A student recorded information about a rock sample. The four statements are true, which one is an observation? (1) If placed in water, the rock will sink. (2) The rock is billions of years old. (3) The rock has a mass of 93.5 g. (4) The rock formed by natural events.

Police departments often try to control traffic speed by placing speed-measuring machines on roads that tell motorists how fast they are driving. Traffic safety experts must decide where machines should be placed. In one recent test, police recorded the average speed clocked by cars driving on one busy street close to an elementary school. For a sample of 25 speeds, it was determined that the average amount over the speed limit for the 25 clocked speeds was $11.6 \mathrm{mph}$ with a standard deviation of $8 \mathrm{mph}$. The $95 \%$ confidence interval estimation for this sample is $8.30 \mathrm{mph}$ to $14.90 \mathrm{mph}$.

a) What is the margin of error for this problem?

The branch manager of an outlet (Store 1) of a nationwide chain of pet supply stores wants to study characteristics of her customers. In particular, she decides to focus on two variables: the amount of money spent by customers and whether the customers own only one dog, only one cat, or more than one dog and/or cat. The results from a sample of 70 customers are as follows:

• Amount of money spent: $\bar{X}=\$ 21.34, S=\$ 9.22$.
• Thirty-seven customers own only a dog.
• Twenty-six customers own only a cat.
• Seven customers own more than one dog and/or cat. The branch manager of another outlet (Store 2 ) wishes to conduct a similar survey in his store. The manager does not have access to the information generated by the manager of Store 1. Answer the following questions: Based on your answers to (c) and (d), how large a sample should the manager take?

A sample of a compound of xenon and fluorine was confined in a bulb with a pressure of 18 torr. Hydrogen was added to the bulb until the pressure was 72 torr. Passage of an electric spark through the mixture produced Xe and HF. After the HF was removed by reaction with solid KOH, the final pressure of xenon and unreacted hydrogen in the bulb was 36 torr. What is the empirical formula of the xenon fluoride in the original sample? (Note: Xenon fluorides contain only one xenon atom per molecule.)

A Gallup poll surveyed a random sample of 439 American teenagers. One question that they were asked was, "How strict are your parents compared to most of your friends' parents?" The choices were "more strict,' "less strict,” and "about the same.” The choice "more strict" was selected by 171 of the respondents . What is the research question of interest? What is the population parameter of interest? What percentage of the sample responded with "more strict"? Draw a figure to illustrate this situation

In this exercise, identify the type of sample and explain why the sample is biased.

A news station asks its viewers to participate in an online poll about the presidential candidates.

Two identical tetrahedral dice are rolled. Their four vertices are clearly labelled 1, 2, 3, and 4. The result when one die comes to rest is the number on the uppermost vertex. Illustrate the sample space of 16 possible results when the two dice are rolled.

In one hour, a factory packaged 150 boxes of light bulbs. Estimate the total number of defective light bulbs packaged that hour based on a sample of 8 boxes containing the following numbers of defective bulbs: 5, 3, 5, 1, 2, 9, 4, 3.

A 30.0-mL sample of 0.165 M propanoic acid is titrated with 0.300 M KOH. Calculate the pH at each volume of added base: 0 mL, 5 mL, 10 mL, equivalence point, one-half equivalence point , 20 mL, 25 mL. Sketch the titration curve.

The half-life of palladium-100, ${ }^{100} \mathrm{Pd}$, is four days. (So half of any given quantity of ${ }^{100} \mathrm{Pd}$ will disintegrate in four days.) The initial mass of a sample is one gram.

Find the mass that remains after 16 days.

Two friends each choose a slice of pizza with one topping. The available toppings are tomatoes (T), jalapeños (J), onions (O), and eggplant (E). Write an organized list using the format (Friend 1, Friend 2) to represent the sample space of toppings chosen between the two friends.

In the United States, the probability of having twins (usually about 1 in 90 births) rises to about 1 in 10 for women who have been taking the fertility drug Clomid. Among a random sample of 10 pregnant women, what's the probability that

a) at least one will have twins if none were taking a fertility drug?

b) at least one will have twins if all were taking Clomid?

c) at least one will have twins if half were taking Clomid?

The 1990 census "long form" was sent to a random sample of 17% of the nation's households. One question asked the total 1989 income of the householder. (The householder is the person in whose name the dwelling unit is owned or rented.) Suppose that the households that returned the long form are an SRS of the population of all households in each district. In Middletown, a city of 40,000 persons, 2621 householders reported their income. The mean of the responses was $\bar{x}$=23,453, and the standard deviation was s=8721. The sample standard deviation for so large a sample will be very close to the population standard deviation $\sigma$. Use these facts to give an approximate 99% confidence interval for the 1989 mean income of Middletown householders.

In each exercise. a. find n. b. compute $\Sigma x_{i}$. c. determine the sample mean. Round your answer to one more decimal place than that used for the observations. From Wikipedia, we found that the ages of the justices of the U.S. Supreme Court, as of September 9, 2013, are as follows, in years.