A random sample of 10 shipments of stick-on labels showed the following order sizes.

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A random sample of 19 lunch orders at Noodles and Company showed a mean bill of $12.83 with a standard deviation of $6.71. Find the 99 percent confidence interval for the mean bill of all lunch orders. (Round your answers to 4 decimal places.)

The 99% confidence interval is from to

References

Worksheet Difficulty: 1­Easy Learning Objective: 08­06 Know when to use Students t instead of z to estimate μ.

The Environmental Protection Agency (EPA) requires that cities monitor over 80 contaminants in their drinking water. Samples from the Lake Huron Water Treatment Plant gave the results shown here. Only the range is reported, not the mean (presumably the mean would be the midrange).

Substance MCLG Range Detected Allowable MCLG Origin of Substance

Chromium 0.40 to 0.61 100 Discharge from steel and pulpmills, natural erosion

Barium 0.004 to 0.015 2 Discharge from drilling wastes,metal refineries, natural erosion

Fluoride 1.06 to 1.15 4 Natural erosion, water additive, discharge from fertilizer and aluminum factories

MCLG = Maximum contaminant level goal

For each substance, estimate the standard deviation σ by assuming Uniform Distribution and Normal Distribution shown in Table 8.11 in Section 8.8. (Round your answers to 4 decimal places.) Uniform Distribution Normal Distribution Chromium Barium Fluoride

References

Worksheet Difficulty: 2­Medium Learning Objective: 08­09 Sample Size Determination for a Proportion

0.0606 0.035 0.0032 0.0018 0.026 0.015

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(a) A poll of 2,224 likely voters was conducted on the president’s performance. Approximately what margin of error would the approval rating estimate have? (Round your answer to 4 decimal places.)

Margin of error

(b) The poll showed that 48 percent approved the president’s performance. Construct a 90 percent confidence interval for the true proportion. (Round your answers to 4 decimal places.)

The 90% confidence interval to

(c) The percentage of all voters opposed is likely to be 50 percent.

Yes, the confidence interval contains .50 No, the confidence interval does not contain .50

References

Worksheet Difficulty: 2­Medium Learning Objective: 08­07 Construct a 90, 95, or 99 percent confidence interval for π.

Find the interval [ ] within which 95 percent of the sample means would be expected to fall, assuming that each sample is from a normal population.

(a) μ = 159, σ = 20, n = 44. (Round your answers to 2 decimal places.)

The 95% range is from to .

(b) μ = 1,036, σ = 25, n = 6. (Round your answers to 2 decimal places.)

The 95% range is from to .

(c) μ = 44, σ = 3, n = 20. (Round your answers to 3 decimal places.)

The 95% range is from to .

References

Worksheet Learning Objective: 08­03 State the Central Limit Theorem for a mean.

Difficulty: 1­Easy Learning Objective: 08­04 Explain how sample size affects the standard error.

The fuel economy of a 2011 Lexus RX 350 2WD 6 cylinder 3.5 L automatic 5−speed using premium fuel is a normally distributed random variable with a mean of μ = 26 MPG and a standard deviation of σ = 2.5

0.0205

0.423 0.458

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MPG.

(a)What is the standard error of , the mean from a random sample of 16 fill−ups by one driver? (Round your answer to 4 decimal places.)

Standard error of

(b)Within what interval would you expect the sample mean to fall, with 90 percent probability? (Round your answers to 4 decimal places.)

The interval is from to

References

Worksheet Learning Objective: 08­03 State the Central Limit Theorem for a mean.

Difficulty: 2­ Medium

Learning Objective: 08­04 Explain how sample size affects the standard error.

[The following information applies to the questions displayed below.] Concerns about climate change and CO2 reduction have initiated the commercial production of blends of

biodiesel (e.g., from renewable sources) and petrodiesel (from fossil fuel). Random samples of 32 blended fuels are tested in a lab to ascertain the bio/total carbon ratio.

(a) If the true mean is 0.913 with a standard deviation of 0.004, within what interval will 98 percent of the sample means fall? (Round your answers to 4 decimal places.)

The interval is from to

Hint #1

References

Worksheet Learning Objective: 08­03 State the Central Limit Theorem for a mean.

Difficulty: 2­ Medium

Learning Objective: 08­04 Explain how sample size affects the standard error.

0.625

24.972 27.028

Hints

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(b) If the true mean is 0.913 with a standard deviation of 0.004, what is the sampling distribution of ?

rev: 09_10_2012, 06_05_2013_QC_31318

Exactly Normal with μ = 0.913 and σ = 0.004.

Approximately Normal with μ = 0.913 and σ = 0.004.

Exactly Normal with μ = 0.913 and

Approximately Normal with μ = 0.913 and

Hint #1

References

Multiple Choice Learning Objective: 08-03 State the Central Limit Theorem for a mean.

Difficulty: 2-Medium Learning Objective: 08-04 Explain how sample size affects the standard error.

(c) Which theorem did you use to answer part (b)?

Pythagorean Theorem

Law of Large Numbers

Chebyshev's Theorem

Central Limit Theorem

Hint #1

References

Multiple Choice Learning Objective: 08-03 State the Central Limit Theorem for a mean.

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Difficulty: 2-Medium Learning Objective: 08-04 Explain how sample size affects the standard error.

[The following information applies to the questions displayed below.] Use the sample information = 34, σ = 4, n = 10 to calculate the following confidence intervals for μ assuming the sample is from a normal population.

(a) 90 percent confidence. (Round your answers to 4 decimal places.)

The 90 percent confidence interval is from to

References

Worksheet Difficulty: 1­Easy Learning Objective: 08­05 Construct a 90, 95, or 99 percent confidence interval for μ.

(b) 95 percent confidence. (Round your answers to 4 decimal places.)

The 95 percent confidence interval is from to

References

Worksheet Difficulty: 1­Easy Learning Objective: 08­05 Construct a 90, 95, or 99 percent confidence interval for μ.

(c) 99 percent confidence. (Round your answers to 4 decimal places.)

The 99 percent confidence interval is from to

References

Worksheet Difficulty: 1­Easy Learning Objective: 08­05 Construct a 90, 95, or 99 percent confidence interval for μ.

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(d) Describe how the intervals change as you increase the confidence level.

The interval gets narrower as the confidence level increases.

The interval gets wider as the confidence level increases.

The interval stays the same as the confidence level increases.

The interval gets wider as the confidence level decreases.

References

Multiple Choice Difficulty: 1-Easy Learning Objective: 08-05 Construct a 90, 95, or 99 percent confidence interval for μ.

[The following information applies to the questions displayed below.]

A random sample of 135 items is drawn from a population whose standard deviation is known to be σ = 60. The sample mean is = 870.

(a) Construct an interval estimate for μ with 98 percent confidence. (Round your answers to 4 decimal places.)

The 98 percent confidence interval is from to .

rev: 04_04_2014_QC_47908

References

Worksheet Learning Objective: 08­04 Explain how sample size affects the standard error.

Difficulty: 1­Easy Learning Objective: 08­05 Construct a 90, 95, or 99 percent confidence interval for μ.

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(b)Construct an interval estimate for μ with 98 percent confidence, assuming that σ = 120. (Round your answers to 4 decimal places.)

The 98 percent confidence interval is from to .

References

Worksheet Learning Objective: 08­04 Explain how sample size affects the standard error.

Difficulty: 1­Easy Learning Objective: 08­05 Construct a 90, 95, or 99 percent confidence interval for μ.

(c) Construct an interval estimate for μ with 98 percent confidence, assuming that σ = 240. (Round your answers to 4 decimal places.)

The 98 percent confidence interval is from to .

References

Worksheet Learning Objective: 08­04 Explain how sample size affects the standard error.

Difficulty: 1­Easy Learning Objective: 08­05 Construct a 90, 95, or 99 percent confidence interval for μ.

(d) Describe how the confidence interval changes as σ increases.

The interval gets narrower as σ increases.

The interval stays the same as σ increases.

The interval gets wider as σ decreases.

The interval gets wider as σ increases.

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References

Multiple Choice Learning Objective: 08-04 Explain how sample size affects the standard error.

Difficulty: 1-Easy Learning Objective: 08-05 Construct a 90, 95, or 99 percent confidence interval for μ.

The Ball Corporation's beverage can manufacturing plant in Fort Atkinson, Wisconsin, uses a metal supplier that provides metal with a known thickness standard deviation σ = 0.000742 mm. If a random sample of 48 sheets of metal resulted in an = 0.2731 mm.

Calculate the 95 percent confidence interval for the true mean metal thickness. (Round your answers to 4 decimal places.)

The 95% confidence interval to

References

Worksheet Learning Objective: 08­04 Explain how sample size affects the standard error.

Difficulty: 2­ Medium

Learning Objective: 08­05 Construct a 90, 95, or 99 percent confidence interval for μ.

Find a confidence interval for μ assuming that each sample is from a normal population. (Round the value of t to 3 decimal places and your final answers to 2 decimal places.) (a) = 28, s = 5, n = 6, 90 percent confidence.

The 90% confidence interval is to (b) = 49, s = 4, n = 19, 99 percent confidence.

The 99% confidence interval is to (c) = 126, s = 15, n = 21, 95 percent confidence.

The 95% confidence interval is to

Hint #1

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References

Worksheet Difficulty: 1­Easy Learning Objective: 08­06 Know when to use Student’s t instead of z to estimate μ.

A random sample of 16 pharmacy customers showed the waiting times below (in minutes).

15 12 17 17 14 16 17 22 19 23 14 25 17 12 17 18

Click here for the Excel Data File

Find a 90 percent confidence interval for μ, assuming that the sample is from a normal population. (Round the value of t to 3 decimal places. Round your final answers to 3 decimal places.)

The 90% confidence interval to

References

Worksheet Difficulty: 2­Medium Learning Objective: 08­06 Know when to use Student’s t instead of z to estimate μ.

A random sample of 10 shipments of stick­on labels showed the following order sizes.

22,485 56,758 59,762 17,671 16,301 12,262 48,307 51,196 47,326 31,943

Click here for the Excel Data File

(a) Construct a 95 percent confidence interval for the true mean order size. (Round your answers to the nearest whole number.)

The 95 percent confidence interval to

(b) The confidence interval can be made narrower by

decreasing the sample size or increasing the confidence level. decreasing the sample size or decreasing the confidence level. increasing the sample size or decreasing the confidence level. increasing the sample size or increasing the confidence level.

References

Worksheet Difficulty: 2­Medium Learning Objective: 08­06 Know when to use Student’s t instead of z to estimate μ.

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Calculate the standard error. May normality be assumed? (Round your answers to 4 decimal places.)

Standard Error Normality (a) n = 29, π = 0.20 (Click to select) (b) n = 45, π = 0.18 (Click to select) (c) n = 90, π = 0.57 (Click to select) (d) n = 442, π = 0.001 (Click to select)

References

Worksheet Difficulty: 1­Easy Learning Objective: 08­07 Construct a 90, 95, or 99 percent confidence interval for π.

Find the margin of error for a poll, assuming that 95% confidence and = 0.1.

(a) n = 40 (Round your answer to 4 decimal places.)

Margin of error

(b) n = 160 (Round your answer to 4 decimal places.)

Margin of error

(c) n = 400 (Round your answer to 4 decimal places.)

Margin of error

(d) n = 1,600 (Round your answer to 4 decimal places.)

Margin of error

References

Worksheet Difficulty: 1­Easy Learning Objective: 08­07 Construct a 90, 95, or 99 percent confidence interval for π.

Of 54 bank customers depositing a check, 23 received some cash back.

(a) Construct a 90 percent confidence interval for the proportion of all depositors who ask for cash back. (Round your answers to 4 decimal places.)

The 90% confidence interval is from to

(b)May normality of p be assumed?

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Yes No

References

Worksheet Difficulty: 2­Medium Learning Objective: 08­07 Construct a 90, 95, or 99 percent confidence interval for π.

The city fuel economy of a 2009 Toyota 4Runner 2WD 6 cylinder 4 L automatic 5­speed using regular gas is a normally distributed random variable with a range 16 MPG to 21 MPG.

(a) Estimate the standard deviation using Method 3 (the Empirical Rule for a normal distribution). (Round your answer to 4 decimal places.)

Standard deviation

(b)What sample size is needed to estimate the mean with 90 percent confidence and an error of ± 0.25 MPG? (Enter your answer as a whole number (no decimals). Use a z­value taken to three decimal places in your calculations.)

Sample size

Hint #1

References

Worksheet Difficulty: 2­Medium Learning Objective: 08­09 Calculate sample size to estimate a mean or proportion.

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