Chapter 6 quiz 1 c 087 z c 151 2 0723 0749 e 0013 p

Chapter 6 Quiz
1. C = 0.87;
Z
c
= 1.51
2. (0.723, 0.749)
- E = 0.013
-
^ p = 0.736
3. You construct a 95% confidence interval for a population mean using a random sample. The
confidence interval is 24.9 <
μ
< 31.5. Is the probability that
μ
is in this interval 0.95? No.
With 95% confidence, the mean is in the interval (24.9, 31.5).
4. It is necessary to check that n
^ p≥
5 and n
^ q≥ 5
, because if either of the values are less than 5,
the distribution may not be normally distributed, thus
Z
c
cannot be used to calculate the
confidence interval.
5. In a survey of 2275 adults, 729 say that they believe in UFOs. A 90% confidence interval for the
population proportion is (0.304, 0.336). With 90% confidence, it can be said that the population of
adults who believe in UFOs is between the endpoints of the given confidence interval.
6. A biologist reports a confidence interval of (4.3, 5.5) when estimating the mean height (in
centimeters) of a sample of seedlings.
- The estimated margin of error is 0.6
- The sample mean is 4.9
7.
- The sampling error is -0.33
8. A researcher wishes to estimate, with 90% confidence, the population proportion of adults who think
Congress is doing a good or excellent job. Her estimate must be accurate within 2% of the true
proportion
A.) The minimum sample size needed assuming that no prior information is available: n = 1692, 1691,
1681, 1702
B.) The minimum sample size needed using a prior study found that 36% of the respondents said that
they think Congress is doing a good or excellent job: n = 1559
C.) Having an estimate of the population proportion reduces the minimum sample size needed.
9. Confidence level c = 0.90 and sample size n = 27.
t
c
= 1.706
10. (3.77, 6.93)
- The sample mean is 5.35
- The margin of error is 1.58
11. Let p be the population proportion. In a survey of 1185 adults from country A, 202 said that they were
not confident that the food they eat in country A is safe.
- The point estimate for p,
^ p,is 0.170
- The point estimate for q,
^ q,is 0.830
12. In a survey of 1120 adults from country A, 131 said that they were not confident that the food they
eat in country A is safe.
- The point estimate for p,
^ p,is 0.117
- The point estimate for q,
^ q,is 0.883
13. Confidence level c = 0.99 and sample size n = 18.
T
C
= 2.898
14. (0.670, 0.698)
- E = 0.014
-
^ p = 0.684
53

15. A biologist reports a confidence interval of (4.2, 5.2) when estimating the mean height (in
centimeters) of a sample of seedlings.
- The estimated margin of error is 0.5
- The sample mean is 4.7
16. The sampling error is -0.44
17. In a survey of 2336 adults, 724 say they believe in UFOs.
A.) A 99% confidence interval for the population proportion is (0.285, 0.335)
B.) With 99% confidence, it can be said that the population proportion of adults who believe in UFOs
is between the end points of the given confidence interval.
18. You construct a 95% confidence interval for a population mean using a random sample. The
confidence interval is 24.9 <
μ
< 31.5. Is the probability that
μ
is in this interval 0.95?
- No. With 95% confidence, the mean is in the interval (24.9, 31.5)
19. (3.45, 8.13)
- The sample mean is 5.79
- The margin of error is 2.34
20. C = 0.97
-
z
c
= 2.17
21. A researcher wishes to estimate, with 99% confidence, the population proportion of adults who think
Congress is doing a good or excellent job. Her estimate must be accurate within 5% of the true
proportion.