exam 3 review

The time needed for college students to complete a certain paper-and-pencil maze follows a Normal distribution with a mean of 30 seconds and a standard deviation of 3 seconds. You wish to see if the mean time m is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. Assume that s remains unchanged at 3 seconds. You decide to test the hypotheses H0: m = 30 versus Ha: m ≠ 30 at the 1% significance level. What is the range of x bar-values for which you will not reject H0?

A) (27.424, 32.576)

What is the value of the test statistic?

A) -2.5

Suppose X has the B(20, .5) distribution. Find the P(X < 10).

A) .412

A college basketball player is known to make 80% of his free throws. Over the course of the season, he will attempt 100 free throws. Assuming free-throw attempts are independent, what is the probability that he makes at least 90 free throws?

A) 0.0057

Birth weights of babies born to full-term pregnancies follow roughly a Normal distribution. At Meadowbrook Hospital, the mean weight of babies born to full-term pregnancies is 7 pounds with a standard deviation of 14 ounces (1 pound = 16 ounces). Dr. Watts (who works at Meadowbrook Hospital) has four deliveries (all for full-term pregnancies) coming up during the night. Assume that the birth weights of these four babies can be viewed as a simple random sample. What is the probability that all four babies will weigh more than 7.5 pounds?

A) 0.0065

A researcher plans to conduct a test of hypotheses at the 1% significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. What is the probability that the researcher will commit a Type I error?

A) 0.01

A manufacturer of a specific part used in the operation of a gas turbine engine is concerned because the part is designated as critical-to-quality (CQT) and is costly to produce. The process that is used to produce the part has been studied extensively and has been shown to be stable and predictable for some lengthy period of time. When the process is in the stable state, the crucial measurement on the CQT part is known to be Normally distributed with a mean of m = 1.58 centimeters and a standard deviation of s = 0.10 centimeters. In order to check on the status of the production process, a monitoring plan has been established, which requires that a sample of four manufactured parts should be selected at random each hour. If the mean (x bar) of the sample exceeds 1.71 centimeters, then the process is stopped and examined for possible problems, and then repairs are made to the process if needed. If, in fact, the process has changed and the process mean has shifted to m = 1.73, what is the probability that this rule regarding (x bar) will fail to detect the shift?

A) 0.3446

The scores of individual students on the American College Testing (ACT), college readiness assessment, have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students?

A) 1.0

Suppose X has the B(20, .5) distribution. What is the mean of X?

A) 10

What is the value of the statistic, p hat, that represents the proportion of women in California who have less than a high school education?

A) 3599/33,938

A study was done to compare the amount of time per day students at public and private universities spend on Facebook. The study was composed of 200 students from a private university and 300 students from a public university. The time that students at a private university spent on Facebook had a Normal distribution with a mean of 220 minutes and a standard deviation of 36 minutes. The time that students at a public university spent on Facebook had a Normal distribution with a mean of 200 minutes and standard deviation of 49 minutes. Students at a community college spend twice as much time on Facebook than students at a public university. What is the mean time that students at a community college spend on Facebook?

A) 400

It is estimated that 75% of all young adults between the ages of 18 and 35 do not have a landline in their homes and only use a cell phone at home. What is the proportion of young adults who do not own a landline?

A) 75%

You perform 1000 significance tests using a significance level, α, of 0.05. Assume that all of the null hypotheses for the 1000 significance tests are true. How many of the 1000 significance tests would not result in a Type 1 error?

A) 950

A one-question survey is to be distributed to a random sample of 1500 adults in Ohio. The question asks if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let p hat denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. What is the probability that p hat will be more than 50%?

A) Less than 0.0001

It is claimed that 55% of marriages in the state of California end in divorce within the first 15 years. A large study was started 15 years ago and has been tracking hundreds of marriages in the state of California. Suppose 100 marriages are randomly selected. What is the probability that less than 20 of them ended in a divorce?

A) Less than 0.0001

The level of calcium in the blood of healthy young adults follows a Normal distribution with a mean of m = 10 milligrams per deciliter and a standard deviation of s = 0.4 milligrams. A clinic measures the blood calcium of 100 healthy pregnant young women at their first visit for prenatal care. The mean of these 100 measurements is x bar = 9.8. Is this evidence that the mean calcium level in the population of healthy pregnant young women is less than 10? To answer this, test the hypotheses H0: m = 10 versus Ha: m < 10 at the 5% significance level. What is the value of the P-value?

A) Less than 0.0002

Suppose X has the B(20, .5) distribution. A Normal approximation for X is

A) N(10, 2.236).

When the mean is large, Poisson probabilities can be approximated using the _______ distribution.

A) Normal

______ significance determines whether the observed differences between the observed sample mean and population mean are beneficial.

A) Practical

What is needed to compute a margin of error?

A) Sample size, standard deviation, and z*

What is needed to compute a sample size, n, to obtain a confidence interval with a specified margin of error, m?

A) Standard deviation, m, and z*

True or False. Since confidence intervals are based on the sampling distribution of the sample mean, it is possible to form confidence intervals when sampling from slightly skewed distributions due to the central limit theorem.

A) True

The significance level, a, is also the probability of committing a _________ error.

A) Type I

Based on the results, the null hypothesis would ______ at the .05 significance level

A) be rejected

Based on the results, the null hypothesis would ______ at the .10 significance level.

A) be rejected

Based on the central limit theorem, the sampling distribution of the sample mean becomes more Normal as the sample size _______.

A) increases

Very _____ sample sizes will allow very small effects to become statistically significant.

A) large

The alternative hypothesis is ________.

A) one sided

The null hypothesis is a statement about the ________.

A) population parameter

In order to reduce the standard deviation from the sampling distribution of the sample mean, you should ________.

A) take larger samples

True or False. Probability calculations from a binomial distribution can be found using a Normal approximation for large sample sizes.

A) true

A fair die is rolled 12 times. Let X = the number of times an even number occurs on the 12 rolls. What is the appropriate distribution for the random variable X?

D) A binomial distribution with a mean of 6

Suppose a 99% confidence interval for the mean weight of high school girls (in pounds) is calculated as (102.3, 106.5). If we had measured the weights of each of the girls in kilograms (2.2 pounds = 1 kilogram), then the confidence interval for the mean weight of high school girls in kilograms would have been

B) (46.5, 48.4)

It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all-season tires traveling at 90 kilometers per hour, the mean stopping time in fresh snow is known to be 215 meters, with a standard deviation of s = 2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of nine snow tires from the manufacturer on a snow-covered test track. The tests resulted in a mean stopping distance of = 212.9 meters. Using the sample results and assuming that stopping distance is a Normally distributed random variable, what is the value of the test statistic?

B) -2.52

It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all-season tires traveling at 90 kilometers per hour, the mean stopping time in fresh snow is known to be 215 meters, with a standard deviation of s = 2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of nine snow tires from the manufacturer on a snow-covered test track. The tests resulted in a mean stopping distance of x bar = 212.9 meters. - Using the sample results and assuming that stopping distance is a Normally distributed random variable, what is the value of the test statistic?

B) -2.52

Suppose we wish to test the hypotheses H0: m = 10 versus Ha: m < 10, where m represents the mean age of children not in high school who are members of a large gymnastics club in a metropolitan area. Assume age follows a Normal distribution with s = 2. A random sample of 16 ages is drawn from the population, and we find the sample mean of these observations to be = 8.76. What is the value of the P-value?

B) 0.0066

Suppose we wish to test the hypotheses H0: m = 10 versus Ha: m < 10, where m represents the mean age of children not in high school who are members of a large gymnastics club in a metropolitan area. Assume age follows a Normal distribution with s = 2. A random sample of 16 ages is drawn from the population, and we find the sample mean of these observations to be x bar = 8.76. What is the value of the P-value?

B) 0.0066

A one-question survey is to be distributed to a random sample of 1500 adults in Ohio. The question asks if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let p hat denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. What is the standard deviation, , of the sampling distribution of p hat?

B) 0.0126

A major car manufacturer wants to test a new engine to determine if it meets new air pollution standards. The mean emission, m, of all engines of this type must be approximately 20 parts per million of carbon. If it is higher than that, they will have to redesign parts of the engine. Ten engines are manufactured for testing purposes and the emission level of each is determined. Based on data collected over the years from a variety of engines, it seems reasonable to assume that emission levels are roughly Normally distributed with s = 3 parts per million of carbon. What is the value of the P-value?

B) 0.0175

A researcher plans to conduct a test of hypotheses at the 1% significance level. She designs her study to have a power of 0.90 at a particular alternative value of the parameter of interest. What is the probability that the researcher will commit a Type II error for the particular alternative value of the parameter at which she computed the power?

B) 0.10

Suppose that a particular candidate for public office is in fact favored by p = 48% of all registered voters. A polling organization is about to take a simple random sample of voters and will use p hat, the sample proportion, to estimate p. Suppose that the polling organization takes a simple random sample of 500 voters. What is the probability that the sample proportion will be greater than 0.5, causing the polling organization to predict the result of the upcoming election incorrectly?

B) 0.185

The actual arrival time of the commuter bus at the final bus stop as compared to the scheduled arrival time is known to be Normally distributed with a mean of 1 minute and a standard deviation of 3 minutes (a negative value meaning the bus arrived early, a positive value meaning the bus arrived late). You ride the bus frequently and are under the impression that the mean arrival time is much later than they claim. You decide to test the hypotheses H0: m = 1 versus Ha: m > 1. You take a simple random sample of 10 trips and record the differences between the actual arrival time and the scheduled arrival time. You decide to reject H0 if > 3. If, in fact, the true mean is 2 minutes, what is the probability of a Type II error?

B) 0.8541

In tests of significance about an unknown parameter, what does the test statistic represent?

D) A measure of compatibility between the null hypothesis and the data

Chocolate bars produced by a certain machine are labeled 8.0 ounces. The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces. The quality control manager plans to take a simple random sample of size n from the production line. How big should n be so that the sampling distribution X BAR has a standard deviation of 0.01 ounces?

B) 100

Chocolate bars produced by a certain machine are labeled 8.0 ounces. The distribution of the actual weights of these chocolate bars is claimed to be Normal with a mean of 8.1 ounces and a standard deviation of 0.1 ounces. The quality control manager plans to take a simple random sample of size n from the production line. How big should n be so that the sampling distribution of X BAR has a standard deviation of 0.01 ounces?

B) 100

A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons. The manufacturer of this gasoline tank considers the largest 2% of these tanks too large to put on the market. How large does a tank have to be to be considered too large?

B) 15.31 gallons

The length of time it takes to get through the security checks at a very large urban airport is a random variable with a mean of m = 20.6 minutes and a standard deviation of s = 8.4 minutes. A simple random sample of 36 airline passengers is to be observed going through security. What is the mean (MU X BAR) of the sampling distribution of the sample mean (X BAR)?

B) 20.6 minutes

The power for a one-sided test of the null hypothesis m = 10 versus the alternative m = 8 is equal to 0.8. Assume the sample size is 25 and s = 4. With the power equal to 80%, the decision rule would be to reject the null hypothesis if the observed sample mean is less than _______________.

B) 8.67

A popular Web site among college students is www.studentinfo.com. It lists information about jobs both in the United States and abroad. The management of the Web site claims that half of all college students know about it. You do not quite believe this and think it is much less than half. You decide to ask a sample of 10 students if they know about the Web site. Out of the 10 students asked, only two had heard of the Web site. If the management of the Web site is correct about the proportion of all college students who know about the Web site, what is the distribution of the number of students who know about the Web site in a simple random sample of 10 students?

B) B(10, 0.5)

True or False - The central limit theorem does not apply to discrete random variables.

B) False

True or False. A test of significance can be used to test differences in categorical data.

B) False

True or False. Confidence intervals are resistant to outliers in the data set.

B) False

True or False. The null and alternative hypotheses are stated in terms of the statistics from the random sample

B) False

True or False. The purpose of forming confidence intervals is to find the exact value of the true population mean based on a random sample.

B) False

True or False. The results obtained from a test of significance can always be trusted as long as the data collection methods are correct

B) False

True or False. The results obtained from a test of significance can always be trusted as long as you use a random sample.

B) False

The weights of medium oranges packaged by an orchard are Normally distributed with a mean of 14 ounces and a standard deviation of 2 ounces. Ten medium oranges will be randomly selected from a package. What is the sampling distribution of the sample mean weight of a random sample of 10 medium oranges?

B) N(14, 0.63)

Suppose a study was done to determine if the average amount of sleep that students get the day before an exam is less than 6 hours. An SRS of 100 students from a university was taken and a mean of 5.5 hours was computed from the sample. The figure below provides the results of the analysis. Suppose the alternative hypothesis is Ha: m ≠ 6. Would the null hypothesis be rejected at the .01 level?

B) No

Thousands of batteries are produced every day in a certain manufacturing plant. The quality control specialist is interested in how long it takes for each battery to fail when used in a moderately sized appliance, like a portable radio or CD player. The quality control specialist will take a simple random sample of 2000 batteries produced at this plant over the next four days. These batteries will be put into a variety of moderately sized appliances and the average x bar of all failure times will be computed. Which of the following probability distributions is most appropriate to model the average time until failure of these 2000 batteries?

B) The Normal distribution

Are the results of the study likely biased toward one race/ethnicity group?

B) Yes, because most of the women in the study were white.

The probability you accept the null hypothesis when in fact the alternative hypothesis is true is called __________.

B) a Type II error

A free cholesterol screening program is set up in the downtown area during lunch hour. Individuals can walk in and have their cholesterol measured for free. One hundred seventy-three people use the service, and their average cholesterol is 217 mg/dL. The value 217 is an example of _________.

B) a statistic

As you increase the margin error of a confidence interval, the confidence level _________. (Note: Assume the sample size is fixed.)

B) decreases

The larger the level of confidence, C, the ______ the confidence interval.

B) larger

Suppose X has the B(20, .5) distribution. The Normal approximation is ____ accurate because _______.

B) very; p is close to .5, np ≥ 10, and n(1 - p) ≥ 10

A test was established of H0: m = 24 against the alternative Ha: m ≠ 24 using a level of significance of a = 0.05. The variable in question is known to be Normally distributed with s = 3. Hence, the null hypothesis would be rejected if a sample of size 16 has a mean < 22.53, or > 25.47. Suppose the distribution of the variable shifts to a new mean, m = 24.8, but the standard deviation s does not change. What is the power of this test?

C) 0.188

A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 15.0 gallons and a standard deviation of 0.15 gallons. What proportion of tanks will hold between 14.75 and 15.10 gallons of gas?

C) 0.6997

During the summer months, the prices of nonsmoking rooms with a king-sized bed in hotels in a certain area are roughly Normally distributed with a mean of $131.80 and a standard deviation of $29.12. What percentage of nonsmoking rooms with a king-sized bed cost more than $150?

C) 26.60%

A college basketball player makes 5/6 of her free throws. Assume free throws are independent. What is the probability that she makes exactly three of her next four free throws?

C) 4 (1/6)^1 95/6)^3

The Big Smiles Portrait Studio is conducting a survey among their clients. One of the questions being asked is if they would recommend the studio to a friend. The studio has given the survey to a simple random sample of 65 clients during the past 2 weeks. If the true proportion of clients who are very satisfied with the Big Smiles Portrait Studio would recommend the studio to a friend is 82%, how many clients in the sample would we expect to answer yes on the survey question?

C) 53.3

The heights of young American women, in inches, are Normally distributed with a mean of m and a standard deviation of s = 2.4. A simple random sample of four young American women is selected and their heights measured. The four heights, in inches, are 63, 69, 62 and 66. Based on these data, what is a 99% confidence interval for m?

C) 65.00 ± 3.09

The number of undergraduates at Johns Hopkins University is approximately 2000, while the number at Ohio State University is approximately 40,000. Suppose the actual proportion of undergraduates at Johns Hopkins University who feel drinking is a problem among college students is 67%. What is the mean of the sampling distribution of the percentage of students who feel drinking is a problem in repeated simple random samples of 50 Johns Hopkins undergraduates?

C) 67%

Suppose that the population of the scores of all high school seniors who took the SAT Math (SAT-M) test this year follows a Normal distribution with standard deviation s = 100. You read a report that says, "On the basis of a simple random sample of 100 high school seniors that took the SAT-M test this year, a confidence interval for m is found to be 512.00 ± 25.76." What was the confidence level used to calculate this confidence interval?

C) 99%

It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all-season tires traveling at 90 kilometers per hour, the mean stopping time in fresh snow is known to be 215 meters, with a standard deviation of s = 2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of nine snow tires from the manufacturer on a snow-covered test track. The tests resulted in a mean stopping distance of x bar = 212.9 meters. What are the appropriate null and alternative hypotheses to test the manufacturer's claim?

C) H0: m = 215 against Ha: m < 215

Suppose you are going to roll a six-sided die 60 times and record , the proportion of times that an even number (2, 4, or 6) is showing. Suppose you decide to roll the die 200 times instead of 60 times. How will this affect the center and spread of the sampling distribution of ?

C) The center will remain the same, but the spread will decrease.

Suppose you are going to roll a six-sided die 60 times and record p hat , the proportion of times that an even number (2, 4, or 6) is showing. Suppose you decide to roll the die 200 times instead of 60 times. How will this affect the center and spread of the sampling distribution of p hat?

C) The center will remain the same, but the spread will decrease.

A simple random sample of 50 students is taken from a local community college, which has a total of about 1500 students. Another simple random sample of 50 students is taken from a large state university, which has a total of approximately 20,000 students. The sampled students each answer a one-question survey which reads, "About how many MP3 songs do you own?" The sample average number of MP3 songs owned is calculated for the two sets of students. What can we conclude about the sampling variability in the sample average number of MP3 songs of the students sampled from the small community college as compared to that in the sample average of the students sampled from the large state university?

C) The sample mean from the small community college has about the same sampling variability as that from the large state university because the sample sizes are equal

A random experiment was conducted to see if a newly formulated drug produced a different effect on the mean time to recovery than that achieved using the standard drug. It is known that the mean time to recovery for the standard drug is 26 days. Following an extensive random experiment involving 65 patients, the data gathered were used to construct a 95% confidence interval estimate for the mean recovery time (in days) for patients on the new drug. The 95% confidence interval was found to be (24.6, 27.8). What conclusion can be reached in this case concerning the new drug relative to the standard drug?

C) There is insufficient evidence to reject the claim that there is no difference between the new drug and the standard drug with respect to mean recovery time.

The scores of individual students on the American College Testing (ACT), a college readiness assessment, have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. What is the sampling distribution of the sample mean score for a random sample of 36 students?

C) exactly normal

A population variable has a distribution with a mean of m = 50 and a variance of s2 = 225. From this population a simple random sample of n observations is to be selected and the mean x bar of the sample values calculated. How big must the sample size n be so that the standard deviation of the sample mean x bar is equal to 1.4?

C) n = 115

When constructing confidence intervals, the center of each interval is always _______.

C) x bar

It is known that driving can be difficult in regions where winter conditions involve snow-covered roads. For cars equipped with all-season tires traveling at 90 kilometers per hour, the mean stopping time in fresh snow is known to be 215 meters, with a standard deviation of s = 2.5 meters. It is often advocated that automobiles in such areas should be equipped with special tires to compensate for such conditions, especially with respect to stopping distance. A manufacturer of tires made for driving in fresh snow claims that vehicles equipped with their tires have a decreased stopping distance. A study was done using a random sample of nine snow tires from the manufacturer on a snow-covered test track. The tests resulted in a mean stopping distance of x bar = 212.9 meters. - What is the P-value?

D) 0.006

The time needed for college students to complete a certain paper-and-pencil maze follows a Normal distribution with a mean of 30 seconds and a standard deviation of 3 seconds. You wish to see if the mean time m is changed by vigorous exercise, so you have a group of nine college students exercise vigorously for 30 minutes and then complete the maze. Assume that s remains unchanged at 3 seconds. You decide to test the hypotheses H0: m = 30 versus Ha: m ≠ 30 at the 1% significance level. What is the power of your test at m = 28 seconds?

D) 0.2823

A one-question survey is to be distributed to a random sample of 1500 adults in Ohio. The question asks if they support an increase in the state sales tax from 5% to 6%, with the additional revenue going to education. Let denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in Ohio support the increase. What is the mean, mu p hat, of the sampling distribution of p hat?

D) 0.40

The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with s = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of = 1038. Construct a 92% confidence interval estimate for the mean lifetime m. If it were desired to cut the confidence interval to half its length while keeping the same 92% level, what size sample would be required to achieve this?

D) 100

The lifetime (in hours) of a 60-watt light bulb is a random variable that has a Normal distribution with s = 30 hours. A random sample of 25 bulbs put on test produced a sample mean lifetime of x bar = 1038. Construct a 92% confidence interval estimate for the mean lifetime m. If it were desired to cut the confidence interval to half its length while keeping the same 92% level, what size sample would be required to achieve this?

D) 100

A sample of size n is selected at random from a population that has mean m and standard deviation s. The sample mean x bar will be determined from the observations in the sample. Which of the following statements about the sample mean x bar is/are TRUE? A) The mean of x bar is the same as the population mean (i.e., m). B) The variance of x bar is SD^2/n. C) The standard deviation of x bar decreases as the sample size grows larger. D) All of the above are true. E) Only A and B are true.

D) All of the above are true.

The weights of medium oranges packaged by an orchard are Normally distributed with a mean of 14 ounces and a standard deviation of 2 ounces. Ten medium oranges will be randomly selected from a package. What is the sampling distribution of the number of oranges in the sample that weigh more than 14 ounces?

D) B(10, 0.5)

Which of the following best describes the entry designated by (4) in the table? A) The entry is a correct decision. B) The probability of entry is called power. C) The entry refers to an error of Type II. D) Both A and B describe the entry. E) Both B and C describe the entry.

D) Both A and B describe the entry.

An agronomist has conducted a study on the cellulose content of a variety of alfalfa hay. Knowing that s = 8 mg/g and having the sample results from 15 cuttings for which x bar = 145 mg/g, the agronomist constructed a 90% confidence interval estimate of m, and in addition he tested the hypotheses H0: m = 140 mg/g versus Ha: m > 140 mg/g. For these two procedures to be valid, what assumption(s) must be made? A) The 15 sample cuttings are a simple random sample. B) The cellulose content variable is Normally distributed or at least not extremely non-Normal. C) The experiment conducted to get these data involved a randomized comparison. D) Both A and B must be assumed. E) A, B, and C must be assumed.

D) Both A and B must be assumed.

A report indicated that automobiles manufactured in North America are less fuel efficient than automobiles manufactured in Asia. It is known that automobiles from Asia have a mean fuel efficiency of 22 miles per gallon. To determine if there is evidence to support this claim, a random sample of automobiles manufactured in North America is to be selected and their fuel efficiency determined. The appropriate hypotheses to be tested are __________.

D) H0: m = 22 against Ha: m < 22

Ten years ago at a small high school in Alabama, the mean Math SAT score of all high school students who took the exam was 490, with a standard deviation of 80. This year the Math SAT scores of a random sample of 25 students who took the exam are obtained. The mean score of these 25 students is = 525. We assume the population standard deviation continues to be s = 80. To determine if there is evidence that the scores in the district have improved, the hypotheses H0: m = 490 versus Ha: m > 490 are tested. The P-value is found to be 0.014. A boxplot of the 25 scores is given below. What conclusion can we draw? A) At the 5% significance level, we have proved that H0 is false. B) At the 5% significance level, we have proved that Ha is false. C) It would have been more appropriate to use a two-sided alternative. D) None of the above

D) None of the above

In a test of statistical hypotheses, what does the P-value tell us?

D) The smallest level of significance at which the null hypothesis can be rejected

A researcher is planning to carry out a sample survey in order to estimate the proportion of people in a very large population of interest who have shopped online in the previous 6 months. A simple random sample is to be selected but there is debate about whether to select an SRS of size 500 or of size 1000. With respect to the sample proportion, which statement best describes what can be expected to happen using these two different sample sizes?

D) The statistic from either sample size will be unbiased, but the sampling distribution of the statistic from the sample of size 1000 will show less variability.

A test of significance was conducted in a study involving a random sample of 25 subjects. Based on the test result using the sample mean x bar, it was determined that the P-value was equal to 0.028. Which of the following statements about this P-value is/are TRUE? A) In this situation there is relatively strong evidence against the null hypothesis. B) The P-value was calculated under the assumption that the null hypothesis was true. C) The probability of a value of the test statistic at least as extreme as that observed in this study, assuming the null hypothesis is true, is 0.028. D) All of the above are true statements.

D) all of the above are true statements

Suppose a simple random sample is selected from a population with a mean if m and a variance of s2. The central limit theorem tells us that

D) if the sample size is sufficiently large, the distribution of x bar will be approximately Normal with a mean of m and a standard deviation of SD/ sq rt n.

A study was conducted on the reaction time of female subjects over the age of 50 to a particular light stimulus using a specific type of red light. A random sample of 45 female subjects from this age group in the population was selected and the subject's reaction time (in seconds) determined. Based on the test data, the 99% confidence interval estimate for m was determined to be (0.66, 0.78). From this interval we can conclude that

D) we have 99% confidence in this interval because, in repeated sampling from the population, the method used to determine such confidence intervals will produce intervals 99% of which will contain m

A comprehensive report called the Statistical Report on the Health of Canadians was produced in 1999. In it was reported that 42% of Canadians, 12 years of age or older, had their most recent eye examination within the previous year. If a sample of 100 individuals, 12 years of age or older, were selected at random from the Canadian population, we could use the Normal distribution to approximate the probability that more than 38 of the sampled people had their most recent eye examination in the previous year because A) the population is very much larger than the sample size. B) np > 10, and n(1 - p) > 10. C) independence can be assumed since the people were selected at random. D) the probability of the eye examination can be assumed to be constant from person to person in the sample. E) All of the above

E) All of the above