AP Statistics Study Guide
Given 50 at bats and a probability of getting a hit of any kind using a batting average of .190, what is the probability that the baseball player will get exactly 10 hits.
.138
A radio station has a contest in which contestants roll a regular 6-sided die. If he rolls a 1 or a 2, he wins $50. If he rolls a 3 or a 4, he wins $100. If he rolls a 5, he wins $1000. If he rolls a 6, he doesn't win anything.What is the probability that out of the first 5 contestants, at most 3 of them win some money?
.196
A survey of local car dealers revealed that 64% of all cars sold last month had CD players, 28% had alarm systems, and 22% had both CD players and alarm systems.What is the probability one of these cars selected at random had neither a CD player nor an alarm system?
.3
A radio station has a contest in which contestants roll a regular 6-sided die. If he rolls a 1 or a 2, he wins $50. If he rolls a 3 or a 4, he wins $100. If he rolls a 5, he wins $1000. If he rolls a 6, he doesn't win anything.What is the probability that out of the first 5 contestants exactly 3 win at least $100?
.3125
A sporting goods store announces a "Wheel of Savings" sale. Customers select the merchandise they want to purchase, then at the cash register they spin a wheel to determine the size of the discount they will receive. The wheel is divided into 12 regions, like a clock. Six of those regions are red, and award a 10% discount. The three white regions award a 20% discount and two blue regions a 40% discount. The remaining region is gold, and a customer whose lucky spin lands there gets a 100% discount - the merchandise is free!What is the probability that none of the first four customers gets a discount over 20%?
.316
A radio station has a contest in which contestants roll a regular 6-sided die. If he rolls a 1 or a 2, he wins $50. If he rolls a 3 or a 4, he wins $100. If he rolls a 5, he wins $1000. If he rolls a 6, he doesn't win anything. What is the probability that out of the first 5 contestants exactly 2 win $100?
.33
A radio station has a contest in which contestants roll a regular 6-sided die. If he rolls a 1 or a 2, he wins $50. If he rolls a 3 or a 4, he wins $100. If he rolls a 5, he wins $1000. If he rolls a 6, he doesn't win anything.What is the probability that a contestant will win $50?
.33
Ch14_14b4The American Red Cross says that about 45% of the U.S. population has Type O blood, 40% Type A, 11% Type B, and the rest Type AB.Among four potential donors, what is the probability that at least one person is Type B?
.37
A researcher found that day care providers are more likely to get the flu than people who are not typically around children with a p-value of .004. Briefly explain what this p-value means by filling in the blank in the statement below. If the null hypothesis is true and if you perform the study a large number of times and in exactly the same manner, drawing random samples from the population on each occasion, then, on what percent of occasions, you would get the same or greater difference between groups than what you obtained on this one occasion?
.4%
A sporting goods store announces a "Wheel of Savings" sale. Customers select the merchandise they want to purchase, then at the cash register they spin a wheel to determine the size of the discount they will receive. The wheel is divided into 12 regions, like a clock. Six of those regions are red, and award a 10% discount. The three white regions award a 20% discount and two blue regions a 40% discount. The remaining region is gold, and a customer whose lucky spin lands there gets a 100% discount - the merchandise is free!What is the probability that there is at least one gold winner among the first six customers?
.407
A survey of local car dealers revealed that 64% of all cars sold last month had CD players, 28% had alarm systems, and 22% had both CD players and alarm systems.What is the probability that a car had a CD player unprotected by an alarm system?
.42
If P(A) = 0.2 and P(B) = 0.3, find P(A or B) if it is known that events A and B are not disjoint.
.44
If P(A) = 0.2 and P(B) = 0.3, find P(A or B) if it is known that events A and B are disjoint.
.5
Your company is contracted by a car dealership to do a statistical study. The dealership is interested in testing to see if its percentage of satisfied customers is higher than the industry standard of 67%. The dealership informs your staff that it can only afford a study that surveys a random sample of 100 of their customers.Your staff completes the survey of 100 customers and the results state that 70% of its customers are highly satisfied. What is the value of your test statistic? (Standardize phat using this sample and the original info given)
.638
An inspection procedure at a manufacturing plant involves picking thirty items at random and then accepting the whole lot if at least twenty-five of the thirty items are in perfect condition. If in reality 85% of the whole lot are perfect, what is the probability that the lot will be accepted?
.711
A survey of local car dealers revealed that 64% of all cars sold last month had CD players, 28% had alarm systems, and 22% had both CD players and alarm systems. What is the probability a car with an alarm system had a CD player?
.786
The average outstanding bill for delinquent customer accounts for a national department store chain is $187.50 with a standard deviation of $54.50. In a simple random sample of 50 delinquent accounts, what is the probability that the mean outstanding bill is over $200?
0.0524
Suppose that 35% of all business executives are willing to switch companies if offered a higher salary. If a headhunter randomly contacts an SRS of 100 executives, what is the probability that over 40% will be willing to switch companies if offered a higher salary? Select the closest answer.
0.1472
Buffalo Battery Company has developed a new laptop computer battery. On average, the battery lasts 240 minutes on a single charge. The standard deviation is 16 minutes. Suppose the company randomly samples production during each day at a specified time and selects 8 laptop batteries for testing. The standard deviation of the battery life for the selected batteries is 20 minutes. What is the chi-square statistic represented by this test?Χ2 = [ ( n - 1 ) * s2 ] / σ2
10.938
Family size can be represented by the random variable X. Determine the average family size. X 2 3 4 5 P(X) .17 .47 .26 .10
3.29
EPA is examining the relationship between ozone level (in parts per million) and the population (in millions) of U.S. Cities.Dependent variable: OzoneR-squared = 84.4% s = 5.454 with 16 - 2 = 14 dfVariable Coefficient SE(Coeff)Constant 18.892 2.395Population 6.650 1.910Given that the test statistic is found as t = (b1 - 0) / SE(b1) find the value of the test statistic using the computer printout.
3.4817
Assume that a school district has 10,000 sixth graders. In this district, the average weight of a sixth grader is 80 pounds, with a standard deviation of 20 pounds. Suppose you draw a random sample of 50 students. What is the probability that the average weight of a sampled student will be less than 75 pounds? Give an approximate answer.
3.9%
Determine the probability distribution's missing value. The probability that a tutor sees 0, 1, 2, 3,or 4 students on a given day. x 0 1 2 3 4 P(x) 5/19 6/19 4/19 _____ 1/19
3/19
Assume normal distribution.The mean score on a college placement exam is 500 with a standard deviation of 100. Ninety five percent of the test takers score above what?
336
A reporter believed that police officers were required to write a specific quota of traffic tickets during a month. In order to meet the alleged quota, he believed officers would need to write more tickets during the last week of the month. To investigate the CLAIM, the reporter collected the number of tickets written by the local police force in a month and organized them by weeks as show in the table below. Week # 1st 2nd 3rd 4th Total # tickets 133 112 154 165 564 Expected # tickets 141 141 141 141 564 What is the chi-square component for week 4?
4.0851
After once again losing a football game to the college's arch rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach.The 95% confidence interval for p is _________
0.64 ± 0.094.
An electronic product takes an average of 3.4 hours to move through an assembly line. If the standard deviation is 0.5 hour, what is the probability that an item will take between 3 and 4 hours? Assume normal distribution.
0.6730
If P(X) = 0.23 and P(X and Y) = 0.12 and P(X or Y) = .34, find the complement of P(Y).
0.77
The scores of individual students on the American College Testing (ACT) Program composite college entrance examination have a normal distribution with mean 18.6 and standard deviation 6.0. At Peppermill High School, 36 seniors take the test. If the scores at this school have the same distribution as national scores, what is the standard deviation of the sampling distribution of the average (sample mean) score for the 36 students?
1.0
The city council has 6 men and 3 women. If we randomly choose two of them to co-chair a committee, what is the probability these chairpersons are the same gender? Select the correct fractional response. HINT: Consider there is NO REPLACEMENT of an individual who is already selected.
1/2
The distribution of actual weights of 8-ounce chocolate bars produced by a certain machine is normal with mean 8.1 ounces and standard deviation 0.1 ounces. If a sample of five of these chocolate bars is selected, there is only a 5% chance that the average weight of the sample of five of the chocolate bars will be below _______.(Use the formula backwards to solve for X...do NOT round until the very last step.) Select the closest answer.
7.95 ounces.
Forty-five percent of the WA upper school student body are male. 80% of the females love math, while only 60% of the males love math. What percentage of the TOTAL student body love math? (Stated another way...what is the probability that a randomly selected student will love math?)
71%
Suppose you administer a certain aptitude test to a random sample of 9 students in your school and that the average score is 105. We want to try to determine the mean of the population of all students in the school. Assume a population standard deviation of 15 for the test. What is the z* for a 98% confidence interval?
Around 2.3
Suppose you administer a certain aptitude test to a random sample of 9 students in your school and that the average score is 105. We want to try to determine the mean of the population of all students in the school. Assume a population standard deviation of 15 for the test. What sample size would be needed to have a margin of error of 4 points? Assume we are using a 98% CI with standard deviation of 15.
Around 76 or 77
A recent survey concluded that the proportion of American teenagers who have a cell phone is 0.27. The true population proportion of American teenagers who have a cell phone is 0.29. For samples of size 1,000 that are selected at random from this population, what are the mean and standard deviation, respectively, for the sampling distribution of the sample proportion of American teenagers who have a cell phone.
D 0.29, sqrt (0.29*0.71/1000)
A state's Department of Education reports that 12% of the high school students in that state attend private high schools. The State University wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools.They actually select a random sample of 450 applications, and find that 46 of those students attend private schools. Create a 90% confidence interval.Should the admissions officers conclude that the percentage of private school students in their applicant pool is lower than the statewide enrollment rate of 12%?
No
Suppose the probability of a particular baseball player hitting a homerun is 0.19, based on the player's prior history. Assume the probability of the player hitting a homerun is the same for each at bat and assume that the player has 50 at bats during the season.Suppose we are interested in how many Homeruns this batter gets in a game. Is this situation binomial or geometric?
binomial
A company supplying candy to school vending machines needs to know about candy preferences of middle school and high school age students. A random sample of 400 students was taken. The company wants to know if there is any relationship between the candy choices and the age of students.After performing a chi-square test of independence, the chi-square test statistic = 24.68. The appropriate critical value for df and desired alpha level = 11.34.Is there sufficient evidence to reject the null hypothesis?
YES. We reject the null hypothesis. They are NOT independent.
Suppose the probability of a particular baseball player hitting a homerun is 0.19, based on the player's prior history. Assume the probability of the player hitting a homerun is the same for each at bat and assume that the player has 50 at bats during the season.Suppose we are interested in the number of at bats before the player gets a Homerun. Is this situation binomial or geometric?
geometric
Which two events are most likely to be independent?
having a driver's license, and having blue eyes
An investigator indicates that the power of his test (at a significance of 1%) of a sample mean resulting from his research is 0.87. If n increases, then the power of the test...
increases.
Given the random variable described as A with mean = 80 and standard deviation = 12 , find the mean and standard deviation of the random variable 3X.
mean 3X = 240standard deviation 3X = 36
A consumer organization inspecting new cars found that many had appearance defects (dents, scratches, paint chips, etc.). While none had more than three of these defects, 7% had three, 11% had two, and 21% had one defect. Find the expected number of appearance defects in a new car, and the standard deviation.
mean = .64standard deviation = .93
I select a simple random sample of 4000 batteries produced in a manufacturing plant. I test each and record how long it takes for each battery to fail. I then compute the average of all the failure times. The sampling distribution of this event might be modeled as ....
normal distribution.
The parameter of interest, choice of test, and hypotheses all depend on only the population information. A local newspaper published a report that on the last state math tests, the average performance for a random sample of 15 urban districts was a score of 64. You believe that the performance in these districts was higher. What is the choice of test?
one sample right tail t test for mean
A random variable X has mean mX and standard deviation sX. Suppose n independent observations of X are taken and the average of these n observations is computed. We can assert that if n is very large, the sampling distribution of is approximately normal. This assertion follows from......
the central limit theorem.
Find the expected value of this discrete probability model for random variable X. X 10 20 30P(X) .3 .5 .2
19
Knowing from previous stats that a baseball player has a 19% probability of getting a hit, what is the probability that the first hit will occur on the 4th at bat?
.101
The confidence interval created for the slope resulting from a linear regression analysis is (.079, .173).What is the slope of the LSRL?
.126
An investigator indicates that the POWER of his test (at a significance of 1%) of a sample mean resulting from his research is 0.87. What is the probability that he made a Type II error?
.13
A radio station has a contest in which contestants roll a regular 6-sided die. If he rolls a 1 or a 2, he wins $50. If he rolls a 3 or a 4, he wins $100. If he rolls a 5, he wins $1000. If he rolls a 6, he doesn't win anything.What is the probability that the first one to win $1000 is the 5th contestant?
.08
A state's Department of Education reports that 12% of the high school students in that state attend private high schools. The State University wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools.They actually select a random sample of 450 applications, and find that 46 of those students attend private schools. Create the 90% confidence interval.
(.078, .126)
In a random sample of 300 elderly men, 65% were married, while in a similar sample of 400 elderly women, 48% were married. Determine a 99% confidence interval estimate for the DIFFERENCE between the percentages of elderly men and women who were married.
(.075, .265)
A random sample of 100 traffic tickets given to motorists in a large city is examined. The tickets were classified according to the race of the driver. The results are summarized in the following table. White Black Hispanic Other Number of tickets 46 37 11 6 The proportion of the population of the city in each of the race categories above is the following. White Black Hispanic Other Proportion 0.65 0.30 0.03 0.02 We wish to test whether the racial distribution of traffic tickets in the city is the same as the racial distribution of the population of the city. To do so we use the X2 statistic.The component of this X2 statistic corresponding to the Hispanic category is ______________.
(O - E)2/E = 21.33.
Ch14_20cTo 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 EVERY day?
.00008
EPA is examining the relationship between ozone level (in parts per million) and the population (in millions) of U.S. Cities.Dependent variable: OzoneR-squared = 84.4% s = 5.454 with 16 - 2 = 14 dfVariable Coefficient SE(Coeff)Constant 18.892 2.395Population 6.650 1.910Given that the test statistic is 3.4817, determine the P-value to test the null hypothesis that slope = 0. Decide if the value is STATISTICALLY SIGNIFICANT.
.001833...statistically significant
The confidence interval created for the slope resutling from a linear regresssion is (.079, .173).What is the margin of error associated with this estimate of slope?
.047
The average cost per ounce for glass cleaner is 7.7 cents with a standard deviation of 2.5 cents. What is the z-score of Windex with a cost of 10.1 cents per ounce?
0.96
We have calculated a confidence interval based on a sample of n = 180. Now we want to get a better estimate with a margin of error only one third as large. We need a new sample with n at least ...
1620
Chattahoochee Battery Company has developed a new laptop computer battery. On average, the battery lasts 240 minutes on a single charge. The standard deviation is 16 minutes. Suppose the company randomly samples production during each day at a specified time and selects 12 laptop batteries for testing. The standard deviation of the battery life for the selected batteries is 20 minutes. What is the chi-square statistic represented by this test?Χ2 = [ ( n - 1 ) * s2 ] / σ2
17.188
A state's Department of Education reports that 12% of the high school students in that state attend private high schools. The State University wonders if the percentage is the same in their applicant pool. Admissions officers plan to check a random sample of the over 10,000 applications on file to estimate the percentage of students applying for admission who attend private schools.The admission officers want to estimate the true percentage of private school applicants to within +/- 4% moe, with 90% confidence. How many applications should they sample?
179
A Chi-square distribution has 11 degrees of freedom. Find the χ2 value corresponding to a right-hand tail area of .025
21.920
A Chi-square distribution has 11 degrees of freedom. Find the χ2 value corresponding to a right-hand tail area of .01.
24.725
The independent random variables X and Y are defined by the following probability distribution tables. X 1 3 6 Y 2 3 5 7 P(X) .6 .3 .1 P(Y) .1 .2 .3 .4 Determine the standard deviation of 3Y + 5.
5.44
A reporter believed that police officers were required to write a specific quota of traffic tickets during a month. In order to meet the alleged quota, he believed officers would need to write more tickets during the last week of the month. To investigate the CLAIM, the reporter collected the number of tickets written by the local police force in a month and organized them by weeks as show in the table below. Week # 1st 2nd 3rd 4th Total # tickets 133 112 154 165 564 Expected # tickets 141 141 141 141 564 What is the chi-square component for week 2?
5.965
The weights of cockroaches living in a typical college dormitory are approximately normally distributed with a mean of 80 grams and a standard deviation of 4 grams. The percentage of cockroaches weighing between 77 grams and 83 grams is about:
55%
The independent random variables X and Y are defined by the following probability distribution tables. X 1 3 6 Y 2 3 5 7 P(X) .6 .3 .1 P(Y) .1 .2 .3 .4 Determine the mean of X+Y.
7.2
A survey of some AP Stats students recorded gender and whether the student was left or right-handed. Results were summarized in a table like the one shown. If it turned out that handedness was independent of gender, how may of the AP Stats students were lefty girls? LeftyRightyTotalBoy??66Girl??54Total20100120
9
The test grades at a large school have an approximately normal distribution with a mean of 50. What is the standard deviation of the data so that 80% of the students are within 12 points (above or below) the mean?Draw a sketch to help reason the procedure and be clever.
9.375
Surveys indicate that 5% of the students who took the SATs had enrolled in an SAT prep course. 30% of the SAT prep students were admitted to their first choice college, as were 20% of the other students. You overhear a classmate say he got into the college he wanted. What is the probability he didn't take an SAT prep course?
93%
Daniel believes that in a given confidence interval the researchers should change the confidence level from 98% to 99% so that they can get a more narrow margin with which to "pin down" the true population mean. Do you agree or disagree with Daniel?
Disagree. A higher confidence level produces wider interval not narrower.
In general, how does doubling the sample size change the confidence interval size?
Divides the interval size by the square root of 2.
Tests for adverse reactions to a new drug yielded the results given in the table. Drug Placebo headaches 11 7No headaches 73 91The data will be analyzed to determine if there is sufficient evidence to conclude that an association exists between the treatment (drug or placebo) and the reaction (whether or not headaches were experienced. The results of the test are Χ2 = 1.798 P-value = .1799.Identify the correct conclusion.
Do not reject the null hypothesis. Report that there insufficient evidence to conclude that treatment and reaction are dependent.
TRUE-FALSEThe area under the normal curve is always equal to 1 no matter what the mean and standard deviation are.
True
Suppose you administer a certain aptitude test to a random sample of 9 students in your school and that the average score is 105. We want to try to determine the mean of the population of all students in the school. Assume a population standard deviation of 15 for the test and assume a 98% confidence interval for the mean score for the whole school.Think about what this confidence interval would mean to you.Jasmine says that the confidence interval shows that 98% of all students in this school would score a 105. Is her statement true or false?
False
TRUE-FALSENormal curves with different means always have different standard deviations.
False
The mean value of land per acre from a large sample of farms is $1200 with a standard deviation of $350. We can expect 95% of the data to lie between $850 and $1900.
False
The parameter of interest, choice of test, and hypotheses all depend on only the population information. A local newspaper published a report that on the last state math tests, the average performance for a random sample of 15 urban districts was a score of 64. You believe that the performance in these districts was higher. Name the Hypotheses. Check all that apply
H0: mu = 64 average score was 64 HA: mu > 64 average score was greater than 64
The parameter of interest, choice of test, and hypotheses all depend on only the population information. A large county school district proudly announced that data from a sample of 100 of their high school seniors showed that 70% of the girls were going on to post secondary education after graduation. You want to test this claim.Name the Hypotheses. (check all that apply)
H0: p = .7 proportion of girls going on to post secondary eduation is 70% AND HA: p not = .7 proportion of girls going on to post secondary education is not 70%
A company supplying candy to school vending machines needs to know about candy preferences of middle school and high school age students. A random sample of 400 students was taken. The company wants to know if there is any relationship between the candy choices and the age of students.Write the appropriate set of hypotheses for this situation.
H0: there is not a relationship between the candy choices and age of students Ha: there is a relationship between the candy choices and age of students
TRUE-FALSEThe area under the standard normal curve between 0 and 2 is half the area between -2 and 2.
True
Your company is contracted by a car dealership to do a statistical study. The dealership is interested in testing to see if its percentage of satisfied customers is higher than the industry standard of 67%. Give the appropriate hypotheses for a test of this information.
HO: p = .67, Ha: p > .67
The typical alternate hypothesis for significance testing of slope obtained from a linear regression analysis is ______________________.
Ha: B ≠ 0 the variables are NOT independent
A reporter believed that police officers were required to write a specific quota of traffic tickets during a month. In order to meet the alleged quota, he believed officers would need to write more tickets during the last week of the month. To investigate the CLAIM, the reporter collected the number of tickets written by the local police force in a month and organized them by weeks as show in the table below.State the alternate hypotheses. Week # 1st 2nd 3rd 4th Total # tickets 133 112 154 165 564 Expected # tickets 141 141 141 141 564
Ha: the # tickets written and the week of the month are not independent
A reporter believed that police officers were required to write a specific quota of traffic tickets during a month. In order to meet the alleged quota, he believed officers would need to write more tickets during the last week of the month. To investigate the CLAIM, the reporter collected the number of tickets written by the local police force in a month and organized them by weeks as show in the table below.State the null hypotheses. Week # 1st 2nd 3rd 4th Total # tickets 133 112 154 165 564 Expected # tickets 141 141 141 141 564
Ho: the # tickets written and the week of the month are independent
Which is true about a 99% confidence interval based on a given sample? READ CAREFULLYI. The interval contains 99% of the population.II. Results from 99% of all samples will lie in this interval.III. The interval is wider than a 95% confidence interval would be.
II and III only
Which of the following will reduce the width of a confidence interval?I. Increasing the confidence level.II. Increasing the sample size.III. Decreasing the standard deviation. BE CAREFUL!
II and III only
A certain population is strongly skewed to the left. We want to estimate its mean, so we will collect a sample. Which should be true if we use a large sample rather than a small one?I. The distribution of our sample data will be closer to normal.II. The sampling model of the sample means will be closer to normal.III. The variability of the sample means will be greater.
II only
If the p-value of a test of significance is greater than the level of significance, then use the words "statistically significant" to form a generic conclusion regarding the null hypothesis.
If the p-value of a test of significance is greater than the level of significance then it is NOT statistically significant and we FAIL TO REJECT the null hypothesis
Which has the larger mean and which has the larger standard deviation? Pic: tall and thin peak on left (A), wide and low peak on right (B)
Larger mean, b; larger standard deviation, b
Suppose the average height of a policeman is 71 inches with a standard deviation of 4 inches, while the average for a policewoman is 66 inches with a standard deviation of 3 inches. If a committee looks at all ways of pairing up one male with one female officer, what will be the mean and standard deviation for the difference in heights for the set of possible partners? You will actually be combining random variables...so be careful when determining the standard deviation.
Mean of 5 inches with a standard deviation of 5 inches.
We are about to test a hypothesis using data from a well-designed study. Which is true?I. A large P-value would be strong evidence against the null hypothesis.II. We can set a higher standard of proof by choosing a= 10% instead of 5%.III. If we reduce the risk of committing a Type I error, then the risk of a Type II error will also decrease.
None
Suppose you administer a certain aptitude test to a random sample of 9 students in your school and that the average score is 105. We want to try to determine the mean of the population of all students in the school. Assume a population standard deviation of 15 for the test and assume a 98% confidence interval for the mean score for the whole school.
On the basis of sample, I am 98% confident that the mean score of the school population on the aptitude test will be between 93 and 117.
In the first eight games of this season, LeRoy, a starting player for a major college basketball team, made 25 free throws in 40 attempts. You want to investigate how successful his team should expect him to be at the free throw line this season.Identify the parameter of interest.
The parameter of interest is the proportion of all free throws made out of all attempts.
Which of the following is not true concerning discrete probability distribution?
The standard deviation of the distribution is between -1 and 1.
In the first eight games of this season, LeRoy, a starting player for a major college basketball team, made 25 free throws in 40 attempts. You want to investigate how successful his team should expect him to be at the free throw line this season.Construct a 90% confidence interval for the proportion of free throws LeRoy will make this season.Interpret this confidence interval for Leroy's coaches and teammates.
The team should expect with 90% confidence that Leroy will make between approx 50% and 75% of his free throw shots.
Which of the following is TRUE of chi-square distributions?
They take on only positive values.
A candidate thinks she has a good chance of gaining the votes of anyone who is a Republican or in favor of the death penalty. The portion of the voters that think she has a good chance of gaining the votes is .66 or 66% from .30 (Republicans) and .36 (non-Republicans who favor the death penalty)
True
What is the definition of a Type I error?
Type I error occurs when we reject a null hypothesis that is actually true.
What is the definition of a Type II error?
Type II error occurs when we fail to reject a null hypothesis that is actually false.
From time to time police set up roadblocks to check cars to see if the safety inspection is up to date. At one such roadblock they issued tickets for expired inspection stickers to 22 of 628 cars they stopped.Based on the results at this roadblock, construct and INTERPRET a 95% confidence interval for the proportion of autos in that region whose safety inspections have expired.
We are 95% confident that the true population proportion of autos with expired safety inspections is between approximately 2% and 5%
Suppose that a device advertised to increase a car's gas mileage really does not work. We test it on a small fleet of cars (with Ho: not effective), and our data results in a P-value of 0.004. What probably happens as a result of our experiment?READ CAREFULLY!
We reject Ho, making a Type I error.
We will test the hypothesis that p = 60% versus p > 60%. We don't know it, but actually p is 70%. With which sample size and significance level will our test have the greatest power?
a= 0.05, n = 500
After once again losing a football game to the college's arch rival, the alumni association conducted a survey to see if alumni were in favor of firing the coach. An SRS of 100 alumni from the population of all living alumni was taken. Sixty-four of the alumni in the sample were in favor of firing the coach. Let p represent the proportion of all living alumni who favor firing the coach.Suppose you wish to see if the majority of alumni are in favor of firing the coach.To do this you test the hypothesesH0: p = 0.50, Ha: p > 0.50What is the P-value of this test?
approximately .0025
Tests for adverse reactions to a new drug yielded the results given in the table. The data will be analyzed to determine if there is sufficient evidence to conclude that an association exists between the treatment (drug or placebo) and the reaction (whether or not headaches were experienced.Drug Placeboheadaches 11 7No headaches 73 91 Which chi-square test would be appropriate for this situation?
chi-square for independence
A reporter believed that police officers were required to write a specific quota of traffic tickets during a month. In order to meet the alleged quota, he believed officers would need to write more tickets during the last week of the month. To investigate the CLAIM, the reporter collected the number of tickets written by the local police force in a month and organized them by weeks as show in the table below. Week # 1st 2nd 3rd 4th Total # tickets 133 112 154 165 564 Expected # tickets 141 141 141 141 564 How many degrees of freedom should be used for this chi-square test of independence?
df = 3
A survey conducted by Black Flag (an insect repellant manufacturer) asked whether the action of a certain type of roach disk would be effective in killing roaches. Seventy-nine percent of the respondents agreed that the roach disk would be effective. The number 79% is a
statistic
Inference for regresssion on the population regression slope is based on which of the following distributions?
t-distribution (n - 2 degrees of freedom)
In a hypothesis test, the decision between a one sided test and a two sided alternative hypothesis is based on:
the alternative hypothesis appropriate for the context of the problem.
Suppose the Normal model describes the length of the fish in a neighborhood pond. One particular fish has a z-score of 3.1. This means that ...
the length of the fish was 3.1 standard deviations longer than the average fish in the pond.
The P-value of a test of significance is the probability that:
the observed statistic value could occur if the null hypothesis were correct
The variability of a statistic is described by...
the spread of its sampling distribution.
The choice between a z-test and a t-test for a population mean depends primarily on:
whether the given standard deviation is from the population or the sample.
Police report traffic accidents they investigated last year indicated 40% of the accidents involved speeding, 25% involved alcohol, and 10% involved both risk factors.Do these two risk factors appear to be independent?
yes