Question 1

What is a level 0.90 confidence interval?

Accepted Answer

A) Any interval with margin of error ± 0.90 
B) An interval computed from sample data with a method that produces an interval containing the true value of the parameter of interest with a probability of 0.90 
C) An interval with margin of error ± 0.90, which is also correct 90% of the time 
D) An interval computed from sample data by a method guaranteeing that the probability the interval computed contains the parameter of interest is 0.90 
A) Any interval with margin of error ± 0.90 
B) An interval computed from sample data with a method that produces an interval containing the true value of the parameter of interest with a probability of 0.90 
C) An interval with margin of error ± 0.90, which is also correct 90% of the time 
D) An interval computed from sample data by a method guaranteeing that the probability the interval computed contains the parameter of interest is 0.90 B

Question 2

The level of nitrogen oxides (NOx) in the exhaust of cars of a particular model varies Normally, with standard deviation σ= 0.05 gram per mile (g/mi). Government regulations call for NOx emissions no higher than 0.3 g/mi. A random sample of 12 cars of this particular model is taken and is found to have a mean NOx emission of 0.298 g/mi. What does it mean to say that we have "90% confidence" in this interval?

Accepted Answer

A) The probability that the population mean NOx emission μ is 0.298 is 90%. 
B) The probability that the margin of error equals σ is 90%. 
C) This interval was found using 90% of the data. 
D) This interval was found using a procedure that produces correct results 90% of the time. 
A) The probability that the population mean NOx emission μ is 0.298 is 90%. 
B) The probability that the margin of error equals σ is 90%. 
C) This interval was found using 90% of the data. 
D) This interval was found using a procedure that produces correct results 90% of the time. D

Question 3

A 95% confidence interval for the mean lead concentration in the urine of adult men working with lead (for smelting) is 8.22 to 11.98 micrograms per liter ( μ g/l). Which of the following is the correct interpretation for this confidence interval?

Accepted Answer

A) We are 95% confident that the sample mean lead concentration is between 8.22 and 11.98 μ g/l. 
B) We are 95% confident that the population mean lead concentration is between 8.22 and 11.98 μ g/l. 
C) There is a 95% chance that the mean lead concentration of another random sample from this population would be between 8.22 and 11.98 μ g/l. 
D) There is a 95% chance that a randomly selected man from this population would have a lead concentration between 8.22 and 11.98 μ g/l. 
A) We are 95% confident that the sample mean lead concentration is between 8.22 and 11.98 μ g/l. 
B) We are 95% confident that the population mean lead concentration is between 8.22 and 11.98 μ g/l. 
C) There is a 95% chance that the mean lead concentration of another random sample from this population would be between 8.22 and 11.98 μ g/l. 
D) There is a 95% chance that a randomly selected man from this population would have a lead concentration between 8.22 and 11.98 μ g/l. B

Question 4

A company manufactures U-100 insulin syringes designed to contain 1 milliliter (ml) of a solution containing insulin. The actual distribution of solution volumes in these syringes is Normal, with mean? and standard deviation ?= 0.05 ml. We randomly select 8 syringes and measure the volume of solution in each. The results of these 8 measurements (in ml) are as follows:
?
$$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline 1.05 & 1.04 & 1.06 & 1.01 & 0.98 & 0.98 & 1.03 & 0.99 \
\hline
\end{array}$$ Do these data give evidence that the true population mean solution volume is not 1 ml? Using a significance level of 0.05, what should you conclude?

Accepted Answer

A) The true population mean volume is proven to be 1 ml. 
B) There is significant evidence that the true population mean volume is not 1 ml. 
C) There is significant evidence that the true population mean volume is 1 ml. 
D) There is not enough evidence to say that the true population mean volume is not 1 m. 
A) The true population mean volume is proven to be 1 ml. 
B) There is significant evidence that the true population mean volume is not 1 ml. 
C) There is significant evidence that the true population mean volume is 1 ml. 
D) There is not enough evidence to say that the true population mean volume is not 1 m.

Question 5

A 99% confidence interval for the mean μ of a population is computed from a random sample and found to be 6 ± 3. What may we conclude from this estimate?

Accepted Answer

A) There is a 99% probability that μ is between 3 and 9. 
B) The true mean is 6 and the true margin of error is 3, both with 99% probability. 
C) If we took many, many additional random samples, and from each computed a 99% confidence interval for μ, approximately 99% of these intervals would contain μ. 
D) All of the above 
A) There is a 99% probability that μ is between 3 and 9. 
B) The true mean is 6 and the true margin of error is 3, both with 99% probability. 
C) If we took many, many additional random samples, and from each computed a 99% confidence interval for μ, approximately 99% of these intervals would contain μ. 
D) All of the above

Question 6

A company manufactures U-100 insulin syringes designed to contain 1 milliliter (ml) of a solution containing insulin. The actual distribution of solution volumes in these syringes is Normal, with mean? and standard deviation ?= 0.05 ml. We randomly select 8 syringes and measure the volume of solution in each. The results of these 8 measurements (in ml) are as follows
$$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline 1.05 & 1.04 & 1.06 & 1.01 & 0.98 & 0.98 & 1.03 & 0.99 \
\hline
\end{array}$$ Do these data give evidence that the true population mean solution volume is not 1 m1? The P-value for the appropriate null and alternative hypotheses corresponds to which of the following shaded areas?

Accepted Answer

A) 
  
B) 
  
C) 
  
D)    
A) 
  
B) 
  
C) 
  
D)

Question 7

Suppose the time that it takes for a certain infection to be cured with a drug is Normally distributed, with mean (in days) μ and standard deviation σ= 1 day. The drug manufacturer advertises that its medication works in 5 days, on average, but measurements on a random sample of 400 patients gave a mean infection time of x̄= 5.2 days. Is this evidence that the mean time to be cured is actually more than advertised? To answer this, test the following hypotheses at significance level α= 0.01:
H0: μ= 5 versus Ha: μ> 5
What should you conclude?

Accepted Answer

A) H0 should be rejected. 
B) H0 should not be rejected. 
C) Ha should be rejected. 
D) There is a 5% chance that the null hypothesis is true. 
A) H0 should be rejected. 
B) H0 should not be rejected. 
C) Ha should be rejected. 
D) There is a 5% chance that the null hypothesis is true.

Question 8

You conduct a statistical test of hypotheses and find that the null hypothesis is statistically significant at level α= 0.05. What may you conclude?

Accepted Answer

A) The test would also be significant at level α= 0.10. 
B) The test would also be significant at level α= 0.01. 
C) Both A and B are true. 
D) Neither A nor B is true. 
A) The test would also be significant at level α= 0.10. 
B) The test would also be significant at level α= 0.01. 
C) Both A and B are true. 
D) Neither A nor B is true.

Question 9

A company manufactures U-100 insulin syringes designed to contain 1 milliliter (ml) of a solution containing insulin. The actual distribution of solution volumes in these syringes is Normal, with mean? and standard deviation ?= 0.05 ml. We randomly select 8 syringes and measure the volume of solution in each. The results of these 8 measurements (in ml) are as follows:
?
$$\begin{array} { | l | l | l | l | l | l | l | l | } 
\hline 1.05 & 1.04 & 1.06 & 1.01 & 0.98 & 0.98 & 1.03 & 0.99 \
\hline
\end{array}$$ Do these data give evidence that the true population mean solution volume is not 1 m1? What is the appropriate null hypothesis for this test?

Accepted Answer

A) H0: ?= 0 
B) H0: ?= 1 
C) H0: ?= 1.0175 
D) H0:x?=1.0175 
A) H0: ?= 0 
B) H0: ?= 1 
C) H0: ?= 1.0175 
D) H0:x?=1.0175

Question 10

You measure the lifetime of a random sample of 25 rats that are exposed to 10 Sv of radiation (the equivalent of 1000 REM), for which the LD100 is 14 days. The sample mean is x̄= 13.8 days. Suppose that the lifetimes for this level of exposure follow a Normal distribution, with unknown mean μ and standard deviation σ= 0.75 day. What is the 95% confidence interval for μ based on these data?

Accepted Answer

A) 13.45 to 14.15 
B) 13.51 to 14.09 
C) 13.55 to 14.05 
D) 13.74 to 13.86 
A) 13.45 to 14.15 
B) 13.51 to 14.09 
C) 13.55 to 14.05 
D) 13.74 to 13.86

Question 11

An herbal medicine brand contains amounts of the active ingredient (in milligrams, mg) that vary normally from capsule to capsule. A quality control engineer assesses whether capsules of this brand contain less, on average, than the marketed amount of 10 mg. A random sample of 25 capsules finds a mean content of 9.2 mg per capsule. Which of the following options are the appropriate null and alternative hypotheses?

Accepted Answer

A) H0: μ= 10 versus Ha: μ0: μ= 10 versus Ha: μ≠10 
C) H0: μ= 9.2 versus Ha: μ≠9.2 
D) H0: μ= 9.2 versus Ha: μ< 10 
A) H0: μ= 10 versus Ha: μ0: μ= 10 versus Ha: μ≠10 
C) H0: μ= 9.2 versus Ha: μ≠9.2 
D) H0: μ= 9.2 versus Ha: μ< 10

Question 12

The level of nitrogen oxides (NOx) in the exhaust of cars of a particular model varies Normally, with standard deviation σ= 0.05 gram per mile (g/mi). Government regulations call for NOx emissions no higher than 0.3 g/mi. A random sample of 12 cars of this particular model is taken and is found to have a mean NOx emission of 0.298 g/mi. What is a 90% confidence interval for the mean NOx emission μ of this particular model?

Accepted Answer

A) 0.274 to 0.322 g/mi 
B) 0.272 to 0.324 g/mi 
C) 0.270 to 0.326 g/mi 
D) 0.266 to 0.330 g/mi 
A) 0.274 to 0.322 g/mi 
B) 0.272 to 0.324 g/mi 
C) 0.270 to 0.326 g/mi 
D) 0.266 to 0.330 g/mi

Question 13

An herbal medicine brand contains amounts of the active ingredient (in milligrams, mg) that vary normally from capsule to capsule. A quality control engineer assesses whether capsules of this brand contain different amounts, on average, than the marketed amount of 10 mg. A random sample of 25 capsules finds a mean content of 9.2 mg per capsule. Which of the following options are the appropriate null and alternative hypotheses?

Accepted Answer

A) H0: μ= 10 versus Ha: μ0: μ= 10 versus Ha: μ≠10 
C) H0: μ= 9.2 versus Ha: μ≠9.2 
D) H0: μ= 9.2 versus Ha: μ< 10 
A) H0: μ= 10 versus Ha: μ0: μ= 10 versus Ha: μ≠10 
C) H0: μ= 9.2 versus Ha: μ≠9.2 
D) H0: μ= 9.2 versus Ha: μ< 10

Question 14

Twenty-five patients at a large clinic volunteer to participate in a study focusing on weight loss. These 25 patients had a mean weight loss score of x̄= 4500 g over two weeks. Suppose we know that the standard deviation of the population of weight changes on this particular diet is σ= 100 g. The results of the study were widely critiqued. How could the researchers have improved the quality of their research?

Accepted Answer

A) By running the study for longer than two weeks 
B) By not using a volunteer sample 
C) By sampling fewer people to reduce variability 
D) None of the above 
A) By running the study for longer than two weeks 
B) By not using a volunteer sample 
C) By sampling fewer people to reduce variability 
D) None of the above

Question 15

A company manufactures U-100 insulin syringes designed to contain 1 milliliter (ml) of a solution containing insulin. The actual distribution of solution volumes in these syringes is Normal, with meanμ and standard deviation σ= 0.05 ml. We randomly select 8 syringes and measure the volume of solution in each, and ask if the resulting data give evidence that the true population mean solution volume is not 1 ml. Here is the software output from a one-sample z test on the data collected:
Variable &ensp; N &ensp; Mean &ensp; StDev &ensp; SE &ensp; Mean &ensp; 95% &ensp; CI &ensp; Z &ensp; P
Volumes &ensp; 8 1.0175 &ensp; 0.0320 &ensp; 0.0177 &ensp; (0.9829, 1.0521) &ensp; 0.99 &ensp; 0.322
​
What is the appropriate null hypothesis for this test?

Accepted Answer

A) H0: μ= 0 
B) H0: μ= 1 
C) H0: μ= 1.0175 
D) H0: x̄= 1.0175 
A) H0: μ= 0 
B) H0: μ= 1 
C) H0: μ= 1.0175 
D) H0: x̄= 1.0175

Question 16

What is the upper 0.01 critical value of the standard Normal distribution?

Accepted Answer

A) 1.645 
B) 2.054 
C) 2.326 
D) 2.576 
A) 1.645 
B) 2.054 
C) 2.326 
D) 2.576

Question 17

The distribution of total body protein in adult men with liver cirrhosis is approximately Normal, with standard deviation σ= 0.1 kg. Researchers found that the mean total body protein x̄ of a random sample of 67 adult men with liver cirrhosis is 10.3 kg. Based on these data, what is the margin of error for a 99% confidence interval for μ?

Accepted Answer

A) 0.004 kg 
B) 0.024 kg 
C) 0.031 kg 
D) 0.062 kg 
A) 0.004 kg 
B) 0.024 kg 
C) 0.031 kg 
D) 0.062 kg

Question 18

In formulating hypotheses for a statistical test of significance, the null hypothesis typically is

Accepted Answer

A) a statement of "no effect" or "no difference." 
B) the probability of observing the data you actually obtained. 
C) a statement that the data are all 0. 
D) 0.05. 
A) a statement of "no effect" or "no difference." 
B) the probability of observing the data you actually obtained. 
C) a statement that the data are all 0. 
D) 0.05.

Question 19

The scores of a certain population on the Wechsler Intelligence Scale for Children IV (WISC IV) are thought to be Normally distributed, with mean μ and standard deviation σ= 15. Bill is a child psychologist who obtains a simple random sample of 25 children from this population; each child is given the WISC IV. The mean of the 25 scores is x̄= 104.32. Based on these data, what is the margin of error for a 95% confidence interval for μ?

Accepted Answer

A) 1.18 
B) 4.94 
C) 5.88 
D) 6.99 
A) 1.18 
B) 4.94 
C) 5.88 
D) 6.99

Question 20

You measure the lifetime of a random sample of 25 rats that are exposed to 10 Sv of radiation (the equivalent of 1000 REM), for which the LD100 is 14 days. The sample mean is x̄= 13.8 days. Suppose that the lifetimes for this level of exposure follow a Normal distribution, with unknown mean μ and standard deviation σ= 0.75 day. You read a report that says, "On the basis of a random sample of 25 rats, a confidence interval for the true mean survival time extends from 13.45 days to 14.15 days." What is the confidence level for this interval?

Accepted Answer

A) 90% 
B) 95% 
C) 98% 
D) 99% 
A) 90% 
B) 95% 
C) 98% 
D) 99%

What is a level 0.90 confidence interval?

A 95% confidence interval for the mean lead concentration in the urine of adult men working with lead (for smelting) is 8.22 to 11.98 micrograms per liter ( μ g/l). Which of the following is the correct interpretation for this confidence interval?

A 99% confidence interval for the mean μ of a population is computed from a random sample and found to be 6 ± 3. What may we conclude from this estimate?

You conduct a statistical test of hypotheses and find that the null hypothesis is statistically significant at level α= 0.05. What may you conclude?

What is the upper 0.01 critical value of the standard Normal distribution?

In formulating hypotheses for a statistical test of significance, the null hypothesis typically is

Picturing Distributions With Graphs

Describing Quantitative Distributions With Numbers

Scatterplots and Correlation

Regression

Two-Way Tables

Samples and Observational Studies

Designing Experiments

Essential Probability Rules

Independence and Conditional Probabilities

The Normal Distributions

Discrete Probability Distributions

Sampling Distributions

Exercises

Inference About a Population Mean

Comparing Two Means

Inference About a Population Proportion

Comparing Two Proportions

The Chi-Square Test for Goodness of Fit

The Chi-Square Test for Two-Way Tables

Inference for Regression

One-Way Analysis of Variance: Comparing Several Means

More About Analysis of Variance: Follow-Up Tests and Two-Way Anova

Nonparametric Tests

Multiple and Logistic Regression

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Exam 13: Introduction to Inference

What is a level 0.90 confidence interval?

A 95% confidence interval for the mean lead concentration in the urine of adult men working with lead (for smelting) is 8.22 to 11.98 micrograms per liter ( μ g/l). Which of the following is the correct interpretation for this confidence interval?

A 99% confidence interval for the mean μ of a population is computed from a random sample and found to be 6 ± 3. What may we conclude from this estimate?

You conduct a statistical test of hypotheses and find that the null hypothesis is statistically significant at level α= 0.05. What may you conclude?

What is the upper 0.01 critical value of the standard Normal distribution?

In formulating hypotheses for a statistical test of significance, the null hypothesis typically is

Picturing Distributions With Graphs

Describing Quantitative Distributions With Numbers

Scatterplots and Correlation

Regression

Two-Way Tables

Samples and Observational Studies

Designing Experiments

Essential Probability Rules

Independence and Conditional Probabilities

The Normal Distributions

Discrete Probability Distributions

Sampling Distributions

Exercises

Inference About a Population Mean

Comparing Two Means

Inference About a Population Proportion

Comparing Two Proportions

The Chi-Square Test for Goodness of Fit

The Chi-Square Test for Two-Way Tables

Inference for Regression

One-Way Analysis of Variance: Comparing Several Means

More About Analysis of Variance: Follow-Up Tests and Two-Way Anova

Nonparametric Tests

Multiple and Logistic Regression

Filters