AP Statistics Chapter 10 Pre-testName:
Directions: Work on these sheets. Answer completely, but be concise.A normal probability table is attached.
Part 1: Multiple Choice. Circle the letter corresponding to the best answer.
1.You want to compute a 96% confidence interval for a population mean. Assume that the population standard deviation is known to be 10 and the sample size is 50. The value of z* to be used in this calculation is
(a)1.960
(b) 1.645
(c)1.7507
(d)2.0537
(e)None of the above. The answer is .
2.You want to estimate the mean SAT score for a population of students with a 90% confidence interval. Assume that the population standard deviation is = 100. If you want the margin of error to be approximately 10, you will need a sample size of
(a) 16
(b) 271
(c) 38
(d) 1476
(e) None of the above. The answer is .
3.A significance test gives a P-value of 0.04. From this we can
(a)Reject H0 at the 1% significance level
(b)Reject H0 at the 5% significance level
(c) Say that the probability that H0 is false is 0.04
(d)Say that the probability that H0 is true is 0.04
(e) None of the above. The answer is .
4.A significance test was performed to test the null hypothesis H0: µ = 2 versus the alternative Ha: µ 2. The test statistic is z = 1.40. The P-value for this test is approximately
(a)0.16
(b)0.08
(c)0.003
(d)0.92
(e)0.70
(f) None of the above. The answer is .
5. You have measured the systolic blood pressure of a random sample of 25 employees of a
company located near you. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122, 138). Which of the following statements gives a valid interpretation of this interval?
(a)Ninety-five percent of the sample of employees has a systolic blood pressure between 122 and 138.
(b)Ninety-five percent of the population of employees has a systolic blood pressure between 122 and 138.
(c)If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure.
(d)The probability that the population mean blood pressure is between 122 and 138 is .95.
(e)If the procedure were repeated many times, 95% of the sample means would be between 122 and 138.
(f)None of the above. The answer is .
6.An analyst, using a random sample of n = 500 families, obtained a 90% confidence interval for mean monthly family income for a large population: ($600, $800). If the analyst had used a 99% confidence coefficient instead, the confidence interval would be:
(a)Narrower and would involve a larger risk of being incorrect
(b)Wider and would involve a smaller risk of being incorrect
(c)Narrower and would involve a smaller risk of being incorrect
(d)Wider and would involve a larger risk of being incorrect
(e)Wider but it cannot be determined whether the risk of being incorrect would be larger or smaller
8. The value of z* required for a 70% confidence interval is
(a)-0.5244
(b) 1.036
(c) 0.5244
(d) 0.6179
(e) The answer can’t be determined from the information given.
( f ) None of the above. The answer is ______.
9. A significance test allows you to reject a hypothesis H0 in favor of an alternative Ha at the 5% level of significance. What can you say about significance at the 1% level?
(a)H0 can be rejected at the 1% level of significance.
(b)There is insufficient evidence to reject H0 at the 1% level of significance.
(c)There is sufficient evidence to accept H0 at the 1% level of significance.
(d)Ha can be rejected at the 1% level of significance.
(e)The answer can’t be determined from the information given.
10. A 95% confidence interval for the mean of a population is computed from a random sample and found to be 9 ± 3. We may conclude that
(a)There is a 95% probability that is between 6 and 12.
(b)There is a 95% probability that the true mean is 9 and a 95% chance the true margin of error is 3.
(c)If we took many, many additional random samples and from each computed a 95% confidence interval for , approximately 95% of these intervals would contain .
(d)If we took many, many additional random samples and from each computed a 95% confidence interval for , 95% of them would cover the values from 6 to 12.
(e)All of the above.
11. Which of the following are correct?
I.The power of a significance test depends on the alternative value of the parameter.
II.The probability of a Type II error is equal to the significance level of the test.
III. Type I and Type II errors only make sense when a significance level has been chosen in advance.
(a)I and II only
(b)I and III only
(c) II and III only
(d)I, II, and III
(e)None of the above gives the complete set of true responses.
12. In a test of H0: µ = 100 against Ha: µ 100, a sample of size 80 produces z = 0.8 for the value of the test statistic. The P-value of the test is thus equal to:
(a)0.20
(b)0.40
(c)0.29
(d)0.42
(e)0.21
13. To assess the accuracy of a laboratory scale, a standard weight that is known to weigh 1 gram is repeatedly weighed a total of n times and the mean of the weighings is computed. Suppose the scale readings are normally distributed with unknown mean and standard deviation
= 0.01 g. How large should n be so that a 95% confidence interval for has a margin of error of ± 0.0001?
(a)100
(b)196
(c)27061
(d)10000
(e)38416
14. A 95% confidence interval for µ is calculated to be (1.7, 3.5). It is now decided to test the hypothesis H0: µ = 0 vs. Ha: µ 0 at the = 0.05 level, using the same data as was used to construct the confidence interval.
(a)We cannot test the hypothesis without the original data.
(b)We cannot test the hypothesis at the = 0.05 level since the = 0.05 test is connected to the 97.5% confidence interval.
(c)We can only make the connection between hypothesis tests and confidence intervals if the sample sizes are large.
(d)We would reject H0 at level = 0.05.
(e)We would accept H0 at level = 0.05.
15. Suppose that the population of the scores of all high school seniors who took the SAT Math test this year follows a normal distribution with mean and standard deviation = 100. You read a report that says, “on the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for is 512.00 ± 25.76.” The confidence level for this interval is
(a)90%.
(a)95%.
(b)99%.
(c)99.5%.
(e)over 99.9%.
16. In a statistical test for the equality of a mean, such as H0 µ = 10, if = 0.05,
(a)95% of the time we will make an incorrect inference
(b)5% of the time we will say that there is a real difference when there is no difference
(c)5% of the time we will say that there is no real difference when there is a difference
(d)95% of the time the null hypothesis will be correct
(e)5% of the time we will make a correct inference
17. I collect a random sample of size n from a population and from the data collected compute a 95% confidence interval for the mean of the population. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data?
(a)Use a larger confidence level.
(b)Use a smaller confidence level.
(c)Use the same confidence level, but compute the interval n times. Approximately 5% of these intervals will be larger.
(d)Increase the sample size.
(e)Nothing can guarantee absolutely that you will get a larger interval. One can only say the chance of obtaining a larger interval is 0.05.
18. Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of $2, and the amount spent has a normal distribution with a standard deviation = $30. The number of observations required is closest to
(a)25.
(b)30.
(c)608.
(d)609.
(e)865.
19. Consider the following graph of the mean yield of barley in 1980, 1984, and 1988 along with a 95% confidence interval.
Which of the following is INCORRECT?
(a)Since the confidence intervals for 1984 and 1980 have considerable overlap, there is little evidence that the sample means differ.
(b)Since the confidence intervals for 1988 and 1980 do not overlap, there is good evidence that their respective population means differ.
(c)The sample mean for 1984 is about 195 g/400m2.
(d)The sample mean for 1988 is less than the sample mean for 1984.
(e)The estimate of the population mean in 1988 is more precise than that for 1980 since the confidence interval for 1988 is narrower than that for 1980.
20. Which two sets of hypotheses are the only two of the following that are not flawed?
- Ho: > 12Ha: 12
- Ho: 12Ha: < 12
- Ho: < 12Ha: 12
- Ho: 12Ha: > 12
- Ho: = 12Ha: 12
Part 2: Free Response
Communicate your thinking clearly and completely.
21.It is believed that the average amount of money spent per U.S. household per week on food is about $98, with standard deviation $10. A random sample of 100 households in a certain affluent community yields a mean weekly food budget of $100. We want to test the hypothesis that the mean weekly food budget for all households in this community is higher than the national average.
(a)Perform a significance test at the significance level. Follow the inference toolbox.
(b)Describe a Type I error in the context of this problem. What is the probability of making a Type I error?
(c)Describe a Type II error in the context of this problem. Give two ways to reduce the probability of a Type II error.
22.There are many ways to measure the reading ability of children. Research designed to improve reading performance is dependent on good measures of the outcome. One frequently used test is the DRP or Degree of Reading Power. A researcher suspects that the mean score µ of all third graders in Henrico County Schools is different from the national mean, which is 32. To test her suspicion, she administers the DRP to an SRS of 44 Henrico County third-grade students. Their scores were:
4026391442182543462719
4719263534154440383146
5225353533293441492852
4735482233415127145445
(a)You may assume the standard deviation of scores in Henrico County Schools is known to be = 11. Construct a 92% confidence interval for the mean DRP score in Henrico County Schools. Follow the Inference Toolbox.
(b)Use the confidence interval you constructed in (a) to test the researcher’s claim. Be sure to state your hypotheses and your significance level.
23. You measure the weights of 24 male runners. You do not actually choose an SRS, but you are willing to assume that these runners are a random sample from the population of male runners in your town or city. Here are their weights in kilograms:
67.861.963.053.162.359.755.458.9
60.969.263.768.364.765.656.057.8
66.062.953.665.055.860.469.361.7
Suppose that the standard deviation of the population is known to be = 4.5 kg.
(a)Construct a 95% confidence interval for , the mean of the population from which the sample is drawn. Do NOT follow the Inference Toolbox. Simply report the interval.
(b)Explain the meaning of 95% confidence in part (a).
(c)Based on this confidence interval, does a test of
kg
kg
reject at the 5% significance level? Justify your answer.
Chapter 101