There are 12,500 high school students in a large city school district. Administrators and teachers want to determine the extent to which parents do homework for their children. In an anonymous survey, 150 of the 500 students say that someone else has done their homework at least once. Of those 150 students, 90 or \(\dfrac{90}{150} = 0.6\) or 60% say that a parent has done their homework for them at least once.

In a random sample of 915 adults, 366 say they believe in ghosts.

Among all the banking firms in a large city, five are randomly selected. From each of these, 10 employees are randomly chosen.

A survey is to be conducted to determine the proportion of young adults who earn more than \$7.25 per hour (minimum wage). Two sampling methods are being considered. Method A involves standing on a downtown street corner and randomly picking several young adults to interview every 10 minutes during a 12-hour period. Method B involves posting the question on several popular young adult websites; the viewer simply has to click on one of two possible answers to participate.

A senator's approval rating stood at 65 percent before she took a crucial vote.

Below are all the scores of a school's AP Statistics students on a practice 40 question multiple-choice exam. 33 31 37 39 27 31 40 36 27 27 27 30 34 38 27 29 27 38 37 40 33 36 29 26 34 32 39 32 39 36 32 32 25 31 26 40 33 37 29 26 35 26 37 33 27 28 32 37 33 32

The goals scored per game during a 21-game span for each of two hockey teams is shown below.

In 2015, processed meat was classified as a carcinogen by the World Health Organization (WHO). In a representative sample of eight months, a student counts how many times a month he eats processed meat at school. In an independent representative sample of eight months, he counts how many times he eats processed meat at home. The data are shown in the following table. School: 4 5 5 3 6 4 5 7 Home: 4 3 4 4 3 2 5 4 Calculate a 90% confidence interval estimate for the difference between the mean number of times a month this student eats processed meat at school and at home.

In a random sample of eight students taking a college writing class, the weights in ounces of their term papers and their resulting grades are tabulated below. Assume all conditions for inference are satisfied. Weight (oz): 12.1 11.1 11.1 6.5 4.7 10.7 5.9 14.4 Grade: 78 79 76 65 67 79 77 94

Data on the number of ice cream cones sold on a weekday night and outside temperature for a simple random sample (SRS) of 10 summer days are gathered. A scatterplot and regression output follow.

A dispatcher for a trucking firm believes the greater the number of hours slept before a trucker begins a long haul, the higher the trucker will score on an alertness test required at the halfway distance. The dispatcher looks up the records of a random sample of 18 long-haul truckers and has them fill out a questionnaire about hours of sleep. Some computer graphical output is shown below.

A random sample of adults with various THC levels (a urine test for cannabis) were given a concentration test consisting of a series of small objects, each of which could be fit into an appropriate shaped hole. Each person had five minutes to find the proper holes for as many objects as possible. Computer regression output of number of objects successfully placed plotted against urine THC level (100 ng/mL) is as follows.

A D1 university recruiter claims that 10 percent of its baseball players go on to play professionally after graduation. A reporter contacts a simple random sample (SRS) of baseball players who graduated during the past 20 years and finds that only 32 out of 450 went on to play professionally. Is there sufficient evidence to write an article disputing the university's claim? Give statistical justification for your conclusion.

In past years, 3 percent of all job applicants lied about their education. The HR division of a major company believes the true figure is now higher and plans to investigate a simple random sample (SRS) of applicants to test the hypothesis.

It is difficult to distinguish between marshmallows and mushrooms by taste alone if one is not allowed to see or smell. A person claims he can distinguish between these, and the following test is designed. He will be given a sample of each in random order to taste while blindfolded with his nose pinched. This will be repeated 16 times. Let \(p\) be the proportion of times the person answers correctly.

A company advertises it has a process that can extract a mean of 35 grams of dissolved salts from 1 liter of seawater. A geologist believes the true figure is lower. Using this process, a sample of fifteen 1-liter containers of seawater from 15 random locations yields a mean of 34.82 grams of dissolved salts with a standard deviation of 0.65 grams. Assume the sample distribution is symmetric and unimodal with no outliers.

The cash register totals are noted at a random sampling of 100 sales at each of 2 competing hardware stores.

Store	$5	$10	$25	$50	Mean	SD
A	10	35	48	7	$19.50	$11.56
B	40	30	15	15	$16.25	$15.72

To test whether the company's secretaries type letters quicker from listening to someone speak live or from recorded dictation, an office manager randomly selects five secretaries. He instructs them to time themselves (in seconds) typing a long letter while someone reads the letter to them and then time themselves again typing the same letter from a recording of someone reading the letter. The results are summarized in the following table.

Secretary	1	2	3	4	5
Live Dictation Time (in seconds)	241	247	217	255	255
Recorded Dictation Time (in seconds)	239	248	217	257	259

Each of 300 students was randomly (coin toss) placed into either Professor A's or Professor B's section of a required college writing course. At the end of the semester, students gave a score from 1 to 5 with "poor" = 1 and "great" = 5 for their professor. The results are shown in the following table.

Score	1	2	3	4	5
Professor A Frequency	16	41	53	38	13
Professor B Frequency	45	50	29	11	4

A handyman wishes to test which radial arm saw can cut through lumber more quickly. He picks out a random sampling of five pieces of lumber of various species and thicknesses. The cutting times (in seconds) are summarized in the following table.

Board	A	B	C	D	E
Saw S	3.1	6.8	1.5	4.2	2.8
Saw T	3.3	6.7	1.8	4.5	3.0

At schools using an innovative math program, a simple random sample (SRS) of 100 students results in an average score of 178 with a standard deviation of 27 on a state test. At schools using a traditional approach, an SRS of 150 students results in an average score of 171 with a standard deviation of 31 on the same state test.

An athletic trainer wishes to determine if a newly designed gym shoe enhances athletic performance. Ten professional high jumpers competitively jump on two successive days. For each jumper, a coin toss determines whether he uses his old gym shoes or the new pair on the first day. Each jumper then switches shoes on the next day. Their jump heights (feet) are as follows.

In a baseball game, the slugging average is the mean number of bases per hit. It can be calculated using the following formula. \(\text{Slugging average} = \dfrac{(\text{Singles}) + (\text{Doubles} \times 2) + (\text{Triples} \times 3) + (\text{Home runs} \times 4)}{\text{Total at bats}}\) In a random sampling of 75 hits from each of two major league teams, the distributions of singles (1B), doubles (2B), triples (3B), and homers (HR) are shown in the following table.

	1B	2B	3B	HR
Team A	44	17	10	4
Team B	34	22	12	7

Is there evidence that the two teams have a different slugging average? Give statistical justification for your answer.

Can a particular video game improve a batter's reaction time? Batters' reaction times (fraction of a second between the ball leaving a pitcher's hand and the start of a swing) are measured before and after playing the video game for 25 hours.

A study is performed on 20 different models of luxury SUVs to see if a new gas additive is effective in reducing carbon dioxide (\(\text{CO}_2\)) emissions. Data on \(\text{CO}_2\) emissions (pounds per gallon of gas) are collected before and after input of the additive. A partial computer output follows.

	N	Mean	StDev	SE Mean
Before	20	20.60	7.35	1.64
After	20	20.05	6.84	1.53
Difference	20	0.55	1.90	0.42

A World Health Organization (WHO) report gives average life expectancies for 10 randomly chosen countries in each of two regions of the world: Region 1: 63, 72, 48, 67, 68, 70, 59, 51, 63, 52 Region 2: 78, 73, 57, 69, 74, 86, 70, 66, 91, 77

A random sample of five men were measured for waist sizes (in inches) and percent body fat, giving the following data.

Waist (inches)	32	35	36	39	44
Body Fat (%)	12	23	24	30	40

Doctors are planning a clinical trial of a new "molecularly targeted therapy" for the treatment of leukemia. A random sample of children with leukemia will be treated. After a suitable time period, their disease remission rate will be compared with children being treated with standard chemotherapy for leukemia.

Executives at a company that manufactures a cooler are thinking of moving to the manufacture of a better cooler but only if a test shows that the new cooler will keep drinks cold for over 24 hours. The company's research department proposes a study with \(H_0: \mu = 24\) and \(H_a: \mu > 24\).

In each of the following examples, explain why it is or is not proper to run a chi-square goodness-of-fit test.

In a survey of all 880 students at a college, the number of times during the academic semester in which a student pulled an all-nighter is tabulated and shown in the following table. All-Nighters Pulled 0 1 2 3 4 5 Number of Students 280 210 175 150 50 15

A random survey of 250 high school teachers classified job satisfaction versus subject taught with the following results. Happiness Level

Subject Taught	Unhappy	Mildly Happy	Very Happy
Math	10	25	30
English	20	55	45
History	20	25	20

Random samples of high school students in 2014, 2016, and 2018 were anonymously surveyed about whether or not they had ever cheated on a quiz or test. The resulting counts are as shown in the table.

2014	2016	2018
Admitted to Cheating	78	67	51
Claimed to Never Having Cheated	44	40	59

What does a chi-square test of homogeneity indicate?

During the past year, the proportions of teens eating at Starbucks, Chick-fil-A, and Chipotle have been 0.3, 0.5, and 0.2, respectively. A random survey of 250 teens this past month indicates 71, 136, and 43 visits to Starbucks, Chick-fil-A, and Chipotle, respectively.

A social studies teacher believes that high school students taking social studies classes are more likely than students taking other classes to read newspapers. She randomly picks 40 of her social studies students and 50 students from her other classes, questions them, and gathers the following data.

Read Newspapers	Don't Read Newspapers
Her Social Studies	37	13
Students
Her Other Students	15	35

A random sample of 500 medical records of people who recently had major heart attacks is analyzed for numbers of died versus survived and for education level of the subjects. Some computer output is as follows. Observed (and Expected) Counts

No High School Degree	High School Degree	College Degree
Died	18 (9.9)	38 (42.1)	24 (28)
Survived	44 (52.1)	225 (220.9)	151 (147)

A random sampling of a professor's grades (A or B, C or D, F) in both intro and advanced courses yields the following data.

A, B	C, D	F
Intro	35	55	10
Advanced	22	15	3

500 patients took part in a clinical study using T-cell therapy to treat a particular lymphatic cancer. The following data show the number of these patients who survived for each given number of years.

Survival Years	0	1	2	3	4 or more
Observed Number of Patients	69	106	153	98	74

It is hypothesized that the distribution follows the Poisson distribution: \(P(x) = \dfrac{2^x e^{-2}}{x!}\) where \(e = 2.71828\) and \(x\) is the number of survival years.

In an educational study, there is interest in whether or not there is more variability in the mean verbal scores of 8-year-olds or of 3-year-olds. Summary statistics are given below.

Sample Size	Mean	StDev
Age 8	60	93.5	5.4
Age 3	60	78.6	2.7

To test \(H_0: \sigma_8 = \sigma_3\) versus \(H_a: \sigma_8 > \sigma_3\), the researchers will use the ratio of the sample standard deviations, \(\dfrac{s_8}{s_3}\), as a test statistic.