude that the screening program was effective? Test using =0.05 level of significance. (Round your answer at the nearest 4^th decimal place, if necessary.. What are the hypotheses of the test?

6)In a Pew Research report concerning the rise of automation in the United States, 55% of the participants indicated that they would not ride in a driverless car, and 85% favor a requirement of having a human in the driver's seat in case of an emergency. Suppose that the number of participants was 900. Is there sufficient evidence to conclude, at a confidence level of 97%, that the majority of Americans would not ride in a driverless car? (Round your answer at the nearest 4^th decimal place, if necessary. What is the critical value of the test?