AP Statistics



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AP Statistics - Review for Chapter 22-23 Test

1. In a test for acid rain, an SRS of 49 water samples showed a mean pH level of 4.4 with a standard deviation of 0.35. Find a 90% confidence interval estimate for the mean pH level.

A. (4.39,4.41)

B. (4.32,4.48)

C. (4.08,4.72)

D. (4.05,4.75)

E. (3.82,4.98)

2. One gallon of gasoline is put in each of 30 test autos, and the resulting mileage figures are tabulated with [pic] and s=1.2. Determine a 95% confidence interval estimate of the mean mileage.

A. (28.46,28.54)

B. (28.42,28.58)

C. (28.05,28.95)

D. (27.36,29.64)

E. (27.3,29.7)

3. Two confidence interval estimates 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 the 95% level while the other is at the 99% level, which is which?

A. [pic](16.4,29.8) is the 95% level.

B. [pic](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 standard deviation.

4. Two 90% confidence interval estimates are obtained: I (28.5, 34.5) and II (30.3, 38.2).

a. If the sample sizes are the same, which has the larger standard deviation?

b. If the sample standard deviations are the same, which has the larger sample size?

A. a. I b. I

B. a. I b. II

C. a. II b. I

D. a. II b. II

E. More information is needed to answer these questions.

5. Suppose (25,30) is a 90% confidence interval estimate for a population mean (. Which of the following are true statements?

I. There is a .90 probability that ( is between 25 and 30.

II. If 100 random samples of the given size are picked and a 90% confidence interval estimate is calculated from each, then ( will be in 90 of the resulting intervals.

III. If 90% confidence intervals are calculated from all possible samples of the given size, ( will be in 90% of these intervals.

A. I and II

B. I and III

C. II and III

D. I, II and III

E. None of the above gives the complete set of true responses. See page 586

6. In a study aimed at reducing developmental problems in low-birth-weight babies, 347 infants were exposed to a special educational curriculum while 561 did not receive any special help. After 3 years the children exposed to the special curriculum showed a mean IQ of 93.5 with a standard deviation of 19.1; the other children had a mean IQ of 84.5 with a standard deviation of 19.9. Find a 95% confidence interval estimate for the difference in mean IQs of low-birth-weight babies who receive special intervention and those who do not.

A. 9.0 ( 2.60

B. 9.0 ( 4.42

C. 9.0 ( 6.24

D. 89.0 ( 19.5

E. 89.0 ( 39.0

7. Does socioeconomic status relate to age at time of HIV infection? For 274 high-income HIV-positive individuals the average age of infection was 33.0 years with a standard deviation of 6.3, while for 90 low-income individuals the average age was 28.6 years with a standard deviation of 6.3. Find a 90% confidence interval estimate for the difference in ages of high- and low-income people at the time of HIV infection.

A. 4.4 ( 0.963

B. 4.4 ( 1.26

C. 4.4 ( 2.51

D. 30.8 ( 2.51

E. 30.8 ( 6.3

8. An automotive company executive claims that a mean of 48.3 cars per dealership are being sold each month. A major stockholder believes this claim is high and runs a test by sampling 30 dealerships. What conclusion is reached if the sample mean is 45.4 cars with a standard deviation of 15.4?

A. There is sufficient evidence to prove the executive’s claim is true.

B. There is sufficient evidence to prove the executive’s claim is false.

C. The stockholder has sufficient evidence to reject the executive’s claim.

D. The stockholder does not have sufficient evidence to reject the executive’s claim.

E. There is not sufficient data to reach any conclusion.

9. Table: t* =1.341

Calculator: t* =1.34061

10. Table: t* =1.059

Calculator: t* =1.05932

Label the following problems as being a one-sample, matched-pairs, or two-sample for purposes of using t-procedures. Do this work on a separate sheet. Use formal and complete methodology when answering.

Problem #1 Problem type __One sample T-test for means__________

Let x be a random variable that represents hemoglobin count (HC) in grams per 100 ml of whole blood. The normal hemoglobin count should be 14 for healthy adult women. Suppose that a female patient has taken 12 laboratory blood tests in the past year. The HC data sent to the patient’s doctor were:

19 23 15 21 18 16 14 20 19 16 18 21

(a) Does this information indicate that the population average HC for this patient is higher than

14? Use[pic]. t = 5.5432 p-value = .0001 reject Ho

(b) Construct a 90% confidence interval of the mean HC. What does this interval tell you?

(16.93 , 19.74) evidence that µ > 14

Problem #2 Problem type ___Matched-pairs T-test for Means____________

Are America’s top CEOs really worth all that money? One way to answer this question is to look at

row B, the annual company percentage in revenue, versus row A, the CEO’s annual percentage

salary increase in that same company. A random sample of companies yields the following data:

A |24 |23 |25 |18 |6 |4 |21 |37 | |B |21 |25 |20 |14 |-4 |19 |15 |30 | |

(a) Do these data indicate that the population mean percentage increase in corporate

revenue (row B) is different from the population mean percentage increase in CEO’s salary?

(b) Construct a 95% confidence interval of the difference between percentage increase of

corporate revenue and percentage increase in CEO’s salary. Interpret this interval.

Not independent so we will deal with these in Ch 24….

Problem #3 Problem type ___ 2-Sample T-test for Means_____________

A Pennsylvania study concerning preference for outdoor activities used a questionnaire with a 6-point Likert-like response in which 1 designated “not important” and 6 designated “extremely important”. A random sample of 122 adults was asked about lake fishing as an outdoor activity. The mean response was 4.3 with standard deviation of 1.3. Another random sample of 104 adults was asked about stream fishing as an outdoor activity. For this group, the mean response was 4.0 with s = 1.3.

(a) Does this indicate that the population mean preference for lake fishing is greater than the

population mean preference for stream fishing? Use a 5% level of significance.

t = 1.729 p-value = .0426 Reject Ho there is evidence to support µ1 > µ2

(b) Construct a 99% confidence interval of the mean difference of preference for lake fishing to

preference for stream fishing. Interpret this interval.

(-.1508 , .7508) Zero is captured in interval there is no evidence to support µ1 > µ2

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