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Section 1: Multiple Choice Date: ____________________
A major agricultural company is testing a new variety of wheat to determine whether it is more resistant to certain insects than is the current wheat variety. The proportion of a current wheat crop lost to insects is 4%. This, the company wishes to test the following hypotheses:
H0: p = 0.04
Ha: p < 0.04
Which of the following significance levels and sample sizes would lead to the highe s t p o w e r f o r t h i s t e s t ?
n = 2 0 0 a n d = 0 . 0 1
n = 4 0 0 a n d = 0 . 0 5
n = 4 0 0 a n d = 0 . 0 1
n = 5 0 0 a n d = 0 . 0 1
n = 2 0 0 a n d = 0 . 0 5
A s p a r t o f a b e a r p o p u l a t i o n s t u d y , d a t a w e r e g a t h e r e d o n a s a m p l e o f b l a c k b e a r s i n t h e w e s t e r n U n i t e d S t a t e s t o e x a m i n e t h e relationship between the bears neck girth (distance around the neck) and the weight of the bear. A scatterplot of the data reveals a straight-line pattern. The r2-value from a least-squares regression analysis was determined to be r2 = 0.963. Which one of the following is the correct value and corresponding interpretation of the correlation coefficient?
The correlation is -0.963 and 96.3% of the variation in a bears weight is explained by the least-squares regression line using neck girth as the explanatory variable.
The correlation is 0.963. There is a strong positive linear relationship between a bears neck girth and its weight.
The correlation is 0.981 and 98.1% of the variation in a bears weight is explained by the least-squares regression line using neck girth as the explanatory variable.
The correlation is -0.981. There is a strong negative linear relationship between a bears neck girth and its weight.
The correlation is 0.981. There is a strong positive linear relationship between a bears neck girth and its weight.
Which of the following sampling plans for estimating the proportion of all adults in a medium-sized town who favor a tax increase to support the local school system does not suffer from undercoverage bias?
A random sample of 250 names from the local phone book
A random sample of 200 parents whose children attend one of the local schools
A sample consisting of 500 people from the city who take an online survey
A random sample of 300 homeowners in the town
A random sample of 200 people from an alphabetical list of all adults in the town
In a clinical trial, 30 patients with a certain blood disease are randomly assigned to two groups. One group is then randomly assigned the currently marketed medicine, and the other group receives the experimental medicine. Each week, patients report to the clinic where blood tests are conducted. The lab technician is unaware of which medicine he or she has been given. This design can be described as
a double-blind, completely randomized experiment, with the currently marketed medicine and the experimental medicine as the two treatments.
A single-blind completely randomized experiment, with the currently marketed medicine and the experimental medicine as the two treatments.
A double-blind, matched pairs design, with the currently marketed medicine and the experimental medicine forming a pair.
A double-blind, blocked design that is not a matched pairs design, with the currently marketed medicine and the experimental medicine as the two blocks.
A double-blind, completely randomized observational study
A beef rancher randomly sampled 42 cattle from her large herd to obtain a 95% confidence interval to estimate the mean weight of the cows in the herd. The interval obtained was (1010, 1321). If the rancher had used a 98% confidence interval instead, the interval would have been
wider
narrower
the same width
wider on the upper tail
none of the above
Which of the following is not a property of a binomial setting?
Outcomes of different trials are independent
There is a fixed number of trials, n
The probability of success is the same for each trial
If we use a sample of size 30, the binomial distribution will be approximately Normal
Each trial results in either a success or a failure
Which of the following is false?
A measure of center alone does not completely describe the characteristics of a set of data. Some measure of spread is also needed.
If the original measurements of a data set are expressed in inches, the standard deviation is expressed in square inches.
One of the disadvantages of a histogram is that it doesnt show each individual data point.
Between the range and the Interquartile range, the IQR is a better measure of spread if there are outliers.
If a distribution is skewed, the median and IQR should be reported rather than the mean and standard deviation.
The Environmental protection Agency is charged with monitoring industrial emissions that pollute the atmosphere and water. So long as emission levels stay within specified guidelines, the EPA does not take action against the polluter. If the polluter is in violation of the regulations, the offender can be fined, forced to clean up the problem, or possibly closed. Suppose that for a particular industry acceptable emission level has been set at no more than 5 parts per million (5 ppm). The null and alternative hypotheses are H 0 : = 5 v e r s u s H a : > 5 . W h i c h o f t h e f o l l o w i n g d e s c r i b e s a T y p e I I e r r o r ?
T h e E P A f a i l s t o f i n d e v i d e n c e t h a t e m i s s i o n s e x c e e d a c c e p t a b l e l i m i t s w h e n , i n f a c t , t h e y a r e w i t h i n a c c e p t a b l e l i m i t s .
T h e E P A c o n c l u d e s t h a t e m i s s i o n e x c e e d a c c e p t a b l e l i m i t s when, in fact, they are within acceptable limits.
The EPA concludes that emission exceed acceptable limits when, in fact, they do exceed acceptable limits.
The EPA takes more samples to ensure that they make the correct decision.
The EPA fails to find evidence that emissions exceed acceptable limits when, in fact, they do exceed acceptable limits.
Suppose that the time it takes students to complete a standardized exam is approximately normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. Approximately how much time should be allowed so that 90% of the students have enough time to finish?
A. 32 minutes
B. 41 minutes
C. 58 minutes
D. 65 minutes
E. 68 minutes
In a study on solar panels, the outdoor temperature and current produced were recorded at 200 different times during the year. The regression equation for this relationship is: EMBED Equation.DSMT4 where y = current and x = temperature. One observation was x = 67 degrees and y = 5.5 amps. What is the approximate residual for this observation?
A. 25
B. -25
C. 30
D. -30
E. Cannot be determined without all of the observations
In a particular high school, the number of courses a senior is taking was recorded and summarized in the table below. Find the mean and standard deviation of this distribution.
Number of Courses4567Proportion.2.5.2.1A. mean = 5.5, SD = 1.1
B. mean = 5.5, SD = 1.3
C. mean = 5.2, SD = 0.9
D. mean = 5.2, SD = 1.1
E. Cannot be determined without the sample size
On a final exam in Algebra, the mean score was 23 with a standard deviation of 9. What is the z-score for a student who scored 18 on the exam?
A. 28
B. 9
C. -5
D. 0.56
E. -0.56
Suppose that the results of a recent poll in a particular state said that 63% of respondents were satisfied with the performance of their governor. The margin of error for the poll was EMBED Equation.DSMT45% with 95% confidence. Which of the following statements is correct?
A. There is a 0.95 probability that the population proportion of state residents that are satisfied with the performance of their governor is between 0.58 and 0.68.
B. There is a 0.95 probability that the sample proportion of state residents that are satisfied with the performance of their governor is between 0.58 and 0.68.
C. If the poll were repeated many times, then about 95% of the time the sample proportion of state residents that are satisfied with the performance of their governor would be between 58% and 68%.
D. If the poll were repeated many times and 95% confidence intervals were constructed from the results of each poll, then about 95% of the resulting intervals would include the true population proportion of state residents that are satisfied with the performance of their governor.
E. If the poll were repeated many times and 95% confidence intervals were constructed from the results of each poll, then about 95% of the resulting intervals would include the value 0.63.
A college statistics student wants to estimate the difference in the proportion of males at her school who have a tattoo and the proportion of females at her school who have a tattoo. She surveys 40 males and finds that 12 of them have a tattoo and she surveys 50 females and finds that 8 of them have a tattoo. Which of the following would be the correct standard error to use for a 95% confidence interval for the difference in the proportions of males and females with a tattoo?
EMBED Equation.DSMT4
EMBED Equation.DSMT4
EMBED Equation.DSMT4
1.96EMBED Equation.DSMT4
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If you have four mutually exclusive events with probabilities P(A) = 0.19, P(B) = 0.21, P(C) = 0.33, and P(D) = 0.27, what is P(A or D)?
A. 0.40
B. 0.42
C. 0.46
D. 0.05
E. 0.52
Tossing a die 400 times results in the following outcomes: 46 ones, 68 twos, 73 threes, 59 fours, 69 fives and 78 sixes. Suppose an experiment was conducted to determine whether this die is fair. What is the appropriate test to use in this condition?
A. One-sample proportion z test
B. One-sample p r o p o r t i o n t t e s t
C . t t e s t f o r m a t c h e d p a i r s
D . 2 t e s t f o r g o o d n e s s o f f i t
E . T h e r e i s i n s u f f i c i e n t i n f o r m a t i o n t o d e t e r m i n e w h i c h t e s t i s a p p r o p r i a t e .
A t e a c h e r h a s d e s i g n e d a m a t h t e s t s h e t h i n k s w i l l p r e d i c t a n a v e r a g e s t u d e n t s p e r f o r m a n c e i n M a t h I . She administers the test to a group of randomly selected students who have successfully completed a pre-algebra course with average grades and then records the test scores. At the end of the year she records each students final math grade. Data for the hypothetical study is listed below.
Test score: 53, 48, 39, 72, 64, 69, 23, 78, 36, 85
Final math grade: 56, 64, 76, 94, 81, 79, 88, 97, 55, 79
What is a least-squares regression line for the data?
y = 55.86 + 0.4386x
y = 34.95 + 10.57x
y = 13.26 + 0.565x
y = 60.019 + 0.2977x
y = 58.24 + 1.2977x
Consider a normal distribution that has a mean of 78 and a standard deviation of 6. What is the percentile rank, to the nearest integer, of a value of 82 in this distribution?
A. 82%
B. 78%
C. 75%
D. 84%
E. 80%
Use the following information to answer questions 19 20.
According to sleep researchers, if you are between the ages of 12 and 18 years old, you need 9 hours of sleep to be fully functional. A simple random sample of 28 students was chosen from a large high school, and these students were asked how much sleep they got the previous night. The mean of the responses was 7.9 hours, with a standard deviation of 2.1 hours.
If we are interested in whether students at this high school are getting too little sleep, which of the following represent the appropriate null and alternative hypotheses?
A. H0: = 7 . 9 ; H a : < 7 . 9
B . H 0 : = 7 . 9 ; H a : `" 7 . 9
C . H 0 : = 9 ; H a : `" 9
D . H 0 : = 9 ; H a : < 9
E . H 0 : < 9 ; H a : > 9
W h i c h o f t h e f o l l o w i n g i s t h e t e s t s t a t i s t i c f o r t h e h y p o t h e s i s t e s t ?
A . t = - 2 . 7 7
B . z = - 1 . 2 7
C . t = 0 . 0 0 4
D . z = - 2 . 7 7
E . t = - 0 . 2 77
AP Statistics Practice LEOCT Name: ______________________
Section 2: Free Response Date: ____________________
21. The manufacturer of exercise machines for fitness centers has designed two new elliptical machines that are meant to increase cardiovascular fitness. The two machines are being tested on 30 volunteers at a fitness center near the companys headquarters. The volunteers are randomly assigned to one of the machines and use it daily for two months. A measure of cardiovascular fitness is administered at the start of the experiment and again at the end. The following table contains the differences in the two scores (After Before) for the two machines. Note that higher scores indicate larger gains in fitness.
Machine A Machine B
3, 5, 9
6, 1 4 2, 5, 7
9, 7, 4, 1, 1 3 2, 4, 8, 9
8, 7, 6, 3, 2, 0 2 1, 5, 9
5, 4 1 0
0 2
Write a few sentences comparing the distributions of cardiovascular fitness gains from the two elliptical machines.
Which machine should be chosen if the company wants to advertise it as achieving the highest overall gain in cardiovascular fitness?
Which machine should be chosen if the company wants to advertise it as achieving the most consistent gain in cardiovascular fitness?
Give one reason why the advertising claims of the company for this experiment would be limited.
22. There are four major blood types in humans: O, A, B and AB. In a study conducted using blood specimens from the Blood Bank of Hawaii, individuals were classified according to blood type and ethnic group. The ethnic groups were Hawaiian, Hawaiian-White, Hawaiian-Chinese, and White. Suppose that a blood bank specimen is selected a random.
HawaiianHawaiian-WhiteHawaiian-ChineseWhiteTotalO19034469220653,759A24904671236850,008B17660656816,252AB992362435001Total
Find the probability that the specimen contains type B blood and comes from the White ethnic group.
Find the probability that the specimen contains type O blood or comes from the Hawaiian-Chinese ethnic group? Show your work.
Find the probability that the specimen contains type B blood, given that it comes from the Hawaiian ethnic group.
Are the events type B blood and Hawaiian ethnic group independent? Explain.
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What proportion of the students scored at least 25 points on this test?
What is the 31st percentile of the distribution of test scores?
If a student received a score of 25 points, find the z-score for that student.
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