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inferential statistics
Even You Can Learn Statistics A Guide For Everyone Who Has Ever Been Afraid Of Statistics 2nd Edition David M. Levine, David F. Stephan - Solutions
Do people of different age groups differ in their response to email messages? A survey by the Center for the Digital Future of the University of Southern California (data extracted from A. Mindlin, “Older E-mail Users Favor Fast Replies,” Drill Down, The New York Times, July 14, 2008, p. B3)
Of the 200 respondents who were between the ages of 36 and 50, 82 got their news primarily from newspapers. Of the 200 respondents who were above age 50, 104 got their news primarily from newspapers. Is there evidence of a significant difference in the proportion that get their news primarily from
Where people turn for news is different for various age groups(extracted from P. Johnson, “Young People Turn to the Web for News,”USA Today, March 23, 2006, p. 9D). Suppose that a study conducted on this issue was based on 200 respondents who were between the ages of 36 and 50, and 200
Technology has led to the rise of extreme workers who are on the job 60 hours or more per week. One of the reasons cited by employees as to why they worked long hours was that they loved their job because it is stimulating/challenging/provides an adrenaline rush (extracted from S. Armour, “Hi,
If the assumption of normally distributed populations in the pooledvariance t test has been violated, you should use an alternative procedure such as the nonparametric Wilcoxon rank sum test.
You can use a pie chart to evaluate whether the assumption of normally distributed populations in the pooled-variance t test has been violated.
In testing a null hypothesis about the difference between two proportions, the Z test statistic is computed to be 2.04. The p-value is 0.0207.
The pooled-variance t test assumes that the population variances in the two independent groups are equal.
Repeated measurements from the same individuals are an example of data collected from two related populations.
When you are sampling the same individuals and taking a measurement before treatment and after treatment, you should use the paired t test.
The sample size in each independent sample must be the same in order to test for differences between the proportions of two independent populations.
In testing a hypothesis about the difference between two proportions, the Z test statistic is computed to be 2.04. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tail test is used.
In testing a hypothesis about the difference between two proportions, the p-value is computed to be 0.034. The null hypothesis should be rejected if the chosen level of significance is 0.01.
In testing a hypothesis about the difference between two proportions, the p-value is computed to be 0.043. The null hypothesis should be rejected if the chosen level of significance is 0.05.
The sample size in each independent sample must be the same in order to test for differences between the means of two independent populations.
A statistics professor wanted to test whether the grades on a statistics test were the same for her morning class and her afternoon class. For this situation, the professor should use the:(a) Z test for the difference between two proportions(b) Pooled-variance t test(c) Paired t test
A researcher is curious about the effect of sleep on students’ test performances. He chooses 100 students and gives each student two exams.One is given after four hours’ sleep and one after eight hours’ sleep.The statistical test the researcher should use is the:(a) Z test for the difference
In testing for differences between the means of two related populations, the null hypothesis is:(a) H0 : RD = 2(b) H0 : R D = 0(c) H0 : RD < 0(d) H0 : RD > 0
The t test for the difference between the means of two independent populations assumes that the two:(a) Sample sizes are equal.(b) Sample medians are equal.(c) Populations are approximately normally distributed.(d) All of the above.
The smaller the p-value, the more likely you are to reject the null hypothesis.
The statement of the alternative hypothesis always contains an equality.
The larger the p-value, the more likely you are to reject the null hypothesis.
The statement of the null hypothesis always contains an equality.
For a given level of significance, if the sample size is increased, the probability of committing a type I error will increase.
For a given level of significance, if the sample size is increased, the power of the test will increase.
Which of the following is an appropriate alternative hypothesis?(a) The mean of a population is equal to 100.(b) The mean of a sample is equal to 50.(c) The mean of a population is greater than 100.(d) All of the above.
Which of the following is an appropriate null hypothesis?(a) The mean of a population is equal to 100.(b) The mean of a sample is equal to 50.(c) The mean of a population is greater than 100.(d) All of the above.
The value that separates a rejection region from a non-rejection region is called the _______.
The probability of a type I error is represented by the symbol _______.
The probability of a type _______ error is also called “the level of significance.”
If you reject the null hypothesis when it is false, then you have committed:(a) a type II error(b) a type I error(c) no error(d) a type I and type II error
Which of the following statements is not true about the level of significance in a hypothesis test?(a) The larger the level of significance, the more likely you are to reject the null hypothesis.(b) The level of significance is the maximum risk you are willing to accept in making a type I error.(c)
A test of hypothesis has a type I error probability (F) of 0.01. Therefore:(a) If the null hypothesis is true, you don’t reject it 1% of the time.(b) If the null hypothesis is true, you reject it 1% of the time.(c) If the null hypothesis is false, you don’t reject it 1% of the time.(d) If the
If the p-value is less than F in a two-tail test:(a) The null hypothesis should not be rejected.(b) The null hypothesis should be rejected.(c) A one-tail test should be used.(d) No conclusion can be reached.
The power of a test is the probability of:(a) rejecting a null hypothesis that is true(b) not rejecting a null hypothesis that is true(c) rejecting a null hypothesis that is false(d) not rejecting a null hypothesis that is false
Which of the following is not an appropriate alternative hypothesis?(a) The difference between the means of two populations is equal to 0.(b) The difference between the means of two populations is not equal to 0.(c) The difference between the means of two populations is less than 0.(d) The
Which of the following is an appropriate null hypothesis?(a) The difference between the means of two populations is equal to 0.(b) The difference between the means of two populations is not equal to 0.(c) The difference between the means of two populations is less than 0.(d) The difference between
A type I error is committed when:(a) you reject a null hypothesis that is true(b) you don’t reject a null hypothesis that is true(c) you reject a null hypothesis that is false(d) you don’t reject a null hypothesis that is false
A type II error is committed when:(a) you reject a null hypothesis that is true(b) you don’t reject a null hypothesis that is true(c) you reject a null hypothesis that is false(d) you don’t reject a null hypothesis that is false
You want to estimate the proportion of newspapers printed that have a nonconforming attribute, such as excessive ruboff, improper page setup, missing pages, or duplicate pages. A random sample of n = 200 newspapers is selected from all the newspapers printed during a single day. In this sample, 35
In a survey of 2,395 adults, 1,916 reported that emails are easy to misinterpret, but only 1,269 reported that telephone conversations are easy to misinterpret (extracted from “Snapshots: Open to Misinterpretation,”USA Today, July 17, 2007, p. 1D).(a) Construct a 95% confidence interval
In a survey of 1,000 airline travelers, 760 responded that the airline fee that is most unreasonable was additional charges to redeem points/miles (extracted from “Snapshots: Which Airline Fee Is Most Unreasonable?”, USA Today, December 2, 2008, p. B1). Construct a 95% confidence interval
The following data represent the viscosity (friction, as in automobile oil) taken from 120 manufacturing batches (ordered from lowest viscosity to highest viscosity).
Tuna sushi was purchased from 13 Manhattan restaurants and tested for mercury. The number of pieces it would take to reach what the Environmental Protection Agency considers to be an acceptable level to be regularly consumed was as follows:8.6 2.6 1.6 5.2 7.7 4.7 6.4 6.2 3.6 4.9 9.9 3.3 4.1 Source:
The data in the file MoviePrices contain the price for two tickets with online service charges, large popcorn, and two medium soft drinks at a sample of six Ftheatre chains:$36.15 $31.00 $35.05 $40.25 $33.75 $43.00 Source: Extracted from K. Kelly, “The Multiplex Under Siege,” The Wall Street
The confidence interval estimate that is constructed will always correctly estimate the population parameter.
In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a wider interval.
The t distribution is used to construct confidence intervals for the population mean when the population standard deviation is unknown.
A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.
As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.
Other things being equal, as the confidence level for a confidence interval increases, the width of the interval increases.
For samples of n = 15, the sampling distribution of the mean will be normally distributed:(a) regardless of the shape of the population(b) if the shape of the population is symmetrical(c) if the standard deviation of the mean is known(d) if the population is normally distributed
The Central Limit Theorem is important in statistics because(a) It states that the population will always be approximately normally distributed.(b) It states that the sampling distribution of the sample mean is approximately normally distributed for a large sample size n regardless of the shape of
In estimating the population mean with the population standard deviation unknown, if the sample size is 12, there will be _____ degrees of freedom.
A university dean is interested in determining the proportion of students who are planning to attend graduate school. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are planning to attend graduate school. The 95%confidence
Which of the following assumptions is necessary in order for a confidence interval to be valid?(a) The population sampled from has an approximate normal distribution.(b) The population sampled from has an approximate t distribution.(c) The mean of the sample equals the mean of the population.(d)
As an aid to the establishment of personnel requirements, the manager of a bank wants to estimate the mean number of people who arrive at the bank during the two-hour lunch period from 12 noon to 2 p.m.The director randomly selects 64 different two-hour lunch periods from 12 noon to 2 p. m. and
In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to a ________ interval.(a) narrower(b) wider(c) less significant(d) the same
Sampling distributions describe the distribution of:(a) parameters(b) statistics(c) both parameters and statistics(d) neither parameters nor statistics
Which of the following statements is false?(a) There is a different critical value for each level of alpha (F).(b) Alpha (F) is the proportion in the tails of the distribution that is outside the confidence interval.(c) You can construct a 100% confidence interval estimate of R.(d) In practice, the
A 99% confidence interval estimate can be interpreted to mean that:(a) If all possible samples are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval.(b) You have 99% confidence that you have selected a sample
For samples of n = 1, the sampling distribution of the mean will be normally distributed:(a) regardless of the shape of the population(b) if the shape of the population is symmetrical(c) if the standard deviation of the mean is known(d) if the population is normally distributed
For samples of n = 30, for most populations, the sampling distribution of the mean will be approximately normally distributed:(a) regardless of the shape of the population(b) if the shape of the population is symmetrical(c) if the standard deviation of the mean is known(d) if the population is
Which of the following is true regarding the sampling distribution of the mean for a large sample size?(a) It has the same shape and mean as the population.(b) It has a normal distribution with the same mean as the population.(c) It has a normal distribution with a different mean from the
The sampling distribution of the mean requires ________ sample size to reach a normal distribution if the population is skewed than if the population is symmetrical.(a) the same(b) a smaller(c) a larger(d) The two distributions cannot be compared.
The sampling distribution of the mean can be approximated by the normal distribution:(a) as the number of samples gets “large enough”(b) as the sample size (number of observations in each sample) gets large enough(c) as the size of the population standard deviation increases(d) as the size of
Is the viscosity of a certain chemical normally distributed? Construct a normal probability plot of the viscosity of the chemical. Do you think that the viscosity of the chemical is normally distributed? Explain.
Is the cost of attending an NBA basketball game normally distributed?Construct a normal probability plot of the cost of attending an NBA basketball game. Do you think that the cost of attending an NBA basketball game is normally distributed? Explain.
On page 106, a normal probability plot was constructed for the cost of a meal at city restaurants. Construct a normal probability plot of the cost of a meal at suburban restaurants. Do you think that the cost of a meal at suburban restaurants is normally distributed? Explain.
The owner of a fish market determined that the mean weight for salmon is 12.3 pounds with a standard deviation of 2 pounds.Assuming the weights of salmon are normally distributed, what is the probability that (a) a randomly selected salmon will weigh between 12 and 15 pounds?(b) a randomly selected
A set of final examination grades in an introductory statistics course is normally distributed, with a mean of 73 and a standard deviation of 8.(a) What is the probability of getting a grade below 91 on this exam?(b) What is the probability that a student scored between 65 and 89?(c) The
Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, what is the probability that(a) X is between 47 and 54?(b) X is less than 55?(c) There is a 90% chance that X will be less than what value?
The U.S. Department of Transportation maintains statistics for mishandled bags per 1,000 airline passengers. In 2007, airlines had seven mishandled bags per 1,000 passengers (extracted from R. Yu, “Airline Performance nears Twenty Year Low,” USA Today, April 8, 2008, p. B1).What is the
The quality control manager of Marilyn’s Cookies is inspecting a batch of chocolate-chip cookies that has just been baked. If the production process is in control, the mean number of chip parts per cookie is 6.0.What is the probability that in any particular cookie being inspected there are(a)
The number of power outages at a power plant has a Poisson distribution with a mean of four outages per year. What is the probability that in a year there will be(a) no power outages?(b) four power outages?(c) at least three power outages?
A campus program enrolls undergraduate and graduate students. Of the students, 70% are undergraduates. If a random sample of four students is selected from the program to be interviewed about the introduction of a new fast-food outlet on the ground floor of the campus building, what is the
A venture capitalist firm that specializes in funding risky high-technology startup companies has determined that only one in ten of its companies is a “success” that makes a substantive profit within six years.Given this historical record, what is the probability that in the next three
Suppose that a judge’s decisions are upheld by an appeals court 90% of the time. In her next ten decisions, what is the probability that(a) eight of her decisions are upheld by an appeals court?(b) all ten of her decisions are upheld by an appeals court?(c) eight or more of her decisions are
The number of arrivals per minute at a bank located in the central business district of a large city was recorded over a period of 200 minutes with the following results:(a) Compute the expected number of arrivals per day.(b) Compute the standard deviation.
Similarly, the player can bet $1 that the sum will be over 7—that is, 8, 9, 10, 11, or 12. Here, the player wins $1 if the result is over 7 but loses $1 if the result is 7 or under. A third method of play is to bet $1 on the outcome 7. For this bet, the player wins $4 if the result of the roll is
For this bet, the player wins $1 if the result is under 7 and loses $1 if the outcome equals or is greater than
In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7—that is, 2, 3, 4, 5, or
Given the following probability distributions:(a) Compute the expected value of each distribution.(b) Compute the standard deviation of each distribution.(c) Compare the results of distributions A and B.
If the data values are normally distributed, the normal probability plot will follow a straight line.True or False
The diameters of 100 randomly selected bolts follow a binomial distribution.True or False:
Another name for the mean of a probability distribution is its expected value.True or False:
Theoretically, the mean, median, and the mode are all equal for a normal distribution.True or False:
Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, the probability that X is between 47 and 54 is ________.
If a particular set of data is approximately normally distributed, you would find that approximately:(a) 2 of every 3 observations would fall between 1 standard deviation around the mean(b) 4 of every 5 observations would fall between 1.28 standard deviations around the mean(c) 19 of every 20
The normal distribution is _______ in shape:(a) right-skewed(b) left-skewed(c) symmetric
The probability that Z is less than –1.0 is ________ the probability that Z is greater than +1.0.(a) less than(b) the same as(c) greater than
Which of the following about the normal distribution is not true?(a) Theoretically, the mean, median, and mode are the same.(b) About two-thirds of the observations fall within one standard deviation from the mean.(c) It is a discrete probability distribution.(d) Its parameters are the mean, R, and
Which of the following about the normal distribution are true?(a) Theoretically, the mean, median, and mode are the same.(b) About 99.7% of the values fall within three standard deviations from the mean.(c) It is defined by two characteristics R and X.(d) All of the above are true.
A multiple-choice test has 25 questions. There are four choices for each question. A student who has not studied for the test decides to answer all questions by randomly choosing one of the four choices. What probability distribution can be used to compute his chance of correctly answering at least
The mean number of customers who arrive per minute at any one of the checkout counters of a grocery store is 1.8. What probability distribution can be used to find out the probability that there will be no customers arriving at a checkout counter in the next minute?(a) Binomial distribution(b)
A computer lab at a university has ten personal computers. Based on past experience, the probability that any one of them will require repair on a given day is 0.05. To find the probability that exactly two of the computers will require repair on a given day, you can use what probability
Based on past experience, the time you spend on emails per day has a mean of 30 minutes and a standard deviation of 10 minutes. To compute the probability of spending at least 12 minutes on emails, you can use what probability distribution?(a) Binomial distribution(b) Poisson distribution(c) Normal
The smallest number of possible successes in a Poisson distribution is:(a) 0(b) 1(c) n(d) infinite
The quality control manager of Marilyn’s Cookies is inspecting a batch of chocolate chip cookies. When the production process is in control, the mean number of chocolate chip parts per cookie is 6.0. The manager is interested in analyzing the probability that any particular cookie being inspected
What type of probability distribution will most likely be used to analyze warranty repair needs on new cars in the following problem?
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