Math 11-DC1

Math 153 REVIEW Name: _____________________________

4/06, Test 3A (PINK) Janice Dykacz

SHOW ALL WORK WHENEVER POSSIBLE AND/OR STATE THE ROUTINE YOU ARE USING ON YOUR CALCULATOR.

(10 points)

1. A random sample of 702 adult Americans is asked if they intend to file taxes electronically – yes or no. Two hundred and ninety-five persons say yes. Find a 95% confidence interval for the percent in the population of adults who would answer yes. Round answers to two decimal places and then write as percents.

Which routine are you using on the calculator? ________________________________

___________ TO __________

(10 points)

2. A government agency wants to take a poll in Baltimore regarding health issues. They want to estimate the percent of Baltimoreans who believe they are healthy using a 95% confidence interval with a margin of error of not more than 2%. No previous estimate of p is available. How many people should be sampled? Show all work

n = _______________

(10 points)

3. A business would like to estimate the average number of sick days an employee uses per year. How many employees should be surveyed if a 95% confidence interval will be used and if the margin of error should be no more than 0.5 day. Assume that the standard deviation of sick days used per year is 2.0. Find the appropriate sample size for this study. Show all work.

n = _______________

(20 points)

4. The subjects of a medical study of second-hand smoke are workers in food catering jobs. Cotinine levels are measured for the workers; the larger the cotinine level, the larger the concentration of poisonous substances inhaled, such as carbon monoxide. Assume that the cotinine levels for these workers are normally distributed.

a) For the 36 workers who were not exposed to second-hand smoke, the average cotinine level was 5 ng/ml, and the sample standard deviation was 1.7 ng/ml. Find a 90% confidence interval for the (population) mean amount of cotinine in this population. Round off to the nearest tenth.

Which routine are you using on the calculator? ________________________________

__________ TO __________

b) For the 10 workers who were exposed to second-hand smoke at work, the average cotinine level was 11 ng/ml, and the sample standard deviation was 2.2 ng/ml. Find a 90% confidence interval for the (population) mean amount of cotinine in this population. Round off to the nearest tenth.

Which routine are you using on the calculator? ________________________________

__________ TO __________

c) Do you think the population mean levels of cotinine are different in these two populations (those who are NOT exposed to second-hand smoke at work and those who are exposed at work)? ______. You MUST explain your answer.

(10 points)

5. A Physical Education teacher claims that the percent of females who are fans of figure skating is equal to 50%. At the 5% significance level, test her claim against the alternative that the percent of females who are fans of figure skating is not 50%. A random sample of 200 females is taken, and 136 say they are fans of figure skating.

H₀: ________________________

H_a: ________________________

Which routine are you using on the calculator? ____________________________________

1. a = _______

2. Test statistic(Round to 4 decimal places. ________________

p-value (Express in scientific notation – NO E notation) ____________________

3. Conclusion: ____________________________________________

(10 points)

6. The headlines say “Prepare Taxes or Visit Dentist? Poll shows Americans divided.”

When asked if they would rather go to the dentist or prepare their own taxes, 49 percent said they would rather go to the dentist.. Use the Minitab print-out below.

a) How many people were sampled? _______________

b) State the 95% confidence interval for the percent who would choose to go to the dentist. Round off to two decimal places and express as percents.

____________ TO _______________

c) What is the margin of error for this poll? ___________

___________________________________________________________________________

Welcome to Minitab, press F1 for help.

Test and CI for One Proportion

Test of p = 0.5 vs p not = 0.5

Sample X N Sample p 95% CI Z-Value P-Value

1 490 1001 0.489510 (0.458543, 0.520478) -0.66 0.507

___________________________________________________________________________

(10 points)

7. An auto manufacturer wants to test whether the mean miles per gallon of its new ECO auto is 40 miles per gallon or different from 40 miles per gallon.

Data: A random sample of 35 autos is taken. The sample mean is 41, and the sample standard deviation is 4.1. Test at the 1% significance level.

H₀: ________________________

H_a: ________________________

Which routine are you using on the calculator? ____________________________________

1. a = _______

2. Test statistic: (Round to 4 decimal places.) ________________

p-value (Round to 4 decimal places.) ____________________

3. Conclusion: ____________________________________________

(10 points)

8. A regulation for drinking water is that its lead content is less than or equal to15 ppb (parts per billion). Assume lead levels follow a normal distribution. The following data are obtained. Ten collections of water have a mean average lead level of 16 ppb with a sample standard deviation of 0.8 ppb. At the 5% signifcance level, test whether the mean lead level in the population is greater than 15 ppb.

H₀: ________________________

H_a: ________________________

Which routine are you using on the calculator? ____________________________________

1. a = _______

2. Test statistic: ________________

p-value: ____________________

3. Conclusion: ____________________________________________

9. Select the best answer. (4 points)

If the sample size of a poll is decreased (everything else remaining the same),

a) the margin of error decreases

b) the margin of error stays the same

c) the margin of error increases

d) the margin of error becomes negative

e) the sample size does NOT affect the margin of error

10. Select the best answer a) – e). (3 points)

The formula used to calculate a 99% Confidence Interval for a population percent is

a) d)

b) e)

11. Select the best answer. (3 points)

The value of the t-distribution used to calculate a 90% Confidence Interval based on 14 people is

a) 1.761 b) 1.771 c) 2.160 d) 2.977 e) 3.012

Math 153 ANSWER KEY TEST 3 FORM A

April, 2005

1) 1 Prop-z-interval n = 702, x = 295

.38371 TO .45674 .38 TO .46 38% to 46%

2) n = = = 2401

3) = = = 61.4656 or 62 (ONLY round up for sample size)

4) A) T-interval, n = 36, = 5, s = 1.7

(Can also use z-interval 4.5 TO 5.5)

t interval 4.5213 TO 5.4787 4.5 TO 5.5

B) T-interval. n = 10, =11, s = 2.2

9.7247 TO 12.275 9.7 TO 12.3

C) Yes, the confidence intervals do not overlap. We are (95%) confident that the population mean for those not exposed at work is less than the population mean for those exposed at work.

5) H₀ : p = 0.5

H_A: p 0.5