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Mind On Statistics 4th Edition David D Busch, Jessica M Utts, Robert F Heckard - Solutions

Refer to Example
A randomly selected sample of 15 individuals is asked whether they are right-handed or left-handed. In the sample, only one person is left-handed. Explain why a confidence interval for the population proportion should not be computed by using the methods described in this chapter.
In a CBS News/New York Times nationwide poll done in 2009, the proportion of respondents who thought that it should be illegal to use a handheld cellular telephone while driving a car was .80 (80%). The poll’s sample size was 829 (Source: www.pollingreport.com/transpor.htm#Road).a. Find the value
A question in a 2007 Gallup poll asked, “Do you think the penalties for underage drinking should be made more strict, less strict, or remain the same?” The sample proportion that responded “more strict” was .60 (60%). This result will be used to estimate the proportion of all adults in the
In a USA Today/Gallup poll survey carried out in 2009, 57% of 1006 randomly sampled American adults said that abortions should be legal only under certain circumstances when asked, “Do you think abortions should be legal under any circumstance, legal only under certain circumstances or illegal in
In a randomly selected sample of 400 registered voters in a community, 220 individuals say that they plan to vote for Candidate Y in the upcoming election.a. Find the sample proportion planning to vote for Candidate Y.b. Calculate the standard error of the sample proportion.c. Find a 95% confidence
For each confidence interval procedure, provide the confidence level.a. Sample proportion 6 1.645 3 standard error.b. Sample proportion 6 1.96 3 standard error.c. Sample proportion 6 2.326 3 standard error.d. Sample proportion 6 2.576 3 standard error.
Refer to Exercise 10.23. Calculate a 98% confidence interval for the proportion successfully treated. Is this interval wider or narrower than the interval computed in part (b) of Exercise 10.23?
◆ In a survey of 190 college students, 134 students said that they believe there is extraterrestrial life (Data source:pennstate3 dataset at the companion website).a. Find p^ 5 sample proportion who believe that there is extraterrestrial life.b. Find a 95% confidence interval estimate of the
Suppose that a new treatment for a certain disease is given to a sample of 200 patients. The treatment was successful for 166 of the patients. Assume that these patients are representative of the population of individuals who have this disease.a. Calculate the sample proportion successfully
Refer to Exercise 10.3, which described a Gallup poll. The poll surveyed a random sample of 439 American teenagers, and one question that they were asked was, “How strict are your parents compared to most of your friends’ parents?”The choices were “more strict,” “less strict,” and
Suppose that a survey is planned to estimate the proportion of a population that is left-handed. The sample data will be used to form a confidence interval. Explain which one of the following combinations of sample size and confidence level will give the widest interval.(i) n 5 400, confidence
Suppose that in a random sample of 300 employed Americans, there are 57 individuals who say that they would fire their boss if they could. Calculate a 95% confidence interval for the population proportion. Write a sentence or two that interprets this interval.
U.S. News and World Report (December 19, 1994, pp. 62–71)reported on a survey of 1000 American adults, conducted by telephone December 2–4, 1994, designed to measure beliefs about apocalyptic predictions. One of the results reported was that 59% of the sample said that they believe the world
For the following examples, specify which of the five parameters stated on page 374 is appropriate. Give and define appropriate notation for the parameter of interest. If two symbols are involved, such as m1 2 m2, define each symbol.a. Do men and women feel the same away about dating someone who
For the following examples, specify which of the five parameters stated on page 374 is appropriate. Give and define appropriate notation for the parameter of interest. If two symbols are involved, such as m1 2 m2, define each symbol.a. The parameter of interest is the proportion of the population
Explain whether the width of a 95% confidence interval would increase, decrease, or remain the same as a result of the following changes in the design of a survey. Assume that sampling will be from the same population in all cases.a. A planned sample size is increased from 500 to 1000.b. A planned
Explain whether the width of a confidence interval would increase, decrease, or remain the same as a result of each of the following changes:a. Increase the confidence level from 95% to 99%.b. Decrease the confidence level from 95% to 90%.
Taking into account the purpose of a confidence interval described in Section 10.1, explain what is wrong with the following statement: “Based on the survey data, a 95%confidence interval estimate of the sample proportion is.095 to .117.”
Suppose 200 different researchers all randomly select samples of n 5 400 individuals from a population. Each researcher uses his or her sample to compute a 95% confidence interval for the proportion who have blue eyes in the population. About how many of the confidence intervals will cover the
A CNN/Time poll conducted in the United States October 23–24, 2002, asked, “Do you favor or oppose the legalization of marijuana?” In the nationwide poll of n 5 1007 adults, 34% said that they favored legalization. The margin of error was given as 3.1% (Source:
Parade Magazine reported that “nearly 3200 readers dialed a 900 number to respond to a survey in our Jan. 8 cover story on America’s young people and violence” (February 19, 1995, p. 20). Of those responding, “63.3% say they have been victims or personally know a victim of violent
Answer Thought Question 10.2 on p. 374.
In a 1997 survey done by the Marist College Institute for Public Opinion, 36% of a randomly selected sample of n 5 935 American adults said that they do not get enough sleep each night (Source: http://www.mipo.marist.edu).The margin of error was reported to be 3.5%.a. Use the survey information to
Read the examples of questions based on a “parameter of interest” in the section titled “Curiosity and Confidence Intervals” (p. 371). Create your own example of something that interests you, and translate it into a question about a population parameter.
Suppose that a survey is done to estimate the proportion of U.S. adults who think that the use of handheld cell phones while driving should be illegal. In the survey, 72% of a randomly selected national sample of n 5 836 individuals said that the use of cell phones while driving should be
Refer to Exercise 10.3 about a Gallup poll on how strict teenagers perceive their parents to be in comparison to other parents, based on a random sample of 439 teenagers. The choice “more strict” was selected by 171 of the respondents.Suppose that in fact the true population percentage of
What is the likelihood that a 95% confidence interval will not cover the true population value? Explain.
A survey is done to estimate the proportion of U.S. adults who think that cell phone use while driving should be illegal. In the survey, 54% of a randomly selected sample of 1025 individuals said that cell phone use while driving should be illegal
A Gallup poll surveyed a random sample of 439 American teenagers. One question that they were asked was, “How strict are your parents compared to most of your friends’parents?” The choices were “more strict,” “less strict,” and“about the same.” The choice “more strict” was
This is also Exercise 2.6. For each of the following statistical summaries, explain whether it is a population parameter or a sample statistic.a. A highway safety researcher wants to estimate the average distance at which all drivers can read a highway sign at night. She measures the distance for a
In each part of this question, explain whether the proportion that is described is a sample proportion or a population proportion.a. In the 1990 U.S. Census, it was found that about one in nine Americans were at least 65 years old at that time.b. A randomly selected group of 500 registered voters
Suppose that 35% of the students at a university favor the semester system, 60% favor the quarter system, and 5% hav ?
Suppose the population of IQ scores in the town or city where you live is bell-shaped, with a mean of 105 and a standard deviation of 15. Describe the distribution of possible sample means that would result from random samples of 100 IQ scores.
Give an example of a scenario of interest to you for which the sampling distribution of p^ would be approximately normal. Explain why the conditions for it to be approximately normal are satisfied for your example.
Refer to Exercise 9.138. Redraw the picture under the assumption that you will collect 100 measurements instead of only 9. Discuss how the picture differs from the one in the previous exercise.
Suppose that you are interested in estimating the average number of miles per gallon of gasoline your car can get. You calculate the miles per gallon for each of the next nine times you fill the tank. Suppose that in truth, the values for your car are bell-shaped, with a mean of 25 miles per gallon
This is also Thought Question 9.4. Verify that if the raw data for each individual in a sample is 1 when the individual has a certain trait and 0 otherwise, then the sample mean is equivalent to the sample proportion with the trait. You can do this by using a formula, explaining it in words, or
According to the Sacramento Bee (April 2, 1998, p. F5), “A 1997–98 survey of 1027 Americans conducted by the National Sleep Foundation found that 23% of adults say they have fallen asleep at the wheel in the last year.”a. Conditions 2 and 3 needed for the sampling distribution of p^ to be
A recent Gallup poll found that of 800 randomly selected drivers surveyed, 70% thought that they were better-thanaverage drivers. It is reasonable to define “average” so that in the population, at most only 50% of all drivers can be“better than average.”a. Draw a picture of the possible
Refer to Exercise 9.133. Suppose the truth is that .12, or 12%, of the students are left-handed and you take a random sample of 200 students. Draw a picture similar to Figure 9.2(p. 325), showing the possible sample proportions for this situation.
Suppose you want to estimate the proportion of students at your college who are left-handed. You decide to collect a random sample of 200 students and ask them which hand is dominant. Go through the conditions for which the sampling distribution of a sample proportion is approximately normal, and
Answer Thought Question 9.1 on page 326.
Refer to Exercise 9.130 about the TVMeans applet. Assume that the sampling distribution of the sample mean is approximately normal for random samples of n 5 49 observations.a. Use the Empirical Rule to find the interval of values into which the sample mean will fall about 95% of the time for random
Use the TVMeans applet, which selects random samples from a population modeled by using responses given by college students to a question asking how many hours they watch television in a typical week. The mean for the population is m 5 8.352 hours and the standard deviation is s 5 7.723 hours.
This exercise concerns possible sample means for random samples of n 5 75.a. Use the applet to generate 500 different random samples of n 5 75 observations. What is the approximate shape of the resulting histogram of sample means?b. Approximately, what were the smallest and largest values among the
This exercise concerns possible sample means for random samples of n 5 36.a. Use the applet to generate 500 different random samples of n 5 36 observations. What is the approximate shape of the resulting histogram of sample means?b. Approximately, what were the smallest and largest values of the
Refer to Exercise 9.125. Now define the statistic of interest to be the proportion correct, X/10. What is the mean of the sampling distribution of this statistic? Explain how you found your answer.
Suppose someone who takes a ten-question true–false test doesn’t know any of the answers and randomly selects true or false for each question. Define the statistic X 5 number correct.a. Describe the sampling distribution of X. (Hint: This distribution was introduced in Chapter 8.)b. What is the
Suppose that two fair dice are rolled and H 5 higher of the two faces. If both dice show the same value, H is that value.Construct the sampling distribution of H, listing all possible values and their probabilities.
Consider the population of net gains for tickets in the California Decco lottery game described in Examples 9.13 and 9.14. The possible values are $4999, $49, $4, 0, and 2$1;the mean is 2$0.35, and the standard deviation is $29.67.Suppose that someone buys ten tickets each week.a. Explain why the
Are there situations for which the sampling distribution of a statistic consists of a single possible value, which has probability 1 of occurring each time? If not, explain why not. If so, explain how that could happen and give an example.
The I Ching is an ancient Chinese system of asking for advice. In one version, three pennies are flipped, and if the number of heads is odd (1 or 3), a “broken line” is recorded, while if it is even (0 or 2), a “solid line” is recorded. This process is repeated six times, and then the
Use a computer to simulate the numbers drawn for the Cash 5 lottery game 1000 times, and draw a histogram for the values of H 5 highest number drawn. Compare your histogram to the one shown in Figure 9.13 (p. 348).
Define L to be the lowest of the five numbers drawn in the Cash 5 lottery game in Example 9.15. Describe the shape of the sampling distribution of L, and explain how you know.
In a large retirement community, 60% of households have no dogs, 30% have one dog, and 10% have two dogs.Following a news story about how the elderly have trouble walking their dogs in the winter weather, a magnanimous group of teenagers decides that it will randomly select two households in the
A soft drink called Crash is so popular that vending machines allocate the top two selection buttons to it. Over the long run, of those who buy Crash, 60% push the top button and 40% push the lower button, and this behavior seems to be independent from one purchase to the next. Suppose that a
Refer to Exercise 9.114.a. For each of the ten possible samples listed in part (a) of Exercise 9.114, give the value of the range R 5 H 2 L, where H is the highest number and L is the lowest number.b. Use the results of part (a) to find the probability that R 5 4.c. Summarize the results of part
Suppose that a simple random sample of n 5 2 numbers will be selected from the list of values 1, 2, 3, 4, 5.a. There are ten possible equally likely samples of n 5 2 numbers that could be selected (1 and 2, 1 and 3, etc.)List the ten possible samples, and give H 5 highest number for each sample.b.
Suppose that a simple random sample of n 5 2 numbers will be selected from the list of values 1, 3, 5, 7, 9.a. There are ten possible equally likely samples of n 5 2 numbers that could be selected (1 and 3, 1 and 5, etc.).List the ten possible samples, and calculate the sample mean x for each
and 1.725.d. t-distribution with df 5 10, upper 5%.e. t-distribution with df 5 10, area below 2t and above 1t (same t) totals 5%.
Draw a picture illustrating each of the following distributions, showing the t-values marking the specified areas and the proportion of the t-distribution that falls in that area.Note: The use of either statistical software or Excel is necessary.a. t-distribution with df 5 10, middle 95%.b.
Are there any (finite) values for which the area above that value is the same for all t-distributions? If so, specify the value(s) and the area(s). If not, explain why not.
as “to reject the notion that chance alone can explain the sample results.” Explain how the question in part (a) fits that description of hypothesis testing.
support that allegation? Explain.b. The question in part (a) is an example of hypothesis testing, the goal of which was described in Section
Refer to Exercise 9.109. Suppose that allegations were made that the (unknown) population mean salary of women who work in that job is lower than the known population mean salary of $80,000 for men.a. Does the sample information for the 100 women in Exercise
The mean salary for a population of women who work in a traditional male job is $80,000. A random sample of 100 women is taken from this population and the sample mean and standard deviation are found to be x 5 $78,000 and s 5 $4000.a. Compute the standardized statistic for the sample mean in this
The mean IQ score in a population is 100. A random sample of 25 IQ scores is taken from this population and the values for the sample mean and standard deviation are found to be x 5 105 and s 5 10.a. Compute the standardized statistic for the sample mean in this situation.b. Draw a picture of the
In each of the following situations, which of the two distributions would be more spread out?a. Standard normal distribution or t-distribution with df 5 10.b. t-distribution with df 5 5 or t-distribution with df 5 25.c. t-distribution with df 5 100 or normal distribution with standard deviation 5
Suppose that a random sample of 36 IQ scores is drawn from a population of IQ scores with mean 5 100 and standard deviation 5 15.a. Find the standardized statistic for x 5 97.b. Find the standardized statistic for x 5 105.c. Give numerical values for the mean and standard deviation of the sampling
Explain the difference between what is represented by s and s, the two different symbols for standard deviation.
Draw a picture of each of the following distributions. Shade the area above the value given, and label the proportion of the distribution that falls in that region, as in Figure 9.12(p. 344). You do not have to label the vertical axis. Note: For parts (b) and (c), the use of either statistical
In each situation, find the value of the standardized statistic for the sample mean, and indicate whether the standardized statistic is a t-statistic or a z-statistic.a. x 5 175, m 5 170, s 5 24, n 5 4.b. x 5 175, m 5 170, s 5 20, n 5 4.c. x 5 161, m 5 170, s 5 18, n 5 36.
In each situation, find the value of the t-statistic for the sample mean x and give the value of degrees of freedom (df).a. x 5 56, m 5 50, s 5 15, n 5 25.b. x 5 50, m 5 50, s 5 20, n 5 9.
In each situation, find the value of the t-statistic for the sample mean x and give the value of degrees of freedom (df).a. x 5 5, m 5 10, s 5 20, n 5 16.b. x 5 15, m 5 10, s 5 20, n 5 16.
Explain whether or not each of the following would ever differ for two random samples of the same size from the same population.a. The sample mean x.b. The standard deviation of the sampling distribution of x.c. The standard error of x.d. The standardized z-score for the observed value of x.e. The
Home prices in a city have mean m 5 $200,000 and standard deviation s 5 $25,000. For n 5 25 randomly selected homes, the mean price is x 5 $208,000. Find the value of the standardized statistic (z-score) for this sample mean.
In each part, give the value of the standardized statistic(z-score) for the sample mean:a. x 5 92, m 5 100, s 5 16, n 5 4.b. x 5 92, m 5 100, s 5 16, n 5 64.c. x 5 10.15, m 5 10.0, s 5 5, n 5 10,000.
In each part, give the value of the standardized statistic(z-score) for the sample mean:a. x 5 74, m 5 72, s 5 10, n 5 25.b. x 5 70, m 5 72, s 5 10, n 5 25.
A blind taste test is done to compare Cola 1 and Cola 2.Among n 5 75 participants, p^ 5 .64 is the proportion preferring Cola 1. If, actually, the two colas are equally preferred in a larger population of tasters, p 5 .5 is the corresponding population proportion. Assuming that p 5 .5, find the
Suppose that an ESP test consists of n 5 75 independent tries, for which there are four possible choices on each try.Suppose that someone is just guessing, so the probability of a correct guess on each try is p 5 .25. Consider two possible sample proportions: p^ 5 .20 (15 correct) and p^ 5 .33(25
In each part, give the value of the standardized statistic(z-score) for the sample proportion.a. p^ 5 .78, p 5 .80, n 5 400.b. p^ 5 .82, p 5 .80, n 5 400.c. p^ 5 .25, p 5 .40, n 5 900.
In each part, give the value of the standardized statistic(z-score) for the sample proportion.a. p^ 5 .60, p 5 .50, n 5 100.b. p^ 5 .60, p 5 .50, n 5 200.
On the basis of past history, a car manufacturer knows that 10% (p 5 .10) of all newly made cars have an initial defect.In a random sample of n 5 100 recently made cars, 13%(p^ 5 .13) have defects. Find the value of the standardized statistic (z-score) for this sample proportion.
Refer to Exercises 9.79 to 9.80, discussing research on whether zinc lozenges helped to reduce the duration of cold symptoms. In the actual experiment (Prasad et al. 2000), the difference in sample means was 3.6 days. Suppose that the population standard deviations and sample sizes are as given in
Suppose that a new diet barely works and that if everyone in the population of overweight adults were to follow it, the weight losses would be bell-shaped with a mean of 0.1 pound and a standard deviation of 5 pounds.a. Describe the sampling distribution of the sample mean for n 5 100.b. Find the
Refer to Exercise 9.75, in which 12 drivers were tested after getting too little sleep and after drinking alcohol. In that exercise, we assumed that the mean difference in erroneous lane drifts during a 2-hour driving period would be 0 for the population, with a standard deviation of 5. Assume that
Refer to Exercise 9.56, in which the proportions of obese children in urban and rural areas are to be compared.Random samples of 900 children from each type of area are taken. Suppose that in fact, 20% of the children are obese in both populations.a. Give numerical values for the mean and standard
In comparing means for two independent samples, suppose that m1 2 m2 5 0, s1 5 s2 5 3, and n1 5 n2 5 30.a. Draw a picture of the appropriate sampling distribution, and show where the value x1 2 x2 5 2 falls on it.b. Find the value of the standardized statistic corresponding to x1 2 x2 5 2.c. Draw a
In a situation for which paired differences are appropriate, suppose that md 5 0, sd 5 10, and n 5 25.a. Draw a picture of the appropriate sampling distribution, and show where the value d 5 23 falls on it.b. Find the value of the standardized statistic corresponding to d 5 23.c. Draw a picture of
In comparing two proportions, suppose that p1 5 p2 5 .5 and n1 5 n2 5 100.a. Draw a picture of the appropriate sampling distribution, and show where the value p^ 1 2 p^ 2 5 0.13 falls on it.b. Find the value of the standardized statistic corresponding to p^ 1 2 p^ 2 5 0.13.c. Draw a picture of the
Using the formula z 5 Sample statistic 2 Population parameter s.d.1sample statistic2 give the formula for the standardized statistic in each of the following cases.a. The sample statistic is x1 2 x2.b. The population parameter is p1 2 p2.c. The sample statistic is d.
In addition to the sample size n, what population value(s)must be known to find a standardized score for a sample mean x?
In addition to the sample size n, what population value(s)must be known to find a standardized score for a sample proportion p^?
inches, respectively. Heights within each sex are bell-shaped. Suppose random samples of nine men’s and nine women’s heights are measured and the difference in the sample means is found (men 2 women).a. What is the mean of the sampling distribution of x1 2 x2 in this situation?b. What is the
The mean and standard deviation for the heights of adult men are about 70 inches and 3 inches, respectively; for adult women, they are about 65 inches and
days for the 25 participants who took zinc lozenges and 8.1 days for the 23 participants who took placebo lozenges, for a difference of 3.6 days. Is this difference reasonable on the basis of the figure you drew in part (c)? You can explain in words or show where the value falls on the figure.e.
(repeated here) for this scenario, and then answer part (e).a. What is the mean of the sampling distribution of the difference in sample means?b. What is the standard deviation of the sampling distribution of the difference in sample means?c. Assuming that the conditions are met to make it
Refer to Exercises 9.78 and 9.79. Suppose that in truth, there is no difference in the mean duration of symptoms that would occur if everyone in the population were to take zinc lozenges and the mean duration if everyone were to take placebo lozenges. Assume that the standard deviations for
(p. 340).d. In the study by Prasad et al. (2000), the sample mean duration of symptoms was 4.5 days for the 25 participants who took zinc lozenges and 8.1 days for the 23 participants who took placebo lozenges, for a difference of 3.6 days. Is this difference reasonable based on the figure you drew

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