91影视

A study of road rage asked separate random samples of $596$men and $523$women about their behavior while driving. Based on their answers, each re-spondent was assigned a road rage score on a scale of $0$to $20$. Are the conditions for performing a two-sample t test satisfied?

a) Maybe; we have independent random samples, but we need to look at the data to check Normality.

(b) No; road rage scores in a range between $0$ and $20$ can鈥檛 be Normal.

(c) No; we don鈥檛 know the population standard deviations.

(d) Yes; the large sample sizes guarantee that the corresponding population distributions will be Normal.

(e) Yes; we have two independent random samples and large sample sizes.

Suppose the probability that a softball player gets a hit in any single at-bat is .$300$. Assuming that her chance of getting a hit at a particular time at bat is independent of her other times at bat, what is the probability that she will not get a hit until her fourth time at bat in a game?

(a) $\left(\begin{array}{l}4\\ 3\end{array}\right)(0.3{)}^1(0.7{)}^3$

(b) $\left(\begin{array}{l}4\\ 3\end{array}\right)(0.3{)}^3(0.7{)}^1$

(c) $\left(\begin{array}{c}4\\ 1\end{array}\right)(0.3{)}^3(0.7{)}^1$

(d) $(0.3{)}^3(0.7{)}^1$

(e)role="math" localid="1650371346957" $(0.3{)}^1(0.7{)}^3$

Explain why the conditions for using two-sample z procedures to perform inference about $p1-p2$are not met in the settings

Broken crackers We don鈥檛 like to 铿乶d broken crackers when we open the package. How can makers reduce breaking? One idea is to microwave the crackers for $30$seconds right after baking them. Breaks start as hairline cracks called 鈥渃hecking.鈥� Assign $65$newly baked crackers to the microwave and another $65$to a control group that is not microwaved. After one day, none of the microwave group and $16$ of the control group show checking.^$8$

Researchers are interested in evaluating the effect of a natural product on reducing blood pressure. This will be done by comparing the mean reduction in blood pressure of a treatment (natural product) group and a placebo group using a two-sample t-test. The researchers would like to be able to detect whether the natural product reduces blood pressure by at least $7$points more, on average than the placebo. If groups of size $50$are used in the experiment, a two-sample t-test using role="math" localid="1650436089340" $伪=0.01$will have a power of $80\%$to detect a $7$-point difference in mean blood pressure reduction. If the researchers want to be able to detect a $5$-point difference instead, then the power of test

(a) would be less than $80\%$.

(b) would be greater than $80\%$.

(c) would still be $80\%$.

(d) could be either less than or greater than $80\%$, depending on whether the natural product is effective.

(e) would vary depending on the standard deviation of the data.

R10.1. Which procedure? For each of the following settings, say which inference procedure from Chapter 8, 9, or 10 you would use. Be specific. For example, you might say, 鈥淭wo-sample z test for the difference between two proportions.鈥� You do not need to carry out any procedures.
(a) Do people smoke less when cigarettes cost more? A random sample of $500$smokers was selected. The number of cigarettes each person smoked per day was recorded over a one-month period before a $30\%$ cigarette tax was imposed and again for one month after the tax was imposed.
(b) How much greater is the percent of senior citizens who attend a play at least once per year than the percent of people in their twenties who do so?
Random samples of $100$senior citizens and $100$ people in their twenties were surveyed.
(c) You have data on rainwater collected at $16$ locations in the Adirondack Mountains of New York State. One measurement is the acidity of the
water, measured by pH on a scale of $0$to $14$(the pH of distilled water is $7.0$). Estimate the average acidity of rainwater in the Adirondacks.
(d) Consumers Union wants to see which of two brands of calculator is easier to use. They recruit $100$ volunteers and randomly assign them to two
equal-sized groups. The people in one group use Calculator A and those in the other group use Calculator B. Researchers record the time required for each volunteer to carry out the same series of routine calculations (such as figuring discounts and sales tax, totaling a bill) on the assigned calculator.

T10.11. Researchers wondered whether maintaining a patient's body temperature close to normal by heating the patient during surgery would affect wound infection rates. Patients were assigned at random to two groups: the normothermic group (patients' core temperatures were maintained at near normal, $36.5掳\mathrm{C}$, with heating blankets) and the hypothermic group (patients" core temperatures were allowed to decrease to about$34.5掳\mathrm{C}$). If keeping patients warm during surgery alters the chance of infection, patients in the two groups should have hospital stays of very different lengths. Here are summary statistics on hospital stay (in number of days) for the two groups:

$\begin{array}{lccc}\text{Group}& n& \stackrel{炉}{x}& s_x\\ \text{Normothemic}& 104& 12.1& 4.4\\ \text{Hypothermic}& 96& 14.7& 6.5\\ & & & \end{array}$

(a) Construct and interpret a $95\%$confidence interval for the difference in the true mean length of hospital stay for normothermic and hypothermic patients.

(b) Does your interval in part (a) suggest that keeping patients warm during surgery affects the average length of patients' hospital staves? Justify your answer.

A fast-food restaurant uses an automated filling machine to pour its soft drinks. The machine has different settings for small, medium, and large drink cups. According to the machine鈥檚 manufacturer, when the large setting is chosen, the amount of liquid dispensed by the machine follows a Normal distribution with mean $27$ounces and standard deviation $0.8$ounces. When the medium setting is chosen, the amount of liquid dispensed follows a Normal distribution with mean $17$ounces and standard deviation $0.5$ounces. To test the manufacturer鈥檚 claim, the restaurant manager measures the amount of liquid in a random sample of $25$cups filled with the medium setting and a separate random sample of $20$cups filled with the large setting. Let ${\overline{x}}_1-{\overline{x}}_2$be the difference in the sample mean amount of liquid under the two settings (large 鈥� medium). What is the shape of the sampling distribution of${\stackrel{炉}{x}}_1-{\stackrel{炉}{x}}_2$. Why?

Listening to rap Is rap music more popular among young blacks than among young whites? A sample survey compared $634$randomly chosen blacks aged $15$to $25$with $567$randomly selected whites in the same age group. It found that $368$of the blacks and $130$of the whites listened to rap music every day.$10$ Construct and interpret a $95$% con铿乨ence interval for the difference between the proportions of black and white young people who listen to rap every day.

A random sample of 100 of a certain popular car model last year found that 20 had a certain minor defect in the brakes. The car company made an adjustment in the production process to try to reduce the proportion of cars with the brake problem. A random sample of 350 of this year's model found that 50 had the minor brake defect.

(a) Was the company's adjustment successful? Carry out an appropriate test to support your answer.

(b) Describe a Type I error and a Type Il error in this setting, and give al possible consequence of each.

The correlation between the heights of fathers and the heights of their (grownup) sons is$r=0.52$ , both measured in inches. If fathers鈥� heights were measured in feet and sons鈥� heights were measured in furlongs (one furlong equals 7920 inches), the correlation between heights of fathers and heights of sons would be

(a) much smaller than 0.52.

(b) slightly smaller than 0.52.

(c) unchanged; equal to 0.52.

(d) slightly larger than 0.52.

(e) much larger than 0.52.