Download ap statistics – chapter 10 review

AP STATISTICS – CHAPTER 10 REVIEW
_____1. You want to compute a 96% confidence interval for a population mean. Assume that σ = 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
_____2. You want to estimate the mean SAT score for a population of students with a 90% confidence
interval. Assume that σ = 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
_____3. A significance test gives a p-value of 0.04. From this we can
(a) Reject Ho at the 1% significance level
(b) Reject Ho at the 5% significance level
(c) Say that the probability that Ho is false is 0.04
(d) Say that the probability that Ho is true is 0.04
_____4. In a test of Ho: 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
_____5. 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 μ and standard deviation σ = 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 μ is 512.00 ± 25.76.” The confidence level for this
interval is
(a) 90%
(b) 95%
(c) 99%
(d) 99.5%
(e) over 99.9%
_____6. A certain population follows a normal distribution with mean μ and standard deviation σ = 2.5.
You collect data and test the hypothesis Ho: μ = 1 and Ha: μ ≠ 1. You obtain a p-value of 0.022.
Which of the following is true?
(a) A 95% confidence interval for μ will include the value 1.
(b) A 95% confidence interval for μ will include the value 0.
(c) A 99% confidence interval for μ will include the value 1.
(d) A 99% confidence interval for μ will include the value 0.
_____7. The government claims that students earn an average of $4500 during their summer break. A
random sample of students gave a sample average of $3975 and a 95% confidence interval was found
to be $3525 < μ < $4425. This interval is interpreted to mean that:
(a) If the study were to be repeated many times, there is a 95% probability that the true average
summer earnings is not $4500 as the government claims.
(b) Because our specific confidence interval does not contain the value $4500, there is a 95%
probability that the true average summer earnings is not $4500.
(c) If we were to repeat our survey many times, then about 95% of all the confidence intervals will
contain the value $4500.
(d) If we repeat our survey many times, then about 95% of our confidence intervals will contain the
true value of the average summer earnings of students.
_____8. To determine the reliability of experts used in interpreting the results of polygraph
examinations in criminal investigations, 280 cases were studied. The results were:
TRUE STATUS
INNOCENT GUILTY
EXAMINER’S “INNOCENT” 131
15
DECISION
“GUILTY”
9
125
If the hypotheses were Ho: suspect is innocent vs. Ha: suspect is guilty, then we could estimate the
probability of making a Type II error as:
(a) 15/280
(b) 9/280
(c) 15/140
(d) 9/140
(e) 15/146
9. A student is helping another student learn about confidence intervals. He says to her, “I am 95%
confident that all of the test scores lie between 75 and 83”. Comment on his sentence.
10. When asked to explain the meaning of “the P-value was P = 0.03”, a student says, “This
means there is only a 3% chance that the null hypothesis is true.” Is this a correct explanation?
Explain.
11. Randomly selected statistics students participated in an experiment to test their ability to
determine when 1 min (60 seconds) has passed. Forty students yielded a mean of 58.3 sec.
(a) Assuming that σ = 9.5 sec, construct a 95% confidence interval and state in a sentence your
findings.
(b) Is it likely that students can determine when exactly 1 minute has passed?
(c) Find the sample size to have a margin of error no bigger than 2.
12. In the past, the mean score of the seniors at Valley High on the ACT college entrance exam has
been 20. This year a special course is offered, and all 53 seniors planning to take the ACT test
enroll in the course. The mean of their ACT scores is 22.1. The principal believes that the new
course has improved the students’ ACT scores. Assume that ACT scores vary normally with σ =
6. Test the principal’s claim at the 1% level by stating the null and alternative, drawing a picture,
stating the test statistics and p-value, whether you reject or retain, and finally a complete
sentence stating your conclusion. Based on your answer, what error could you have made?
13. The probability that a senior dares to cut Miss Biro’s class after Disney is 12%. This year Miss
Biro has 135 students. What is the probability that more than 17% will cut her class?
MULTIPLE CHOICE ANSWERS: D, B, B, D, C, C, D, C