# Standard normal probabilities

Questions 1 â?" 5: According to an article in The New York Times, 19.3% of New York City adults

smoked in 2003. Suppose that a survey is conducted this year. 8 out of 80 randomly chosen

New York City residents reply that they smoke. At a significance level of 0.05, test the claim that

the rate is still 19.3%.

1. Identify H0, Ha.

A) H0: p = 0.193 vs. Ha: p > 0.193

B) H0: p = 0.1 vs. Ha: p < 0.1

C) H0: p = 0.1 vs. Ha: p > 0.1

D) H0: p = 0.193 vs. Ha: p < 0.193

E) H0: p = 0.193 vs. Ha: p â? 0.193

2. Compute the test statistic. (2 decimal places)

A. 1.08 B. â?" 1.08 C. â?" 2.11 D. 2.11 E. None of the others

3. Compute the P-value. (4 decimal places)

A. 0.9826 B. 0.0174 C. 0.9890 D. 0.0348 E. None of the others

4. At a significance level of 0.05, does the sample provide sufficient evidence to reject that

the percent of smokers in New York City is still 19.3%?

A. yes B. no C. more information is needed to determine

5. If the actual rate is 23.1%, what type of error does it introduce?

A. Type I Error B. Type II Error C. No Error

Questions 6 â?" 10: A recent study reveals that 64 out of 100 Americans prefer to live away from

cities. At a significance level of 0.01, does the sample show strong evidence that more than half

of all Americans prefer to live away from cities?

6. Identify H0, Ha.

A) H0: p = 0.5 vs. Ha: p > 0.5

B) H0: p = 0.5 vs. Ha: p < 0.5

C) H0: p = 0.5 vs. Ha: p â? 0.5

D) H0: p â? 0.5 vs. Ha: p = 0.5

E) H0: p â? 0.5 vs. Ha: p < 0.5

7. Compute the test statistic. (2 decimal places)

A. â?" 2.80 B. 2.80 C. â?" 2.34 D. 2.34 E. None of the others

8. Compute the P-value. (4 decimal places)

A. 0.0037 B. 0.0026 C. 0.9974 D. 0.9963 E. None of the others

9. At a significance level of 0.01, does the sample provide sufficient evidence to support

that more than half of all Americans prefer to live away from cities?

A. yes B. no C. more information is needed to determine

10. If the actual proportion is 0.5, what type of error does it introduce?

A. Type I Error B. Type II Error C. No Error

Questions 11 â?" 15: An article reported that the birth ratio of girls to boys in China is 100:114

(46.7% girls). Suppose you don't believe the reported figure. You conduct a study. In the study,

you count the number of girls and boys born in 150 randomly selected recent births. There are

60 girls and 90 boys. Based on your study, do you think that the percent of girls born in China is

less than 46.7%, at a significance level of 0.05?

11. Identify H0, Ha

A) H0: p = 0.467 vs. Ha: p > 0.467

B) H0: p = 0.467 vs. Ha: p < 0.467

C) H0: p = 0.467 vs. Ha: p â? 0.467

D) H0: p â? 0.4 vs. Ha: p = 0.4

E) H0: p â? 0.4 vs. Ha: p < 0.4

12. Compute the test statistic. (2 decimal places)

A. 2.68 B. â?" 2.68 C. 1.64 D. â?" 1.64 E. None of the others

13. Compute the P-value. (4 decimal places)

A. 0.0618 B. 0.0096 C. 0.0505 D. 0.9495 E. None of the others

14. At a significance level of 0.05, does the sample provide sufficient evidence to support

your claim?

A. yes B. no C. more information is needed to determine

15. If the actual percentage is 45.2%, what type of error does it introduce?

A. Type I Error B. Type II Error C. No Error

Questions 16 â?" 20: An organization thinks that teenagers spend an average of more than 4.5

hours per week on the telephone. A random sample of 15 randomly chosen teenagers was

surveyed. The sample mean was 5.5 hours with a sample standard deviation of 2.0 hours. At a

significance level of 0.1, test the organization's claim.

16. Identify H0, Ha.

A) H0: ? = 5.5 vs. Ha: ? < 5.5

B) H0: ? = 4.5 vs. Ha: ? < 4.5

C) H0: ? = 4.5 vs. Ha: ? > 4.5

D) H0: ? = 5.5 vs. Ha: ? > 5.5

E) H0: ? = 5.5 vs. Ha: ? â? 5.5

17. Compute the test statistic. (3 decimal places)

A. 1.936 B. â?" 1.936 C. â?" 2.324 D. 2.324 E. None of the others

18. Find the range of the P-value.

A) less than 0.001

B) between 0.01 and 0.025

C) between 0.005 and 0.01

D) between 0.025 and 0.05

E) between 0.001 and 0.005

19. At a significance level of 0.1, does the sample provide sufficient evidence to support the

organizationâ??s claim?

A. yes B. no C. more information is needed to determine

20. If the actual average hours spent on the telephone by teenagers is 4.3 hours, what type

of error does it introduce?

A. Type I Error B. Type II Error C. No Error

Questions 21 â?" 25: A study was done to test the claim that the average cost of a daily

newspaper is 35 cents. A random sample of 31 newspapers yields a mean of 30 cents. Assume

that the population standard deviation of the cost of a daily newspaper is 9 cents. At a

significance level of 0.05, test the above claim.

21. Identify H0, Ha.

A) H0: ? = 30 vs. Ha: ? > 30

B) H0: ? = 30 vs. Ha: ? â? 30

C) H0: ? = 35 vs. Ha: ? â? 35

D) H0: ? â? 30 vs. Ha: ? = 30

E) H0: ? â? 35 vs. Ha: ? = 35

22. Compute the test statistic. (2 decimal places)

A. â?" 3.81 B. â?" 3.09 C. 3.09 D. 3.81 E. None of the others

23. Find the P-value.

A. 0.9990 B. 0.0090 C. 0.0505 D. 0.0010 E. None of the others

24. At a significance level of 0.05, does the sample provide sufficient evidence to reject the

claim that the average cost of a daily newspaper is 35 cents?

A. yes B. no C. more information is needed to determine

25. If the actual mean price of a daily newspaper is 32 cents, what type of error does it

introduce?

A. Type I Error B. Type II Error C. No Error