AP Stat Final
To determine the mean cost of groceries in a certain city, an identical grocery basket of food is purchased at each store in a random sample of ten stores. If the average cost is $47.52 with a standard deviation of $1.59, find a 98% confidence interval estimate for the cost of these groceries in the city.
$47.52 ± $1.42
Suppose that for a typical FedEx package delivery, the cost of the shipment is a function of the weight of the package. You find out that the regression equation for this relationship is (cost ^of delivery) = 2.258*(weight) + 2.448. If a package you want to ship weighs 28.205 ounces, what would you expect to pay for the shipment?
$66.13
A survey is to be taken to estimate the proportion of people who support the NATO decision to be actively involved in the Balkans. If 200 people were surveyed and 123 supported the NATO decision, which of the following is a 95% confidence interval for the true proportion:
(.548, .682)
Consumers Energy states that the average electric bill across the state is $50.68. You want to test the claim that the average bill amount is actually more than $50.68. What are the appropriate hypotheses for this test?
H0: μ = 50.68, HA: μ > 50.68
A statistics professor wants to examine the number of hours that seniors and freshmen study for the final. Specifically, the professor wants to test if the average number of hours that seniors study is less than the average number of hours that freshmen study. If the seniors are considered group 1, and the freshmen are considered group 2, what are the hypotheses for this scenario?
H0: μ1 = μ2, HA: μ1 < μ2
A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They'll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. Indicate which inference procedure would be used.
2 Proportion Z-Test
A national poll reported that 43% of high school students travel out of the city over break. In a group of 5 friends, find the probability that exactly 3 traveled outside city limits.
0.026
The distribution of heights of students at a large high school is known to be approximately normal with =67.5 inches and . A simple random sample of 10 students is drawn and their mean height is calculated. Find the probability that is more than 69 inches.
0.057
An electronic component takes an average of 3.4 hours to go through an assembly line. If the standard deviation is 0.5 hours and the times are normally distributed, what is the probability that a component will take less than 3 hours to move through the line?
0.212
Automobile manufacturers are interested in the difference in reaction times for drivers reacting to traditional incandescent lights and to LED lights. A sample of 18 drivers are told to press a button as soon as they see a light flash in front of them and the reaction time was measured in milliseconds. Each driver was shown each type of light. The average difference between the two reaction times (traditional - LED) was 92.59 ms with a standard deviation of 24.238 ms. Calculate a 95% confidence interval for the average difference in the reaction times to the two types of light for all drivers.
(80.537, 104.643)
Suppose a different package delivery also determines the cost of the shipment based on the weight of the package measured in ounces. If 10 packages in a city are sampled and the regression output is given below, report the regression equation.
(cost of ^delivery) = 0.617(weight) + 5.479
A trucking firm determines that its fleet of trucks has a mean of 12.4 miles per gallon and a standard deviation of 1.2 miles per gallon on cross country hauls. Assume that the distribution of fuel efficiency is normal. What is the probability that one of its trucks averages less than 10 miles per gallon?
.0228
An NCAA official claims that the average 5K time for students trying out for college cross- country teams is 17 minutes. A Big East coach believes the true figure is lower among Big East universities. He picks an SRS of 30 recruits and calculates their mean 5K time is 16 minutes 52 seconds, with a standard deviation 25 seconds. What is the P-value for the appropriate test?
.045
Which of the following values is typically used for ?
.05
If benny is a 62% free throw shooter, what's the probability that his first miss is on the 4th show?
.091
If benny is a 62% free throw shooter, what's the probability that he makes 7 out of 10 shots?
.232
In a simple random survey of 89 teachers of high school AP Statistics, 73 said that it was the most satisfying, most enjoyable course they had ever taught. Establish a 98% confidence interval estimate of the proportion of all high school AP Statistics teachers who feel this way.
.820 ± .095
The scores on a college entrance exam are normally distributed with and .If a SRS of 25 students is drawn from this population, what is the probability that the mean score for these students will be less than 525?
.894
Two-tailed alternatives are phrased in terms of:
/=
Suppose that the probability of a baseball player getting a hit in an at bat is 0.3179. If the player has 36 at bats during a week, what's the probability that he gets greater than 20 hits?
0.0009
A bag of starbursts has 5 red, 4 pink, 8 yellow, and 7 orange left. If you randomly take out 4 starbursts, what's the probability that at least one is pink?
0.518
If 7 luxury cars (from #64) are selected, find the probability that no more than 1 are silver.
0.610
The principal samples 56 parents and finds that 37 of them check their email regularly. He wants to use this information to see if the rate is higher than he predicts. Indicate which inference procedure would be used.
1 Proportion Z-Test
A researcher tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She surveys 120 randomly chosen people and performs a test. Indicate which inference procedure would be used.
1 Sample T-test
The American Medical Association (AMA) wishes to determine the percentage of obstetricians who are considering leaving the profession because of the rapidly increasing number of lawsuits against obstetricians. How large a sample should be taken to find the answer to within ±3% at the 95% confidence level?
1068
While attempting to measure its risk exposure for the upcoming year, an insurance company notices a trend between the age of a customer and the number of claims per year. It appears that the number of claims keep going up as customers age. After performing a regression, they find that the relationship is (claims ^per year) = 0.451(age) + 3.307. If a customer is 45.804 years old and they make an average of 12.51 claims per year, what is the residual?
11.455
A soft drink dispenser can be adjusted to deliver any fixed number of ounces of soft drink. If the machine is operating with a standard deviation in delivery equal to 0.3 ounces, what should be the mean setting so that a 12-ounce cup will overflow about 1% of the time? Assume a normal distribution for ounces delivered.
12.70 oz
According to infoplease, 18.8% of the luxury cars manufactured in 2003 were silver. If there are 800 luxury cars on a lot, how many would you expect to be silver?
150.4
Some students do homework with the TV on. Some researchers want to see if people can work as effectively with as without distraction. They will randomly select 30 people to stay in a room and do relatively easy crosswords puzzles. Everyone will hear music playing at random times. Researchers will count the number of completed puzzles for each environment. Indicate which inference procedure would be used.
2 Sample T-Test
Your father wants to get your mother a new front-loading washing machine. He is trying to decide between two brands. His deciding factor is the "cycle time", the number of minutes it took each machine to wash a load of clothes. Indicate which inference procedure would be used.
2 Sample T-Test
At one SAT test site students taking the test for a second time volunteered to inhale supplemental oxygen for 10 minutes before the test. In fact, some received oxygen, but others were given just normal air. Test results showed that 42 of 66 students who breathed oxygen improve their SAT scores, compared to only 35 of 63 students who did not get the oxygen. Which procedure should we use to see if there is evidence that breathing extra oxygen can help test takers think more clearly?
2-Proportion z-test
A study was conducted to determine the effectiveness of varying amounts of vitamin C in reducing the number of common colds. A survey of 450 people provided the following data.
43
The following table shows ceremonial ranking and type of pottery shreds for a random sample of 1014 shreds at a location in the Sand Canyon Archaeological Project, Colorado.
67
A survey is conducted to determine the percentage of students at state universities who change their major at least once. In an SRS of 100 students 78% indicated that they graduated with a major different from the one with which they entered college. Determine a 95% confidence interval for the percentage of students who change their major.
69.9% to 86.1%
Fill in the blanks. Suppose the probability of a baseball player getting a hit in an at bat is 0.3038. If the player bats 28 times during a week, his number of hits should be around ______ give or take_______. Assume each at bat is independent.
8.506 , 2.4335
Suppose there is a correlation of r = 0.9 between number of hours per day students study and GPAs. Which of the following is a reasonable conclusion?
81% of the variation in GPAs can be explained by variation in number of study hours per day.
One-tailed alternatives are phrased in terms of:
< or >
A golf instructor is interested in seeing the amount of improvement for beginning golfers during the course of a 4-week clinic. Before the clinic, each golfer played all 18 holes of the course and the score for each round was recorded. The same was done when the players completed the course. Which of the following should she use?
Confidence interval for mean difference
An Archaeopteryx is an extinct animal having feathers like a bird but also having very prominent teeth. Five fossilized specimen of this creature have been found with the lengths of the femur (a leg bone) plotted against the lengths of the humerus (a bone in the upper arm):
A positive correlation is likely because the above test yields a P-value of .0039.
Investigators at an agricultural research facility randomly assigned equal numbers of chickens to be housed in two rooms. One group of chickens experienced normal day/night cycles, while in the other room lights were left on 24 hours a day to see if those chickens would lay more eggs. After collecting data for several days the researchers tested the hypothesis against the one-tail alternative and found P = 0.22. Which is true?
About 22% of all samples of this size would produce a this extreme given the null is true.
The p-value for a test is 0.36. Which is true for this p-value?
About 36% of all samples this size would produce a test statistic at least as extreme as ours if the null hypothesis is true
Absorption rates into the body are important considerations when manufacturing a generic version of a brand-name drug. A pharmacist read that the absorption rate into the body of a new generic drug (G) is the same as its brand-name counterpart (B). She has a researcher friend of hers run a small experiment to test against the alternative . Which of the following would be a Type II error?
Deciding that the absorption rates are the same, when in fact they are not.
A contact lens wearer read that the producer of a new contact lens boasts that their lenses are cheaper than contacts from another popular company. She collected some data, then tested the null hypothesis H0 : . against the alternative HA : . Which of the following would be a Type I error?
Deciding that the new lenses are cheaper, when in fact they are not.
Of type I and type II error, which is traditionally regarded as more serious?
Depends on the situation
Which of the following is true of the null and alternative hypotheses?
Exactly one hypothesis must be true
An AP Student performs a 1-sample t test. His hypotheses are vs . He plans to test at the 5% level. He calculates t = 2.05 with a sample of size 15. Assuming that all of the conditions for the test have been satisfied, his decision should be...
Fail to reject Ho because p > .05
A marketing research firm wanted to determine whether an individual's favored Age Group and Social Network were related. For age they grouped by 8-17, 18-34, 35-55, and 55+, and the social networks they investigated were Facebook, Google+, and Twitter. To test at the 0.1 level to determine if age group and social network are dependent, what are the appropriate hypotheses?
HO: Age Group and Social Network are not related to each other. HA: Age Group and Social Network are associated with each other.
An auto racing mechanic team claims that at a pit stop they can change all four tires and fill the gas tank in 15 seconds. A driver is skeptical of this claim and thinks the team can't be that fast. Which of the following gives the null and alternative hypotheses that the driver should test?
Ho : μ = 15 seconds Ha : μ > 15 seconds
Which of the following is the correct set of hypotheses to test whether the average number of room cancellations per day at a large hotel has increased by 7
Ho : μ = 7 Ha : μ > 7
Which of the following is true about Student's t-models?
I, II, III
Which statement correctly compares t-distributions to the normal distribution?
I, II, and III
If the confidence interval is changed from 95% to 90%, what will happen? I. The margin of error will increase II. The critical value will change III. The sample size will be smaller
II only
Which of the following statements about the correlation coefficient are true?
III only
Which of the following is an appropriate conclusion for a test which gives the following output
If you increase your GPA, you will increase your ACT score
Which of the following would result in the narrowest confidence interval?
Large sample size and 95% confidence
It's common for a movie's ticket sales to open high for the first couple of weeks, then gradually taper off as time passes. Hoping to be able to better understand how quickly sales decline, an industry analyst keeps track of box office revenues for a new film over its first 20 weeks. What inference method might provide useful insight?
Linear Regression Test
You conduct a hypothesis test and you observe values for the sample mean and sample standard deviation when n = 25 that do not lead to the rejection of . You calculate a p-value of 0.0667. What will happen to the p-value if you observe the same sample mean and standard deviation for a sample > 25?
May either increase or decrease
The death rate from a particular form of cancer is 23% during the first year. When treated with an experimental drug, one 15 out of 84 patients die during the initial year. Is this strong evidence to claim that the new medication reduced the morality rate?
No, because the p-value is .1313
A pet food manufacturer runs an experiment to determine whether three brands of dog food are equally preferred by dogs. In the experiment, 150 dogs are individually presented with three dishes of food, each containing a different brand, and their choices are noted. Tabulations show that 62 dogs go to brand A, 43 to brand B, and 45 to brand C. Is there sufficient evidence to say that dogs have preferences among the brands? Test at the 10% significance level.
No, with x^2 = 4.36, there is not sufficient evidence at the 10% level.
Which of the following are true statements?
None are true
Both over-the-counter niacin and the prescription drug Lipitor are known to lower blood cholesterol levels. In one double-blind study Lipitor outperformed niacin. The 95% confidence interval estimate of the difference in mean cholesterol level lowering was (18, 41). Which of the following is a reasonable conclusion?
None of the above.
The weight of an aspirin tablet is 300 milligrams according to the bottle label. An FDA investigator weighs a simple random sample of seven tablets and obtains weights of 299, 300, 305, 302, 299, 301, and 303 milligrams, respectively. In which of the following intervals is the p-value located for a test to see if the label is accurate?
P > .10
Several volunteers engage in a special exercise program intended to lower their blood pressure. We measure each person's initial blood pressure, lead them through the exercises daily for a month then check blood pressures again. To see if the program lowered blood pressure significantly ,which test should be done?
Pair t-test
Before doing a t test, Jessi looks at the histogram of her 60 data values (below). Which is correct based on the graph?
She should not do the test because the data is skewed right
A basketball coach studied how the number of offensive rebounds affects the number of points scored in a game. He takes a sample of 25 games and reads the following output.
Since the p-value is small, there's no evidence of a correlation between rebounds & points
Your friend tells you that the proportion of active Major League Baseball players who have a batting average greater than .300 is greater than 0.73, a claim you would like to test. The hypotheses for this test are Null Hypothesis: p = 0.73, Alternative Hypothesis: p > 0.73. If you randomly sample 26 players and determine that 14 of them have a batting average higher than .300, what is the test statistic and p-value?
Test Statistic: -2.2, p-value: .986
Do sit down restaurant franchises and fast food franchises differ significantly in stock price? Specifically, is the average stock price for sit-down restaurants greater than the average stock price for fast food restaurants? If sit down restaurants are in group 1 and fast food restaurants are in group 2, the hypotheses for this scenario are Null Hypothesis: μ1 = μ2 Alternative Hypothesis: μ1 > μ2 In a random sample of 37 sit down restaurants, you find that the average stock price is $125.216 with a standard deviation of $26.1814. For 52 fast food restaurants, the average stock price is $136.315 with a standard deviation of $8.0644. Conduct a two sample t-test. What is the test statistic and p-value for this test? Here we can assume the population standard deviations are the same.
Test Statistic: -2.496, p-value: 0.9917
A manufacturer claims that a particular automobile model will get 50 miles per gallon on the highway. The researchers at a consumer-oriented magazine believe that this claim is high and plans a test with a simple random sample of 30 cars. Assuming the standard deviation between individual cars is 2.3 miles per gallon, what should the researchers conclude if the sample mean is 49 miles per gallon?
The P-value of .0086 is sufficient evidence to reject the manufacturer's claim.
The owner of a local golf course wants to examine the difference between the average ages of males and females that play on the golf course. Specifically, he wants to test if the average age of males is less than the average age of females. If the owner conducts a 2 sample t-test and calculates a p-value of 0.0375, what is the appropriate conclusion? Label males as group 1 and females as group 2. (Use a 5 % level of significance.)
The average age of males is significantly less than the average age of females
While attempting to measure its risk exposure for the upcoming year, an insurance company notices a trend between the age of a customer and the number of claims per year. It appears that the number of claims keep going up as customers age. After performing a regression, they find that the relationship is (claims ^per year) = 0.12(age) + 4.55. If a customer is 32.524 years old and they make an average of 8.35 claims per year, the residual is -0.103. Interpret this residual in terms of the problem.
The number of claims per year is 0.103 claims less than what we would expect.
A historian believes that the average height of soldiers in World War II was greater than that of soldiers in World War I. She examines a random sample of records of 100 men in each war and notes standard deviations of 2.5 and 2.3 inches in World War I and World War II, respectively. If the average height from the sample of World War II soldiers is 1 inch greater than from the sample of World War I soldiers, what conclusion is justified from a two-sample hypothesis test where -
The observed difference in average height is significant.
As of 2012, the proportion of students who use a MacBook as their primary computer is 0.49. You believe that at your university the proportion is actually less than 0.49. The hypotheses for this scenario are Null Hypothesis: p = 0.49 Alternative Hypothesis: p < 0.49. You conduct a random sample and run a hypothesis test yielding a p-value of 0.0279. What is the appropriate conclusion based on the data collected at the 5% level of significance?
The proportion of students that use a MacBook as their primary is significantly less than 0.49
Two friends become roommates. Before deciding whether to combine their grocery shopping, they examine a random sample of previous weekly grocery bills for each to determine whether one spends significantly more money than the other on groceries. Assume all conditions are met for conducting a significance test. They set up the hypotheses and . They calculate the following results... t =1.567 with df = 18 and a p-value = 0.068.
The results provide little evidence that roommate A spends more than B at the 0.05 level.
The NCAA requires colleges to report the graduation rates of their athletes. One Big Ten university reported that the graduation rates for a specific year were 21 of 28 female athletes and 24 of 46 male athletes. Is there evidence that a smaller proportion of male athletes than of female athletes graduate?
The sample size is too small to make any type of conclusions.
You work for a company in the marketing department. Your manager has tasked you with forecasting sales by month for the next year. You notice that over the past 12 month's sales have consistently gone up in a linear fashion, so you decide to run a regression the company's sales history. If 10 months are sampled and the regression output is given below, what can we conclude about the slope? (Use a 5 % level of significance.)
The slope is 21.383 and therefore differs from 0.
A political poll asked potential voters if they felt the economy was going to get worse, stay the same, or get better during the next 12 months. The party affiliations of the respondents were also noted. The results are shown in the following table. To test at the 0.01 level to determine if party affiliation and response are dependent, calculate the chi-squared test statistic and p-value.
The test statistic is x^2 = 4.355, the degrees of freedom is 4, and the p-value is 0.3601.
A marketing research firm wanted to determine whether an individual's favored Age Group and Social Network were related. For age they grouped by 8-17, 18-34, 35-55, and 55+, and the social networks they investigated were Facebook, Google+, and Twitter. The table below presents their findings. To test at the 0.05 level to determine if age group and social network are dependent, calculate the chi-squared test statistic and p-value.
The test statistic is x^2 =20.543, the degrees of freedom is 6, and the p-value is 0.0022.
A study was conducted to determine the effectiveness of varying amounts of vitamin C in reducing the number of common colds. A survey of 450 people provided the following information:
There is not sufficient evidence at the 10% level of a relationship between taking vitamin C and catching fewer colds.
What conclusion can be made based off of this interpretation: "Given that tattoo status and hepatitis status are independent, a chi-square value as high as the one obtained would happen .6% of the time due to natural variation."?
There is strong evidence to conclude hepatitis and tattoos are not related.
A piece of medical equipment is not functioning properly, however, in running operational checks, a lab technician does not find evidence of the malfunction. Which type of error is this?
Type II
Is there a significant difference between the cost of a flight on Priceline.com vs. the Airline's own website? A random sample of 26 flights were tracked on Priceline and the flight's airline website and the 90% confidence interval for the mean difference in price (Priceline - Airline Site) was (-156.35, -51.74). Which of the following is the appropriate conclusion?
We are 90% confident that the average difference in price is negative, with the higher price coming from the Airline sites
Suppose the Federal Aviation Administration (FAA) would like to compare the on-time performances of different airlines on domestic, nonstop flights. The following table shows three different airlines and the frequency of flights that arrived early, on-time, and late for each. Identify the correct conclusion using the 0.05 level of significance.
We decide that airline and status are related to one another, based on a p-value of 0.0186
It is reported in USA Today that the average flight cost nationwide is $495.12. You have never paid close to that amount and you want to perform a hypothesis test that the true average is actually greater than $495.12. The hypotheses for this situation are Null Hypothesis: μ =495:12, Alternative Hypothesis: μ > 495:12. You take a random sample of national cost information and perform a one sample mean hypothesis test. You observe a p-value of 0.124. What is the appropriate conclusion? Conclude at the 5% level of significance.
We did not find enough evidence to say the true average flight cost is greater than $495.12.
The Associated Press reported a management consultant believes that on average workers spend 75 minutes a day using personal use of company technology. Suppose that the CEO of a large corporation wants to determine whether the average amount of time spent on personal use for her employees is greater than the reported value of 75 minutes. The CEO did a random sample of 10 employees. The resulting data are: 81, 70, 75, 88, 79, 89, 74, 71, 82, 86. Which is an appropriate interpretation of a 95% confidence interval for this data.
We're 95% confident that the average for all workers is between 74.6 and 84.4 minutes.
A company checking the productivity of its assembly line monitored a random sample of workers for several days. They found that a 95% confidence interval for the mean number of items produced daily by each worker was (23,27). Which is true?
We're 95% sure that the mean daily worker output is between 23 and 27 items.
Suppose that in a certain neighborhood, the cost of a home is proportional to the size of the home in square feet. If the regression equation quantifying this relationship is found to be (co^st) = 80.19(size) + 610.129, what does the slope indicate?
When size increases by 1 square foot, cost increases by 80.19 dollars.
The form of the alternative hypothesis can be:
one or two-tailed
Smaller p-values indicate more evidence in support of:
the alternative hypothesis
A type II error occurs when:
the null hypothesis is incorrectly accepted when it is false
A type I error occurs when:
the null hypothesis is incorrectly rejected when it is true
The null hypothesis usually represents:
the status quo
According to United Nations Population Division, the age distribution of the Commonwealth of Australia is: 21% less than 15 years of age, 67% between 15 and 65 years of age, and 12% are over 65 years old. A random sample of 210 residents of Canberra revealed 40 were less than 15 years of age, 145 were between 15 and 65 years of age, and 25 were over 65 years old. Are the ages of Canberra residents unusual in any way? Indicate which inference procedure would be used.
x^2 GOF Test
We randomly divide 200 volunteers with headaches into two groups who take identical- looking pills. One group gets a homeopathic remedy and the other a placebo. After 20 minutes we ask them to rate their headache pain as "no change", "somewhat better", "much better", or "gone".
x^2 Homogeneity Test
A student wants to find out whether political leaning (liberal, moderate, or conservative) is related to choice of major. He surveys 500 randomly chosen students and performs a test. Indicate which inference procedure would be used.
x^2 indepedence test