1. When the owner of a small business reviews her list of contracts for 2011, she finds that 35% of the contracts were from clients she met at a large conference at the end of 2010. Answer the following questions about this situation.
a. Was this measurement obtained by a sample or a census? What words in the description of the situation make you confident that your answer is correct?
b. Should the owner have taken into account some measure of reliability associated with the value 35%?
2. Assume that the number of sales per day of a app in the Apple iOS App Store is normally distributed.
a. What two parameters of the distribution would you need to be able to determine the probability of sales on a particular day exceeding 100 units?
b. If the probability of sales exceeding 100 units is 20% and the mean daily sales is 86 units, then what is the standards deviation of the distribution?
3. Researchers are studying a new chemical process for producing dyes. Although they don't know it, the yield of the process is normally distributed with µ=550kg and Ó = 75kg. The researchers plan to estimate the process's mean yield by running enough sample to be 90% confident that their computed mean will be within 20kg of the actual mean? Show your work to justify your answer.
4. A health inspector at a restaurant will enter the kitchen and choose 5 stations to inspect from a predetermined list of 15 stations present in most restaurant kitchens.
a. How many different sets of 5 stations exist?
b. If all sets are equally likely, what is the probability of each set?
c. If the inspector were instead to randomly select 13 stations to inspect, how many different sets of 13 stations would exist?
d. If all sets were equally likely, what is the probability of each set?
5. A quality control analyst measures the number of hours a patient in a low-risk condition waits for care at the emergency room of a small hospital. The following data were obtained for 20 patients.
2.26 2.01 3.0 1.22 1.92 1.79 .78 1.89 .71 1.58
2.02 2.77 2.87 .51 .74 1.95 2.76 2.61 3.54 2.95
a. Compute the sample mean, sample median, and range of the data.
b. Compute the sample standard deviation and sample variance.
6. Since careful records have begun being kept in January, Eric's small business has delivered the following quantities of flowers throughout town.
January February March April May June July August
Small Bouquets 85 34 26 24 43 29 30 19
Large Bouquets 23 64 27 18 33 23 20 13
Assuming the data is normally distributed, construct two separate 90% confidence intervals, one for the number of deliveries of small bouquets in September and one for the number of large bouquets in September.
7. Consider the following data values of variables x and y
X 5 4 3 6 9 8 10
y 7 8 10 5 2 3 1
Construct a scatter diagram of the data points and plot the least squares regression line on it. Find the least squares regression line.
8. A quality control experiment is to be done on a machine that fills tubes with toothpaste. Its specifications require that it fill tubes with 4.7 ounces. A random sample of 40 tubes filled by the machine is taken and each tube is weighed. The resulting data are below, with the weight of the tube already having been subtracted from each. Perform a hypothesis test at the 90% confidence level to determine if the machine is performing according to specifications.
4.66 4.61 4.71 4.63 4.70 4.62 4.63 4.61 4.70 4.56
4.60 4.66 4.68 4.57 4.67 4.72 4.67 4.64 4.66 4.75
4.69 4.64 4.67 4.65 4.69 4.65 4.75 4.53 4.57 4.74
4.68 4.67 4.66 4.68 4.64 4.65 4.64 4.80 4.71 4.69