Question/Answers:

 You should work each of the following on your own, then review the solution’s guide. DO NOT look at the solution’s guide first.

1.  The following numbers represent the weights in pounds of six 7-year old children in Mrs. Jones' second grade class (25, 60, 51, 47, 49, 45). Find the mean, median, mode, variance, and standard deviation.

2.  If the variance is 846, what is the standard deviation?

3.  If we have the following data: 34, 38, 22, 21, 29, 37, 40, 41, 22, 20, 49, 47, 20, 31, 34, 66. Draw a stem and leaf. Discuss the shape of the distribution.

4.  For two events, C and D, P(C) = 0.6, P(D)=0.3, and P(C|D) = 0.2. Find P(CÇD). 

5.  If a binomial variable has n=34 and p=0.30, find the mean, variance, and standard deviation.

6.  A company claims that 61% of consumers know about their product.  If the company asks 18 consumers, what is the probability that (a) exactly 10 will say yes, that (b) between 10 and 12 will say yes.

7.  If the population has a mean of 58 and a standard deviation of 23.4, what would be the mean and standard deviation of a sampling distribution with a sample size of 22?

8.  A restaurant asks 40 customers about their service times. If the population mean service time is 28 minutes with a standard deviation of 5.1 minutes, what is the probability that the mean of the sample service times would be less than 26 minutes?

9.  On a dry surface, the braking distance (in meters) of a certain car is a normal distribution with mu = μ = 45.1 m and sigma = σ = 0.5.

a.     Find the braking distance that represents the 91st percentile.

b.     Find the probability that the braking distance is less than or equal to 45 m.

c.     Find the probability that the braking distance is greater than 46.8 m.

d.     Find the probability that the braking distance is between 45 m and 46.8 m.

10.  A sample of 58 days of gas prices has a mean of $2.75 and a standard deviation of $0.86. Construct the 95% confidence interval.

11.  A drug manufacturer wants to estimate the mean heart rate for patients with a certain heart condition. Because the condition is rare, the manufacturer can only find 14 people with the condition currently untreated. From this small sample, the mean heart rate is 101 beats per minute with a standard deviation of 8.

a.     Find a 99% confidence interval for the true mean heart rate of all people with this untreated condition. Show your calculations.

b.       Interpret this confidence interval, and write a sentence that explains it.

12.  Determine the minimum required sample size if you want to be 80% confident that the sample mean is within 2 units of the population mean given sigma = 9.4. Assume the population is normally distributed.

13.  A social service worker wants to estimate the true proportion of pregnant teenagers who miss at least one day of school per week on average. The social worker wants to be within 5% of the true proportion when using a 90% confidence interval. A previous study estimated the population proportion at 0.21.

a.     Using this previous study as an estimate for p, what sample size should be used?

b.     If the previous study was not available, what estimate for p should be used?

14.  A restaurant claims that its speed of service time is less than 15 minutes. A random selection of 49 service times was collected, and their mean was calculated to be 14.5 minutes. Their standard deviation is 2.7 minutes. Is there enough evidence to support the claim at alpha = .07? Write the hypotheses, the p-value, conclusion, and implication for the claim.

15.  To support their claim that the average speed on their road is more than 25 mph, neighbors collect data on 24 cars on a day. Those cars have a mean speed of 26.7mph and a standard deviation of 3.9mph.  Do the neighbors have enough information to support their claim at an alpha of 0.05? Write the hypotheses, the p-value, conclusion, and implication for the claim.

16.  A doctor claims that 30% of patients only have a cold. During one month, the doctor finds that 112 of 420 patients only has a cold. At α=0.06, can the doctor support the claim? Write the hypotheses, the p-value, conclusion, and implication for the claim.

17.  To test if there was a positive relationship between the dependent and independent variables, a hypothesis test found a t-statistic of 1.43 based on a sample size of 20. Based on this information, what could be concluded about the relationship between these variables using an alpha of 0.05?

18.  In a multiple regression with four independent variables and 39 in the sample size, a beta is estimated to be 3.98. Using a standard deviation of this beta of 0.87, find the 95% confidence interval for the beta.

19.  Find the regression equation of the following data.

20.  To predict the annual rice yield in pounds, we use the equation y-hat = 859 + 5.76x1 + 3.82x2,  where x1 represents the number of acres planted and where x2 represents the number of acres harvested and where r2 = 0.94.

a.     Predict the annual yield when 3,200 acres are planted and 3,000 are harvested.

b.     Interpret the results of r² value.