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| m102870 | Using the central limit theorem, what is the distribution of sample means when the population distribution is:
(a) Rectangular?
(b) Normal?
(c) Positively skewed?
(d) Nonmodal?
(e) Multimodal?
(f) Negatively skewed? |
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| m102871 | Using the data listed in Question 15,
In Q 15
Time 1 ______________ Time 2
4 ............................. 8
3 ............................. 2
5 ............................. 7
4 ............................. 6
6 ............................. 3
(a) Compute the mean difference (MD), standard deviation (sD), and standard error for the difference scores (sMD).
(b) Sketch a graph of the distribution of mean difference scores (MD ± sD).
(c) Sketch a graph of the sampling distribution of mean difference scores (MD ± sMD). |
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| m102872 | Volker (2006) stated the following in an article describing recommendations for the use of effect size in school psychology research: "Report at least one measure of effect size for each major [pairwise] comparison ... it is probably best to report only effect size results for comparisons that are statistically significant" (p. 670). Explain why it is not necessary to report effect size estimates for results that are not significant. |
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| m102873 | Wainwright, Leatherdale, and Dublin (2007) evaluated the advantages and disadvantages of using an ANOVA to analyze data with animal models. They explained that animal pups are often raised or clustered together. In terms of the assumptions for an ANOVA, they state,
An analysis that is based on individual pups without taking this clustering into account is likely to over-estimate the statistical significance of any observed effect. Similar concerns apply to [within-subjects] analyses, where the errors in an individual over time are likely to be [related], violating statistical assumptions of independence. (Wainwright et al., 2007, p. 665)
Explain why housing rat pups in clusters might violate the assumption of independence for a within-subjects design. |
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| m102874 | Wan, Friedman, Boutros, and Crawford (2008) studied a possible link between smoking and certain personality traits by sex. In a description of their participants (M ± SD), the researchers stated that "of those who reported smoking, men (n=61) and women (n=93) reported ... similar daily cigarette consumption per day (men: 4.25±6.25 cigarettes per day; women: 3.84±5.26 cigarettes per day)" (Wan et al., 2008, p. 428).
(a) State the degrees of freedom for variance for men and for women.
(b) Assume these data are approximately normally distributed. Is it more likely that men or women smoked at least half a pack (10 cigarettes) per day? Explain. |
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| m102875 | Water parks are a huge summer attraction for vacationers in the United States. The Global Attractions Attendance Report, published by the Themed Entertainment Association, provides the attendance report for theme parks and water parks around the world. The following table provides the total yearly attendance for the top 20 water parks in the United States, in thousands, during one year.
a. Obtain and interpret the quartiles.
b. Determine and interpret the interquartile range.
c. Find and interpret the five-number summary.
d. Identify potential outliers, if any.
e. Construct and interpret a boxplot. |
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| m102876 | We have presented a contingency table that gives a cross-classification of a random sample of values for two variables, x and y, of a population. For each exercise, perform the following tasks.
a. Find the expected frequencies.
b. Determine the value of the chi-square statistic.
c. Decide at the 5% significance level whether the data provide sufficient evidence to conclude that the two variables are associated. |
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| m102877 | We have presented either a contingency table or a joint probability distribution. In each case, determine both P(C1 | R2) and P(R2 | C1). |
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| m102878 | We have presented some simple qualitative data sets for practicing the concepts. For each data set,
a. Determine a frequency distribution.
b. Obtain a relative-frequency distribution.
c. Draw a pie chart.
d. Construct a bar chart.
C A B B A |
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| m102879 | We have provided the probability distributions of the random variables considered in Exercises 5.7-5.10 of Section 5.1. For each exercise, do the following tasks.
a. Find the mean of the random variable.
b. Obtain the standard deviation of the random variable by using one of the formulas given in Definition 5.5. |
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| m102880 | We have studied two approximations to the binomial, the normal approximation and the Poisson approximation (See Section 5.4). Write a brief but complete essay in which you discuss and summarize the conditions under which each approximation would be used, the formulas involved, and the assumptions made for each approximation. Give details and examples in your essay. How could you apply these statistical methods in your everyday life? |
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| m102881 | We now have the tools to solve the chapter Focus Problem. In the book A Guide to the Development and Use of the Myers-Briggs Type Indicators by Myers and McCaully, it was reported that approximately 45% of all university professors are extroverted. Suppose you have classes with six different professors.
(a) What is the probability that all six are extroverts?
(b) What is the probability that none of your professors is an extrovert?
(c) What is the probability that at least two of your professors are extroverts?
(d) In a group of six professors selected at random, what is the expected number of extroverts? What is the standard deviation of the distribution?
(e) Quota Problem Suppose you were assigned to write an article for the student newspaper and you were given a quota (by the editor) of interviewing at least three extroverted professors. How many professors selected at random would you need to interview to be at least 90% sure of fi lling the quota? |
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| m102882 | We repeat the data from Exercises 16.42- 16.47 of Section 16.3 for independent simple random samples from several populations. In each case, conduct a Tukey multiple comparison at the 95% family confidence level. Interpret your results. |
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| m102883 | Wendy s restaurant has been recognized for having the fastest average service time among fast food restaurants. In a benchmark study, Wendy s average service time of 2.2 minutes was less than those of Burger King, Chick-fil-A, Krystal, McDonald s, Taco Bell, and Taco John s (QSR Magazine website, December 2014). Assume that the service time for Wendy s has an exponential distribution.
a. What is the probability that a service time is less than or equal to one minute?
b. What is the probability that a service time is between 30 seconds and one minute?
c. Suppose a manager of a Wendy s is considering instituting a policy such that if the time it takes to serve you exceeds five minutes, your food is free. What is the probability that you will get your food for free? Comment. |
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| m102884 | What about sample size? If we want a confi dence interval with maximal margin of error E and level of confi dence c, then Section 7.1 shows us which formulas to apply for a single mean m and Section 7.3 shows us formulas for a single proportion p.
(a) How about a difference of means? When (1 and (2 are known, the margin of error E for a c% con fidence interval is
Let us make the simplifying assumption that we have equal sample sizes n so that n = n1 = n2. We also assume that n ( 30. In this context, we get
Solve this equation for n and show that
(b) In Problem 15 (football and basketball player heights), suppose we want to be 95% sure that our estimate x̅1 - x̅2 for the difference (1 - (2 has a margin of error E - 0.05 foot. How large should the sample size be (assuming equal sample size- i.e., n = n1 = n2)? Since we do not know (1 or (2 and n ( 30, use s1 and s2, respectively, from the preliminary sample of Problem 15.
(c) In Problem 16 (petal lengths of two iris species), suppose we want to be 90% sure that our estimate x̅1 - x̅2 for the difference (1 - (2 has a margin of error E = 0.1 cm. How large should the sample size be (assuming equal sample size-i.e., n - n1 - n2)? Since we do not know (1 or (2 and n ( 30, use s1 and s2, respectively, from the preliminary sample of Problem 16. |
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| m102885 | What about the sample size n for confi dence intervals for the difference of proportions p1 - p2? Let us make the following assumptions: equal sample sizes n = n1 = n2 and all four quantities n1p1, n1q1, n2p2, and n2q2 are greater than 5. Those readers familiar with algebra can use the procedure outlined in Problem 28 to show that if we have preliminary estimates 1 and 2 and a given maximal margin of error E for a specifi ed con fidence level c, then the sample size n should be at least
However, if we have no preliminary estimates for 1 and 2, then the theory similar to that used in this section tells us that the sample size n should be at least
(a) In Problem 17 (Myers-Briggs personality type indicators in common for married couples), suppose we want to be 99% confi dent that our estimate 1 - 2 for the difference p1 - p2 has a maximal margin of error E = 0.04. Use the preliminary estimates 1 = 289/375 for the proportion of couples sharing two personality traits and 2 = 23/571 for the proportion having no traits in common. How large should the sample size be (assuming equal sample size-i.e., n - n1 - n2)?
(b) Suppose that in Problem 17 we have no preliminary estimates for 1 and 2 and we want to be 95% con fident that our estimate 1 - 2 for the difference p1 - p2 has a maximal margin of error E = 0.05. How large should the sample size be (assuming equal sample size-i.e., n - n1 - n2)? |
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| m102886 | What advantage does the sign test have over the Wilcoxon signed-rank test? |
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| m102887 | What are an advantage and a disadvantage of using only the sample mean to estimate the population mean? |
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| m102888 | What are counting rules? Why are they important? |
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| m102889 | What are the three rules for constructing a histogram? |
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