These statistics were calculated from two random samples:

$$\hat{p}_1=.60 \quad n_1=225 \quad \hat{p}_2=.55 \quad n_2=225$$

Calculate the p-value of a test to determine whether there is evidence to infer that the population proportions differ

Many stores sell extended warranties for products they sell. These are very lucrative for store owners. To learn more about who buys these warranties a random sample of a store’s customers who recently purchased a product for which an extended warranty was available was drawn. Among other variables each respondent reported whether they paid the regular price or a sale price and whether they purchased an extended warranty. Can we conclude at the 10% significance level that those who paid the regular price are more likely to buy an extended warranty?

The manager of a dairy is in the process of deciding which of two new carton-filling machines to use. The most important attripute is the consistency of the fills. In a preliminary study she measured the fills in the 1-liter carton and listed them here. Can the manager infer that the two machines differ in their consistency of fills?

$$\begin{array}{lrrrrrr}\text { Machine 1 } & .998 & .997 & 1.003 & 1.000 & .999 & \\ & 1.000 & .998 & 1.003 & 1.004 & 1.000 & \\ \text { Machine 2 } & 1.003 & 1.004 & .997 & .996 & .999 & 1.003 \\ & 1.000 & 1.005 & 1.002 & 1.004 & .996 & \end{array}$$

The president of a large company is in the process of deciding whether to adopt a lunchtime exercise program. The purpose of such programs is to improve the health of workers and, in so doing, reduce medical expenses. To get more information, he instituted an exercise program for the employees in one office. The president knows that during the winter months medical expenses are relatively high because of the incidence of colds and flu. Consequently, he decides to use a matched pairs design by recording medical expenses for the 12 months before the program and for 12 months after the program. The “before” and “after” expenses (in thousands of dollars) are compared on a month-to-month basis and shown here.

Estimate with 95% confidence the mean savings produced by exercise programs.

Recent studies seem to indicate that using a cell phone while driving is dangerous. One reason for this is that a driver’s reaction time may slow while he or she is talking on the phone. Researchers at Miami (Ohio) University measured the reaction times of a sample of drivers who owned a cell phone. Half the sample was tested while on the phone and the other half was tested while not on the phone. Can we conclude that reaction times are slower for drivers using cell phones?

Random sampling from two normal populations produced the following results:

$$\begin{array}{lll}\bar{x}_1=63 & s_1=18 & n_1=50 \\ \bar{x}_2=60 & s_2=7 & n_2=45\end{array}$$

Repeat part (a) doubling the sample sizes.

An oil company sends out monthly statements to its customers who purchased gasoline and other items using the company’s credit card. Until now, the company has not included a preaddressed envelope for returning payments. The average and the standard deviation of the number of days before payment is received are 9.8 and 3.2, respectively. As an experiment to determine whether enclosing preaddressed envelopes speeds up payment, 150 customers selected at random were sent preaddressed envelopes with their bills. The numbers of days to payment were recorded. Do the data provide sufficient evidence at the 10% level of significance to establish that enclosure of preaddressed envelopes improves the average speed of payments?

The manager of a branch of a major bank wants to improve service. She is thinking about giving $1 to any customer who waits in line for a period of time that is considered excessive. (The bank ultimately decided that more than 8 minutes is excessive.) However, to get a better idea about the level of current service, she undertakes a survey of customers. A student is hired to measure the time spent waiting in line by a random sample of 50 customers. Using a stopwatch, the student determined the amount of time between the time the customer joined the line and the time he or she reached the teller. The times were recorded. Construct a 90% confidence interval estimate of the mean waiting time for the bank’s customers.

In a random sample of 200 observations, we found the proportion of successes to be 48%. Estimate with 95% confidence the population proportion of successes.

Random samples from two binomial populations yielded the following statistics:

$$\hat{p}_1=.45 \quad n_1=100 \quad \hat{p}_2=.40 \quad n_2=100$$

Describe what happens to the p-value when the sample sizes increase

A diet doctor claims that the average North American is more than 20 pounds overweight. To test his claim, a random sample of 20 North Americans was weighed, and the difference between their actual and ideal weights was calculated. The data are listed here. Do these data allow us to infer at the 5%significance level that the doctor’s claim is true?

$$\begin{array}{llllllllll}16 & 23 & 18 & 41 & 22 & 18 & 23 & 19 & 22 & 15 \\ 18 & 35 & 16 & 15 & 17 & 19 & 23 & 15 & 16 & 26\end{array}$$

Random samples from two binomial populations yielded the following statistics:

$$\hat{p}_1=.45 \quad n_1=100 \quad \hat{p}_2=.40 \quad n_2=100$$

Repeat part (a) increasing the sample sizes to 400.

Discuss the effect on the width of the confidence interval estimate of reducing the sample proportion.

The weights of a random sample of cereal boxes that are supposed to weigh 1 pound are listed here. Estimate the variance of the entire population of cereal box weights with 90% confidence.

$$\begin{array}{llllllll}1.05 & 1.03 & .98 & 1.00 & .99 & .97 & 1.01 & .96\end{array}$$