Use either the critical-value approach or the P-value approach to perform the required hypothesis test. Response Insurance collects data on seat-belt use among U.S. drivers. Of 1000 drivers 25-34 years old, 27% said that they buckle up, whereas 330 of 1100 drivers 45-64 years old said that they did. At the 10% significance level, do the data suggest that there is a difference in seat-belt use between drivers 25-34 years old and those 45-64 years old? [SOURCE: USA TODAY Online]

In an attempt to increase sales, a breakfast cereal company decides to offer a promotion. Each box of cereal will contain a collectible card featuring one NASCAR driver: Kyle Busch; Dale Earnhardt, Jr.; Kasey Kahne; Danica Patrick; or Jimmie Johnson. The company says that each of the 5 cards is equally likely to appear in the 100,000 boxes of cereal that are part of this promotion. You buy 12 boxes and let X = the number of Kyle Busch cards in the sample. Calculate the mean and standard deviation of the sampling distribution of X.

Based on long experience, an airline has found that about 6% of the people making reservations on a flight from Miami to Denver do not show up for the flight. Suppose the airline overbooks this flight by selling 267 ticket reservations for an airplane with only 255 seats. Let n = 267 represent the number of ticket reservations. Let r represent the number of people with reservation s who show up for the flight. Which expression represents the probability that a seat will be available for everyone who shows up holding a reservation? $P(255 \leq r)$; $P(r \leq 255)$; $P(r \leq 267)$; $P(r=255)$

Find each integral. $\int \csc ^{2} \pi t d t$

A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of $32 and a standard deviation of$20. Explain why you cannot determine the probability that the next Sunday customer will spend at least $40.

A grocery store's receipts show that Sunday customer purchases have a skewed distribution with a mean of $32 and a standard deviation of$20. Is it likely that the next 50 Sunday customers will spend an average of at least $40? Explain.

A certain tennis player makes a successful first serve $70\%$ of the time. Assume that each serve is independent of the others. She serves 80 times in a match. What 's the probability she makes at least 65 first serves?

You are an explorer on an alien plant and find an island chain inhabited by several species of what you decide to call “Snarfs.” Some strongly resemble mainland Snarfs but others are quite different. Hypothesize how colonization and speciation occurred.

Gastric freezing was once a recommended treatment for ulcers in the upper intestine. Use of gastric freezing stopped after experiments showed it had no effect. One randomized comparative experiment found that 28 of the 82 gastric-freezing patients improved, while 30 of the 78 patients in the placebo group improved. We can test the hypothesis of "no difference" in the effectiveness of the treatments in two ways: with a two-sample z test or with a chi-square test. State appropriate hypotheses for a chi-square test.

To get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates he'll get stopped on about 15% of work days. During a certain 5-day work week, what is the probability that he a) gets stopped on Monday and again on Tuesday? b) gets stopped for the first time on Thursday? c) gets stopped every day? d) gets stopped at least once during the week?

To get to work, a commuter must cross train tracks. The time the train arrives varies slightly from day to day, but the commuter estimates he'll get stopped on about 15% of work days. During a certain 5-day work week, what is the probability that he gets stopped on Monday and again on Tuesday?

Your teacher brings two large bags of colored goldfish crackers to class. Bag 1 has 25% red crackers and Bag 2 has 35% red crackers. Using a paper cup, your teacher takes an SRS of 50 crackers from Bag 1 and a separate SRS of 40 crackers from Bag 2. Let $\hat{p}_{1}-\hat{p}_{2}$ be the difference in the sample proportions of red crackers. What is the shape of the sampling distribution of $\hat{p}_{1}-\hat{p}_{2} ?$ Why?

For any cumulative distribution function F(x), show that if $a \leq b,$ then $F(a) \leq F(b)$

You do not need a lot of money to invest in a mutual fund. However, if you decide to put some money into an investment, you are usually advised to leave it in for (at least) several years. Why? Because good years tend to cancel out bad years, giving you a better overall return with less risk. To see what we mean, let's use a 3-year moving average on the Calvert Social Balanced Fund (a socially responsible fund). $$ \begin{array}{l|rrrrrr} \hline \text { Year } & 1990 & 1991 & 1992 & 1993 & 1994 & 1995 \\ \hline \text { % Return } & 1.78 & 17.79 & 7.46 & 5.95 & -4.74 & 25.85 \\ \hline \end{array} $$ $$ \begin{array}{ccccc} \hline \text{Year} & 1996 & 1997 & 1998 & 1999 & 2000 \\ \hline \text{\\% Return} &9.03 & 18.92 & 17.49 & 6.80 & -2.38 \\ \hline \end{array} $$ Use a calculator with mean and standard deviation keys to verify that the mean annual return for all 11 years is approximately 9.45%, with standard deviation 9.57%.