Mar 31, 2017

- Solve the problem.
**1.**Find the critical value of z_{α}_{/2 }that corresponds to a degree of confidence of 91%.- 1.34
- 1.70
- 1.75
- 1.645

**2.**The following confidence interval is obtained for a population proportion, p:

0.817 < p < 0.855

Use these confidence interval limit to find the point estimate, p̂.- 0.817
- 0.833
- 0.836
- 0.839

- Find the margin of error for the 95% confidence interval used to estimate the population proportion.
**3.**n = 186, x = 103- 0.0714
- 0.00260
- 0.0643
- 0.125

- Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
**4.**n = 158, x = 108; 95 percent- 0.611 < p < 0.756
- 0.610 < p < 0.758
- 0.625 < p < 0.743
- 0.626 < p < 0.742

- Find the minimum sample size you should use to assure that your estimate of p̂ will be within the required margin of error around the population p.
**5.**Margin of error: 0.002; confidence level: 93%, p̂ and q̂ are unknown.- 410
- 405
- 204,757
- 204,750

**6.**Margin of error: 0.07; confidence level: 95%; from a prior study, p̂ is estimated by the decimal equivalent of 92%.- 4
- 51
- 174
- 58

- Solve the problem.
**7.**61 randomly selected light bulbs were tested in a laboratory, 50 lasted more than 500 hours. Find a point estimate of the true proportion of all light bulbs that last more than 500 hours.- 0.803
- 0.180
- 0.450
- 0.820

- Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
**8.**When 343 college students are randomly selected and surveyed, it is found that 110 own a car. Find a 99% confidence interval for the true proportion of all college students who own a car.- 0.256 < p < 0.386
- 0.279 < p < 0.362
- 0.271 < p < 0.370
- 0.262 < p < 0.379

- Solve the problem.
**9.**A researcher is interested in estimation the proportion of voters who favor a tax on e-commerce. Based on a sample of 260 people, she obtains the following 99% confidence interval for the population proportion p:

0.113 < p < 0.171.

Which of the statements below is a valid interpretation of this confidence interval?**A:**There is a 99% chance that the true value of p lies between 0.113 and 0.171.**B:**If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, 99% of the time the true value of p would lie between 0.113 and 0.171.**C:**If many different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, in the long run 99% of the confidence intervals would contain the true value of p.**D:**If 100 different samples of size 250 were selected and, based on each sample, a confidence interval were constructed, exactly 99 of these confidence intervals would contain the true value of p.- D
- C
- B
- A

- Determine whether the given conditions justify using the margin of error E = z
_{α}_{/2}**10.**The sample size is n = 9, and σ is not known, and the original population is normally distributed.- No
- Yes

- Use the confidence level and sample data to find the margin of error E.
**11.**Systolic blood pressures for women aged 18–24: 94% confidence; n = 92, x̅ = 114.9 mm Hg, σ = 13.2 mm Hg.- 9.6 mm Hg
- 47.6 mm Hg
- 2.3 mm Hg
- 2.6 mm Hg

- Use the confidence level and sample data to find a confidence interval for estimation the population μ.
**12.**A group of 52 randomly selected students have a mean sore of 20.2 with a standard deviation of 4.6 on a placement test. What is the 90 percent confidence interval for the mean score, μ, of all students taking the test.- 18.7 < μ < 21.7
- 19.0 < μ < 21.5
- 18.6 < μ < 21.8
- 19.1 < μ < 21.3

- Use the margin of error, confidence level, and standard deviation σ to find the minimum sample size required to estimate an unknown population mean μ.
**13.**Margin of error: $100, confidence level: 95%, σ = $403.- 91
- 44
- 108
- 63

- Do one of the following, as appropriate:

(a) Find the critical value z_{α}_{/2};

(b) Find the critical value t_{α}_{/2};

(c) State that neither the normal nor the t distribution applies.**14.**99%; n = 17; σ is unknown; population appears to be normally distributed.- z
_{α}_{/2}_{ }= 2.583 - z
_{α}_{/2 }= 2.921 - z
_{α}_{/2}= 2.567 - z
_{α}_{/2}= 2.898

- z

- Find the margin of error.
**15.**99% confidence interval; n = 201; x̅ = 175; s = 21.- 6.0
- 4.6
- 8.2
- 3.9

- Use the given degree of confidence and sample data to construct a confidence interval for the population mean μ. Assume that the population has a normal distribution.
**16.**The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:

7.6 10.4 9.7 8.4 11.8

7.0 6.5 11.1 10.4 12.4

Determine a 95 percent confidence interval for the mean time for all players.- 8.00 < μ < 10.98
- 8.13 < μ < 10.93
- 8.03 < μ < 11.03
- 8.06 < μ < 11.00

- Solve the problem.
**17.**Find the critical value X^{2}_{L}corresponding to a sample size of 15 and a confidence level of 90 percent.- 31.319
- 23.685
- 29.141
- 21.064

- Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution.
**18.**College students’ annual earnings: 90% confidence; n = 9, x̅ = $3605, s = $800.- $629 < σ < $1044
- $505 < σ < $1764
- $486 < σ < $1566
- $540 < σ < $1533

- Find the appropriate minimum sample size.
**19.**You want to be 95% confident that the sample variance is within 40% of the population variance.- 14
- 11
- 56
- 224

- Use the give degree of confidence and sample data to find a confidence interval for the population standard deviation σ. Assume that the population has a normal distribution.
**20.**The football coach randomly selected ten players and timed how long each player took to perform a certain drill. The times (in minutes) were:

7 12 10 14 10

14 9 11 7 14

Find a 95 percent confidence interval for the population standard deviation σ.- (0.7, 2.2)
- (1.8, 4.5)
- (1.9, 4.5)
- (1.9, 4.9)

*Problems with solutions in Elementary Statistics — Estimating a Population Proportion, Estimating a Population Mean: σ Known, Estimating a Population Mean: σ Not Known, Estimating a Population Variance.***Directions:**

*Choose the correct answer for multiple-choice items.*

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