Question: 1) Wendy and Tim have invited 400 family and friends to their wedding. The couple would like to randomly choose 20 of these guests to give their reception centerpieces to.

a. Describe how the couple assign numbers to their guests if a random number table will be used to determine who will receive the centerpieces?

b. Use the line 30 of the random number table on page 612 - 613 and list the numbers of the first 5 guests that will receive a centerpiece.

2) The career center keeps track of the time it takes graduates to find a full-time job in their desired field. The distribution of the time it takes a graduate to find a full-time job is normal with meanμ=4.5months and standard deviation σ=4.2months. A random sample of 49 recent graduates showed a mean time x ¯=6.5months to get a full-time job. Does this sample provide evidence that the time it takes a graduate to get a full-time job has increased? Use a 1% level of significance.

3) A manufacturer of sinus medication claims that 91% of the patients that use their product are relieved of their symptoms. In a random sample of 150 patients using this sinus medication 134 stated that their symptoms were relieved.

a. What is the sample proportion,p ^, of the patients who stated that their symptoms were relieved?

b. What is the mean and standard deviation for the sampling distribution of p ^?

c. What is the probability that if the true population proportion of patients that are relieved of their symptoms is 91% that the sample proportion would be less than your calculated value of p ^?

4) The Book Worm Club sends each of its members a book once a month. The members then have the option of returning the book without cost within 10 days. A random sample of 360 members showed that 216 had returned at least one book in the past year. Let p be the true proportion of all members who returned at least one book in the past year. Create a 95% confidence interval for p.

5) A doctor whose specialty involves kidney transplants suspects that there is a higher rate of rejection incidents for men in the age group 15 - 25 than for older men. To test this claim she drew a random sample of 200 male kidney transplant patients over age 25. Of these, 40 had rejection incidents. A random sample of 100 male kidney transplant patients in the age group 15 - 25 showed that 30 had rejection incidents. Does the data show that the proportion of the rejection incidents is higher for the 15 - 25 year old patients? Use a significance level of 1%.

6) A basket contains 4 - $1, 11 - $5, 6 - $10, and 4 - $20 bills.

a. What is the probability that if you choose two bills from the basket with replacement that you would choose two $20 bills?

b. What is the probability that if you choose one bill from the basket that you would choose a bill that is more than $5?

c. What is the probability that if you choose two bills without replacement that you would choose a $10 and then a $20 bill?

d. What is the probability that if you choose two bills without replacement that you would choose a $10 and $20 bill regardless of order?

e. What is the probability that if you choose three bills with replacement that you would choose at least one $5 bill?

7) A general manager of an amusement park determined that the amount of time an individual spent in the park is normally distributed with mean μ=3.4 hr. and standard deviation σ=1.1 hr.

a. What is the probability that a single individual will spend more than 4 hours in the park?

b. What are the mean and the standard deviation for the sampling distribution of x ¯ if the sample size is 35?

c. What is the probability that a random sample of 35 individuals would have a mean time of more than 3.8 hours spent in the park? (8 points)

8) Four boxes of Purr Lots Cat Food are found to weigh 12.7, 11.6, 11.2, and 12.4 oz. Create a 99% confidence interval for the true population mean weight of all such boxes of cat food.

9) In a study on the length of calls on a cellular phone, the standard deviation was found to be σ=1.2minutes. In a sample of 60 cellular phone calls the mean length of the call was found to be 6.3 minutes. Create a 90% confidence interval for the true population mean length of a cellular phone call.

10) According to the Harris poll, 71% of Americans believe that the cost of lawsuits is too high. If you survey 500 randomly selected Americans and find that 370 of them hold that belief, do you have sufficient evidence to prove that the actual percentage is not 71%. Use a 5% level of significance.

11) According to an article in USA Today, women in the age group 18 to 25 drive an average of 6,047 miles per year. A random sample of eight undergraduate women at the University of Wyoming in this age group reported that they drove the following number of miles each year:

Use a 10% significance level to test USA Today's claim.

Bonus problem.

Students in grades 4 - 6 were asked whether good grades, athletic ability, or popularity was most important to them. The results of this survey are in the table below.

Use a 5% level of significance to determine if grade level and opinion of what is most important are independent.