AP Statistics… Confidence Intervals Review I
1) Changing from a 95% confidence interval estimate to a 99%
confidence interval estimate, with all other things being equal,
a)increases the interval size by 4%
b)decrease the interval size by 4%
c)increases the interval size by 31%
d)decreases the interval size by 31%
e)This question cannot be answered without knowing the sample size.
2) The 99.7% confidence interval for the mean length of frog jumps is (12.64 cm, 14.44 cm). Which of the following statements is a correct interpretation of 99.7% confidence?
a)Of the total number of frogs in your area of the country, 99.7% can jump between 12.64 cm and 14.44 cm.
b)There’s a 99.7% chance that the mean length of frog jumps falls between 12.64 cm and 14.44 cm.
c)If we were to repeat this sampling many times, 99.7% of the confidence intervals we could construct would contain the true population mean.
d)99.7% of the confidence intervals we could construct after repeated sampling would go from 12.64 cm to 14.44 cm.
e)There’s a 99.7% chance that any particular frog I catch can jump between 12.64 cm and 14.44 cm.
3) One month the actual unemployment rate in France was 13.4%. If during that month you took a survey of 100 Frenchmen and constructed a confidence interval estimate of the unemployment rate, which of the following would be true?
- The center of the interval was 13.4
- The interval contained 13.4
- A 99% confidence interval contained 13.4
a)I and II d) I, II, and III
b)I and III e) None of the above gives the
c)II and III complete set of true responses
4) In a test for acid rain, 49 water samples showed a mean pH level of 4.4. (Assume σ = 0.35) Find a 90% confidence interval for the mean pH level.
a)4.4 + 0.098d) 4.4 + 0.35
b)4.4 + 0.08225e) 4.4 + 0.1027
c)4.4 + 0.1288
5) Two confidence intervals from the same sample are (16.4, 29.8) and (14.3, 31.9). What is the sample mean, and if one estimate is at a 95% level while the other is at the 99% level, which is which?
a) : (16.4, 29.8) is the 95% level
b) : (16.4, 29.8) is the 99% level
c) It is impossible to completely answer this question without
knowing the sample size.
d) It is impossible to completely answer this question without
knowing the sample standard deviation.
e) It is impossible to completely answer this question without
knowing both the sample size and the standard deviation.
6) Hospital administrators wish to learn the average length of stay of all surgical patients. A statistician determines that, for a 95% confidence level of the average length of stay to be within + 0.5 days, 50 surgical patients’ records will have to be examined. How many records should be looked at to obtain a 95% confidence level to within + 0.25 days?
a)25d) 150
b)50e) 200
c)100
7) The number of accidents per day at a large factory is noted for each of 64 days with. (Assume σ = 1.52) With what degree of confidence can we assert that the mean number of accidents per day at the factory is between 3.20 and 3.96?
a)48%d) 95%
b)63%e) 99%
c)90%
8) Two 90% confidence intervals are obtained: I (28.5, 34.5) and II (30.3, 38.2). If the sample sizes are the same, which interval has the larger standard deviation? If the standard deviations are the same, which interval has the larger sample size?
a)I, I
b)I, II
c)II, I
d)II, II
e)More information is needed to answer these questions.
9) Direct mail advertisers send solicitations (junk mail) to thousands of potential customers in the hope that some will buy their product. Suppose a company wants to test the response to a new flyer, and sends it to 1000 randomly selected people. They get 123 orders.
a) Create a 90% confidence interval for the percentage of people the company contacts who may buy the product.
10) A newspaper reports that the governor’s approval rating stands at 65%. The article adds that the poll is based on a random sample of 972 adults and has a margin of error of 2.5%. What level of confidence did the pollsters use?
11) In preparing a report on the economy, we need to estimate the percentages of business that plan to hire additional employees in the next 60 days. How many randomly selected employers must we contact in order to create an estimate in which we are 98% confident with a margin of error of 5%?
12) Vitamin D, whether ingested as a dietary supplement or produced naturally when sunlight falls upon the skin, is essential for strong, healthy bones. A recent study of 2700 children randomly selected from all parts of England found 20% of them deficient in vitamin D. Compute a 96% confidence interval for the proportion of children in England with Vitamin D deficiency.