AP Statistics - Final Exam

Name______

Coefficients:

13.An insurance company collected data concerning fatal vehicle crashes—in particular, the actuaries measured the number of vehicles involved in the crash, and the type of vehicle in which the death occurred. A random sample of fatal crashes was selected, and the following data were collected:

Is there evidence that the type of vehicle is related to the number of vehicles involved in the crash? Support your conclusion with appropriate statistical evidence.

14.A humane society claims that less than 35% of U.S. households own a dog. A local group randomly surveys 400 households and finds that 156 include a dog.

(a) Construct a 95% confidence interval for the actual proportion of local households that own a dog. Interpret this interval for someone who has limited knowledge of statistics.

(b) A government agency want to conduct a follow up study and construct a new interval. Determine the minimum sample size that will guarantee that the margin of error will be no more than 4%.

– Multiple Choice Practice 1 (S)

1. If a student rolls three dice, what is the probability that exactly two of them will show an even number?

1. 3/8
2. 1/2
3. 5/8
4. 2/3
5. 2

1. The probability that a certain movie is sold out for an evening performance is 0.30. Bill wants to take Gina to the movies this weekend. What is the probability that the movie is sold out on both Friday and Saturday nights?

1. 0.09
2. 0.21
3. 0.30
4. 0.49
5. 0.60

1. An alarm in a museum has a main and a backup power supply that are independent of each other. The probability that the main power system will fail is 0.04 and the probability that the backup system will fail is 0.06.

1. What is the probability that both systems will fail?

1. 0.0024
2. 0.010
3. 0.020
4. 0.0376
5. 0.10

1. What is the probability that at least one system works?

1. 0.0024
2. 0.10
3. 0.90
4. 0.9024
5. 0.9976

1. The probability that a call to 911 is an emergency is 0.40. What is the probability that of two successive calls, only one will be an emergency?

1. 0.16
2. 0.24
3. 0.48
4. 0.84
5. 1.00

– Multiple Choice Practice 2 (S)

1. Northwestern University has approximately 5000 students. UCLA has about 20,000 students. A researcher wants to take a simple random sample of about 5% of the student body at both schools. Which of the following statements is correct?

1. the sampling variability is the same for both schools
2. the sampling variability for UCLA is higher than that of Northwestern
3. The sampling variability for UCLA is lower than that of Northwestern
4. No conclusion can be stated without knowing the results of the study
5. The results from both schools ought to be within 5% of each other

1. In a certain town in the northwest during July, the probability that it rains on a given day is 0.24. The probability that the temperature is above 90 degrees is 0.42. The probability that it rains and the temperature is above 90 degrees is 0.18.

1. Given that the temperature is greater than 90 degrees, what is the probability that it is raining?

1. 0.18
2. 0.24
3. 0.43
4. 0.52
5. 0.75

1. What is the probability that the temperature is greater than 90 degrees, given that it is raining?

1. 0.18
2. 0.24
3. 0.43
4. 0.52
5. 0.75

1. Which of the following statements must be true?

1. If two events are dependent, then the probability can exceed 1.
2. The probability of success is always one minus the probability of failure.
3. If two events occur simultaneously, the combined probability is the difference of the individual probabilities.

1. I only
2. II only
3. III only
4. I and II
5. I and III

1. Ball bearings produced at a certain factory have a mean diameter of 6.55 mm with a standard deviation of 0.27mm. If the distribution of diameters is known to be normal, what is the probability that the diameter of a randomly selected ball bearing is between 6.31 mm and 6.62 mm?

1. 0.189
2. 0.259
3. 0.415
4. 0.437
5. 0.621

Practice 3 (S)

1. Using a larger sample will make

(a)a larger confidence interval

(b)a smaller confidence interval

(c)the same interval as before

(d)a larger or smaller interval depending on n

(e)cannot tell from the given information

1. If the standard deviation is larger, the confidence interval

(a)will be larger

(b)will be smaller

(c)will stay the same

(d)will change if the standard deviation is substantially larger

(e)cannot tell from the given information

1. In order to increase the margin of error by a factor of 3, the sample size must be

(a)increased by a factor of 3

(b)decreased by a factor of 3

(c)increased by a factor of 9

(d)decreased by a factor of 9

(e)cannot tell from the given information

1. If the mean of a certain sample is 8, calculate the 95% confidence interval for a sample size of 20.

(a)(0.1853, 0.6147)

(b)(7.825, 8.175)

(c)(7.781, 8.219)

(d)(7.816, 8.184)

(e)none of the above

1. A sample of 80 students is randomly selected. Their average score on the SAT Math is 580. If the standard deviation for all the SAT scores is 100 and the scores are normally distributed, what is the 95% confidence interval for this sample?

(a)(478.09, 521.91)

(b)(481.61, 518.39)

(c)(561.61, 598.39)

(d)(558.09, 601.91)

(e)(549.01, 610.99)

Multiple Choice Practice 4 (S)

1.Two different confidence intervals taken from the same sample are (9.14, 15.34) and (7.43, 17.05). One is based on a 95% confidence level and the other is based on a 99% confidence level. What is the sample mean and which is the 95% confidence interval?

(a) = 12.24; (9.14, 15.34) is the 95% confidence interval

(b) = 12.24; (7.43, 17.05) is the 95% confidence interval

(c) = 12.24, but the interval cannot be determined without knowing the sample size

(d) = 12.24, but the interval cannot be determined without knowing the standard deviation

(e) = 12.24, but the interval cannot be determined without knowing the critical value for

1. In determining a confidence interval, which of the following is false?

(a)increasing the sample size and decreasing the standard deviation will always shrink the confidence interval

(b)decreasing the sample size and increasing the standard deviation will always lengthen the confidence interval

(c)increasing the sample size and increasing the standard deviation will always shrink the confidence interval

(d)increasing the sample size and decreasing the level of confidence will always shrink the confidence interval

(e)increasing the standard deviation and increasing the level of confidence will always lengthen the confidence interval

1. A behavioral psychologist is trying to determine the length of the average vacation stay at a resort. She finds that a random sample of 48 vacations can determine the average length to within a day at a 90% confidence level. If she wants to improve the margin of error to within a half a day, how many vacations need to be examined?

(a)24

(b)48

(c)96

(d)132

(e)192

1. A psychological test is used to measure sociological conformity. The mean test score for all female students nationally is 132. A large university decided to estimate the mean score for females on its campus by testing a random sample of n females and constructing a confidence interval based on their scores. Which of the following statements about the confidence interval must be true?

1. The resulting interval will contain 132
2. The 95% confidence interval for n = 75 will generally be shorter than the 95% confidence interval for n = 40.
3. For n = 100, the 95% confidence interval will be longer than the 90% confidence interval.

(a) I only

(b)II only

(c)III only

(d)II and III

(e)I and III

1. In general, how many more subjects are required to establish a 95% confidence interval instead of a 90% confidence interval?

(a)(1.96/1.645) times as many

(b) times as many

(c)(1.645/1.96) times as many

(d) times as many

(e) times as many

– Multiple Choice Practice 5 (S)

1. The number of spots on a toy leopard is normally distributed with the mean of 10 and standard deviation of 2. A sample of 5 toy leopards is chosen and the mean for the sample is 12. The toy manufacturer wants to know if the mean number of spots on the toy leopard is different from the previously given number.

1. State the alternative hypothesis for the problem above.

(a)the average number of spots is more than 10

(b)the average number of spots is less than 12

(c)the average number of spots is equal to 10

(d)the average number of spots is not equal to 10

(e)the average number of spots is equal to 12

1. State the p-value for the problem above.

(a).0126

(b).0224

(c).0253

(d).1587

(e).3173

1. We may not use the Z-Test when

1. the sample is too small
2. we do not know the population standard deviation
3. the data comes from a non-normal population

(a)I only

(b)II only

(c)III only

(d)I and II

(e)II and III

1. An entrance exam is administered to all the students entering a calculus class at a local high school. Out of 55 people who are planning to take calculus, 40 got a passing grade. Which of these are true?

1. more than 70 percent of all the students taking Calculus passed the entrance exam
2. 55 represents the population
3. 55 represents the sample

(a)I

(b)II

(c)III

(d)I and II

(e)I and III

1. Which of the following measure the probability of rejecting the null hypothesis when in fact it is true?

(a)

(b)1 -

(c)

(d)1 -

(e)p – value

Multiple Choice Practice 6 (S)

1. Which of the following statements is correct?

1. A hypothesis should always be stated in terms of the sample statistic.
2. If the sample size is greater than 1060, the value of the parameter will be correct within 0.01%
3. A small p-value indicates strong evidence against the null hypothesis.

(a)I only

(b)II only

(c)III only

(d)I and II only

(e)II and III only

1. Suppose that a previous study found that the average starting salary for a public school teacher in California is $28,000 with a standard deviation of $7,000. A random sample of 100 teachers has an average salary of $26,500. Assume the salaries are normally distributed.

1. What is the p-value for the test used to check whether the real average teacher’s salary is indeed as was previously stated?

(a)0.162

(b)0.593

(c)0.041

(d)0.032

(e)0.000

1. Is there enough evidence that the average teacher’s salary is not as was previously stated?

(a)the salary is not as previously stated, p-value is very low

(b)the salary is not as previously stated, p-value is very high

(c)the salary is as previously stated, p-value is very low

(d)the salary is as previously stated, p-value is very high

(e)the problem cannot be solved because the p-value is zero.

1. Which of the following measures the probability of failing to reject the null hypothesis when in fact it is false?

(a)

(b) 1 -

(c)

(d) 1 -

(e) p-value

1. A sociologist is curious to see if the mean income of senior citizens has changed since 1975. Suppose the mean income was $7, 568. The sociologist plans to sample senior citizens to determine their income (in 1975 dollars). What is the alternative hypothesis she needs to test?

(a) = $7568

(b) $7568

(c) < $7568

(d) > $7568

(e) $7568

– Multiple Choice Practice 7 (S)

1. A random sample of 10 cars traveling in a hospital zone showed a mean speed of 23.99 mph with a standard deviation of 0.1 mph. What is the 90% confidence interval for the mean speed of all cars in the zone?

(a)23.99 0.006

(b)23.99 0.041

(c)23.99 0.058

(d)23.99 0.081

(e)23.99 0.620

1. A study of 130 people found that the mean commute time for people who work in Washington, D. C. is 28 minutes with a variance of 39 minutes. What is the 95% confidence interval for the true mean commute time for all workers?

(a)(21.3 , 34.7 minutes)

(b)(22.4 , 33.6 minutes)

(c)(26.9 , 29.1 minutes)

(d)(27.1 , 28.9 minutes)

(e)(27.6 , 28.4 minutes)

1. A researcher found that, in a sample of 63 people in Minneapolis, the mean time required to eat an ice cream cone was 12.3 minutes with a standard deviation of 6.2 minutes. What is the margin of error for a 90% confidence interval?

(a) 1.31 minutes

(b) 1.28 minutes

(c) 2.91 minutes

(d) 3.46 minutes

(e) 5.58 minutes

1. A tobacco company claims that the typical adult smoker smokes 10 cigarettes per day. Health specialists believe this figure is too low. They conduct a study of 53 randomly chosen smokers and find the mean of this group is 13.7 cigarettes per day with a standard deviation of 2.3. What is the value of the test statistic associated with this test?

(a)-11.76

(b)0

(c)5.09

(d)11.71

(e)17.76

1. Drive shafts were measured in a sample of 50 motors. The sample mean diameter of the drive shafts was found to be 9.95 mm. The specifications for this part require a 10.00 mm diameter. From previous tests it is known that the standard deviation is 0.15 mm. At the 5% level of significance, should this batch be accepted?

(a)yes, because z = -2.357 and the critical z value = -1.960

(b)yes, because z = -2.357 and the critical z value = -1.645

(c)no, because z = -1.562 and the critical z value = -1.960

(d)no, because z = -1.562 and the critical z value = -1.645

(e)yes, because z = -4.679 and the critical z value = -1.645

– Multiple Choice Practice 8 (S)

1. At Liberty HS a random sample of 20 boys and 25 girls is taken to determine if SAT Math scores differ for the two groups. The 95% confidence interval for the differences in the mean scores is (- 20.57, 35.3). What can you conclude about the scores for boys and girls at Liberty HS?

(a)Girls do better on the SAT Math

(b)Boys do better on the SAT Math

(c)There is no difference in the scores

(d)Cannot make a conclusion because the mean scores are not given

(e)Cannot make a conclusion because the samples are different sizes

1. Classical music is piped throughout a jail with 150 inmates. Over the next month the number of serious fights between inmates drops by 5.27 fights per week with a standard deviation of 2.3 fights per week. What is the 95% confidence interval for the drop in the number of fights per week?

(a)(4.42, 6.12)

(b)(4.56, 5.98)

(c)(4.90, 5.64)

(d)(4.96, 5.58)

(e)(5.03, 5.51)

1. A researcher wants to compare the time spent on homework by students who are on the honor roll with the time spent by students not on the honor roll. An SRS of 60 students on the honor roll found the sample mean to be 6 hours per week with a sample standard deviation of 2.7 hours. An SRS of 40 students not on the honor roll found the sample mean to be 3.5 hours with a sample standard deviation of 1.6 hours. What is the 95% confidence interval for the difference in study time between the two groups?

(a)(1.52, 3.48)

(b)(1.65, 3.35)

(c)(1.78, 3.22)

(d)(2.99, 4.01)

(e)(5.30, 6.70)

1. Two schools are tested for the basket weaving skills taught in a folk arts class. At a Tennessee school 24 students averaged 11.3 baskets in 240 hours with a standard deviation of 2.1 baskets. A New York school had its 27 students average 6 baskets in 240 hours with a standard deviation of 4 baskets. Are the two schools’ averages significantly different?

(a)no, the t-score is 6.02

(b)yes, the t-score is 6.02

(c)no, the t-score is 2.19

(d)yes, the t-score is 2.19

(e)yes, the t-score is 11.3

1. Suppose that two populations are sampled independently. The first sample was of size 6 with a sample variance of 18.2. The second sample was of size 11 with a variance of 20.6. What is the standard error needed for a confidence interval or a significance test?

(a)1.10

(b)1.86

(c)9.68

(d)2.10

(e)2.21

– Multiple Choice Practice 9 (S)

1. A company officer complains that the average long-distance telephone call charged to a certain department is $5.00. Wanting to defend the department, a clerk gathers data on a random sample of 10 calls. The mean is $3.95 with a standard deviation of $1.07. In which of the following intervals is the P-value located?

(a)P < .005