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elementary statistics

Questions and Answers of Elementary Statistics

Community Involvement Claim: Three-fourths of all adults believe that it is important to be involved in their communities. Based on a USA Today/Gallup poll of 1021 randomly selected adults, 89%
Exercise 8 Forming Conclusions. In Exercises 9–12, refer to the exercise identified.Using only the rare event rule, make subjective estimates to determine whether results are likely, then state a
Exercise 7 Forming Conclusions. In Exercises 9–12, refer to the exercise identified.Using only the rare event rule, make subjective estimates to determine whether results are likely, then state a
Exercise 6 Forming Conclusions. In Exercises 9–12, refer to the exercise identified.Using only the rare event rule, make subjective estimates to determine whether results are likely, then state a
Exercise 5 Forming Conclusions. In Exercises 9–12, refer to the exercise identified.Using only the rare event rule, make subjective estimates to determine whether results are likely, then state a
For the random sample of adult females in Data Set 1 from Appendix: Data Sets, the pulse rates have a standard deviation of 11.6.
Claim: The standard deviation of pulse rates of adult women is at least
Claim: The mean pulse rate (in beats per minute) of adult females is 76 or lower. For the random sample of adult females in Data Set 1 from Appendix: Data Sets, the mean pulse rate is 77.5.
Claim: When parents use the XSORT method of gender selection, the proportion of baby girls is greater than 0.5. The latest actual results show that among 945 babies born to couples using the XSORT
Claim: 20% of adults smoke. A recent Gallup survey of 1016 randomly selected adults showed that 21% of the respondents smoke.
Interpreting P-value When the clinical trial of the XSORT method of gender selection is completed, a formal hypothesis test will be conducted with the alternative hypothesis of p 7 0.5, which
Mean Body Temperature A formal hypothesis test is to be conducted using the claim that the mean body temperature is equal to 98.6°F.a. What is the null hypothesis, and how is it denoted?b. What is
We could use these values to test some claim. What is the difference between estimating and hypothesis testing?
Estimates and Hypothesis Tests Data Set 20 in Appendix: Data Sets includes sample weights of the M&Ms referenced in Exercise
M&Ms and Aspirin A package label includes a claim that the mean weight of the M&Ms is 0.8535 g, and another package label includes the claim that the mean amount of aspirin in Bayer tablets is 325
Finding Critical Values In constructing confidence intervals for s or s2, Table 4 in Appendix: Tables can be used to find the critical values x2 L and x2 R only for select values of n up to 101, so
Pick 4 Lottery The dotplot below depicts individual digits selected in the Pick 4 lottery from different states. Can the original list of individual sample digits be identified? Can the sample data
Interbreeding of Cultures Changes in head sizes over time suggest interbreeding with people from other regions. Use the data depicted in the accompanying dotplots and construct 95% confidence
Age Discrimination? The accompanying stemplots depict ages of applicants who were unsuccessful in winning promotion and ages of applicants who were successful in winning promotion (based on data from
Confidence level is 99%, s is not known, and the dotplot of a sample of 40 values of professional baseball player salaries is as shown below. . 2000 4000 6000 8000 10000 12000 Salary (thousands of
Confidence level is 90%, s is not known, and the dotplot of IQ scores of 20 randomly selected statistics instructors is as shown below. 126 128 130 .. 132 134 136 138 IQ
Confidence level is 95%, s is known to be $4,385,000, and the dotplot of a sample of Red Sox baseball player salaries is as shown below. 2000 4000 6000 8000 10000 12000 14000 Salary (thousands of
Normality Requirement What does it mean when we say that the confidence interval methods of this section are robust against departures from normality? Does the dotplot below appear to satisfy the
Finite Population Correction Factor For Formulas 2 and 3 we assume that the population is infinite or very large and that we are sampling with replacement. When we have a relatively small population
Flight Departure Delays The normal quantile plot represents flight departure delay times (minutes) from Data Set 15 in the Appendix: Data Sets. z score 3 2.4 1.8 1.2 0.6 0 -0.6 -1.2 -1.8 -2.4 .3.20
White Blood Cell Counts The normal quantile plot represents white blood cell counts of males from Data Set 1 in the Appendix: Data Sets. z score 3 2.4 1.8 1.2 0.6 0 -0.6 -1.2 -1.8 -2.4 33 3.8 4.6 5.4
Body Temperatures The normal quantile plot represents body temperatures of adults from Data Set 3 in the Appendix:Data Sets. z score 3 2.4 1.8 1.2 0.6 0 -0.6 -1.2 -1.8 -2.4 6.5 96.81 97.12 97.43
Ages of Oscar-Winning Actresses The normal quantile plot represents the ages of actresses when they won Oscars. The data are from Data Set 11 in the Appendix: Data Sets. z score 3 2.4 1.8 1.2 0.6 0
Assessing Normality The accompanying histogram is constructed from the platelet counts of the 40 women included in Data Set 1 in the Appendix: Data Sets. If you plan to conduct further statistical
Population Parameters Use the same population of {4, 5, 9} from Example 1 in Section 4.Assume that samples of size n = 2 are randomly selected without replacement.a. Find m and s for the
Using a Formula to Describe a Sampling Distribution Exercise 15 requires the construction of a table that describes the sampling distribution of the proportions of girls from two births. Consider the
IQ Scores. In Exercises 9–12, find the indicated IQ score, and round to the nearest whole number. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100
IQ Scores. In Exercises 9–12, find the indicated IQ score, and round to the nearest whole number. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100
IQ Scores. In Exercises 9–12, find the indicated IQ score, and round to the nearest whole number. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100
IQ Scores. In Exercises 9–12, find the indicated IQ score, and round to the nearest whole number. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100
In a continuous uniform distribution,a. Find the mean and standard deviation for the distribution of the subway waiting times represented in Figure 2.b. For a continuous uniform distribution with m =
Standard Normal Distribution. In Exercises 13–16, find the indicated z score. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. 0 z
Standard Normal Distribution. In Exercises 13–16, find the indicated z score. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. N
Standard Normal Distribution. In Exercises 13–16, find the indicated z score. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. 0.3050
Standard Normal Distribution. In Exercises 13–16, find the indicated z score. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1. 0.8907
Standard Normal Distribution. In Exercises 9–12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
Standard Normal Distribution. In Exercises 9–12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
Standard Normal Distribution. In Exercises 9–12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
Standard Normal Distribution. In Exercises 9–12, find the area of the shaded region. The graph depicts the standard normal distribution of bone density scores with mean 0 and standard deviation 1.
Hypergeometric Distribution If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent.If sampling is done
Multinomial Distribution The binomial distribution applies only to cases involving two types of outcomes, whereas the multinomial distribution involves more than two categories.Suppose we have three
Casino Games When betting on the pass line in the dice game of craps at the Mohegan Sun casino in Connecticut, the table lists the probabilities for the number of bets that must be placed in order to
Happiness In a survey sponsored by Coca-Cola, subjects aged 15–65 were asked what contributes most to their happiness, and the table is based on their responses. P(x) Family/ 0.77 partner Friends
Happiness Groups of people aged 15–65 are randomly selected and arranged in groups of six. The random variable x is the number in the group who say that their family and/or partner contribute most
Fun Ways to Flirt A sociologist randomly selects single adults for different groups of four, and the random variable x is the number in the group who say that the most fun way to flirt is in
Fun Ways to Flirt In a Microsoft Instant Messaging survey, respondents were asked to choose the most fun way to flirt, and the accompanying table is based on the results. P(x) E-mail 0.06 In person
Pickup Line Ted is not particularly creative. He uses this pickup line: “If I could rearrange the alphabet, I’d put U and I together.”The random variable x is the number of girls Ted approaches
Male Color Blindness When conducting research on color blindness in males, a researcher forms random groups with five males in each group. The random variable x is the number of males in the group
Genetic Disorder Four males with an X-linked genetic disorder have one child each. The random variable x is the number of children among the four who inherit the X-linked genetic disorder. XO 0 P(x)
In Exercise 59, let X be the number of girls the couple has.a. Find the probability distribution of X.b. Find the mean μX.c. Find the standard deviation σX.Exercise 59A couple plans to have
In the game of craps, two dice are rolled, and people bet on the outcome. For example, you can bet $1 that the dice will total 7.The probability that you win is 1∕6, and if you win, your profit is
In the New York State Numbers Lottery, you pay $1 and can bet that the sum of the numbers that come up is 13.The probability of winning is 0.075, and if you win, you win $6.50, which is a profit of
In the New York State Numbers Lottery, you pay $1 and pick a number from 000 to 999.If your number comes up, you win $500, which is a profit of $499. If you lose, you lose $1. Your probability of
For the data in Table 2.23:a. Construct a bar graph in which the y-axis is labeled from 0 to 100.b. Compare this bar graph with the bar graphs in Figures 2.23 and 2.24. Does this bar graph tend to
11.54 Do you have a favorite “comfort food”?How do you obtain it? The following graphic lists three methods used by Americans and the percentage each method is used. Which category do you belong
11.23 Skittles Original Fruit bite-size candies are multicolored candies in a bag, and you can “Taste the Rainbow” with their five colors and flavors:green, lime; purple, grape; yellow, lemon;
11.22 [EX11-22] The 2003 U.S. census found that babies entered the world on the days of the week in the proportions that follow. Weekday P(Day) Weekday P(Day) Sunday 0.098 Thursday 0.160 Monday 0.149
11.16 [EX11-016] Over the years, African American actors in major cinema releases are more likely than white actors to have major roles in comedies. The following table shows the percent of all roles
11.6 Using the notation seen in Exercise 11.4, name and find the critical values of 2. a=0.05 n=8 a = 0.01 n = 19 a=0.05 =28 a=0.01 n = 10
11.3 Using Table 8 of Appendix B, find the following:a. 2(10, 0.01)b. 2(12, 0.025)c. 2(10, 0.95)d. 2(22, 0.995) a=0.01 =15 = 0.05 n=26
10.14 [PT10-14] Twenty college freshmen were randomly divided into two groups. Members of one group were assigned to a statistics section that used programmed materials only.Members of the other
10.12 Determine the test statistic, critical region, and critical value(s) that would be used in completing each hypothesis test using the classical procedure with 0.05. a. Ho pi pz 0 Ha: P - P20
10.129 [EX10-129] What dollar amount should someone spend on a Valentine’s Day gift for you?The results found by a Greenfield Online survey of 653 respondents was pictured in the accompanying
10.127 [EX10-127] A constant objective in the manufacture of contact lenses is to improve the level and variation for those features that affect lens power and visual acuity. One such feature
10.114 Determine the critical region and critical value(s) that would be used to test the following hypotheses using the classical approach when Fis used as the test statistic. a. H, vs. H: > with n
10.112 Determine the p-value that would be used to test the following hypotheses when F is used as the test statistic: a. H, = vs. H: > , with n = 10, n = 16, and F = 2.47 F2.47 b. H, = vs. H: >
10.109 Using the F(df1, df2, ) notation, name each of the critical values shown on the following figures. a. = 10 2=12 a = 0.025 b. 125 12=20 a = 0.01 0 C. =9 12-16 a = 0.01 0 d. = 16 2=10 a =
10.107 Explain why the inequality > is
10.95 Determine the critical region and critical value(s) that would be used to test (classical procedure) the following hypotheses when z is used as the test statistic. a. Ho pp vs. Ha: P> pz, with
10.94 Determine the p-value that would be used to test the following hypotheses when z is used as the test statistic. b. H, PA c. HP a. Ho p =p2 vs. Ha: P> P2, with z = 2.47 z PE VS. Ha: PAPB, with z
10.90 Show that the standard error of Pip, which is Pigi P292 + reduces to n n Pq[()+()] when p = when p =P = P.
10.2a. Estimate the mean credit card debt for freshmen with a 95% confidence interval.b. Does the sampled population of sophomores have a significantly higher credit card debt than the national
a. Show that the following is a probability distribution:b. Find P(x 1).c. Find P(x 2).d. Find P(x 2).e. Find the mean of x.f. Find the standard deviation of x. X 1 3 4 5 P(x) 0.2 0.3 0.4 0.1
A random variable that can assume any one of the integer values 1, 2, . . . , n with equal probabilities 1 - bilities of is said to have a uniform distribution. n The probability function is written
[EX05-123] In a germination trial, 50 seeds were planted in each of 40 rows. The number of seeds germinating in each row was recorded as listed in the following table.a. Use the preceding frequency
Learning is a lifetime activity. For some, it means learning from everyday experiences; for others, it means taking classes in a more traditional atmosphere. The percentage of people participating in
The 2000 census produced the following figures for the city of Loveland, Colorado, with respect to the number of available vehicles per household:Replacing the category of “3 or more” with
Patients who have artificial hip-replacement surgery experience pain the first day after surgery.Typically, the pain is measured on a subjective scale using values of 1 to 5. Let x represent the
“How many TV’s are there in your household?”was one of the questions on a questionnaire sent to 5000 people in Japan. The collected data resulted in the following distribution:One of these
Given the binomial probability functiona. Calculate the mean and standard deviation of the random variable by using formulas (5.1), (5.3a), and (5.4).b. Calculate the mean and standard deviation
Let x be a random variable with the following probability distribution:Does x have a binomial distribution? Justify your answer. X 0 1 2 3 P(x) 0.4 0.3 0.2 0.1
Test the following function to determine whether or not it is a binomial probability function.List the distribution of probabilities and sketch a histogram. 5-x for x = 0, 1, 2, 3, 4, 5 T(x) 5 =
If x is a binomial random variable, use Table 2 in Appendix B to determine the probability of x for each of the following: a. n = 10, x = 8, p = 0.3 b. C. d. n = 15, x=3, p = 0.05 e. n=9,x=0, p = 0.5
If x is a binomial random variable, calculate the probability of x for each case. a. n = 4, x = 1, p = 0.3 b. n=3, x = 2, p = 0.8 C. n = 2, x = 0, p d. n = 5, x = 2, p 4 3 e. n = 4, x2, p = 0.5 f. n
Skillbuilder Applet Exercise demonstrates calculating a binomial probability along with a visual interpretation.Suppose that you are in a class of 30 students and it is assumed that approximately 11%
Skillbuilder Applet Exercise demonstrates calculating a binomial probability along with a visual interpretation.Suppose that you buy 20 plants from a nursery and the nursery claims that 95% of its
Consider a binomial experiment made up of three trials with outcomes of success, S, and failure, F, where P(S) p and P(F) q.a. Complete the accompanying tree diagram. Label all branches
Show that each of the following is true for any values of n and k. Use two specific sets of values for n and k to show that each is true. n a. 0 = 1 and n n 1 = = n- (, n- b. ()and()(2)()
Evaluate each of the following. 6! a. 4! e. 4! b. 71 5! 2131 f. 6! c. 0! d. 21 g. (0.3)4 h. 4!(6-4)! 73 1. 1. 52 J. (3) (5)(0.3)(0.7)5 k. (1)(0.2) (0.8)
Skillbuilder Applet Exercise simulates playing a game where a player has a 0.2 probability of winning$3 and a 0.8 probability of losing $1. Repeat the simulations for several sets of 100 plays using
The random variable x has the following probability distribution:a. Find the mean and standard deviation of x.b. What is the probability that x is between and ? X 1 2 3 4 5 P(X) 0.6 10 0.1 0.1
The random variable A has the following probability distribution:a. Find the mean and standard deviation of A.b. How much of the probability distribution is within 2 standard deviations of the
In a USA Today Snapshot (February 22, 2005), the following statistics were reported on pet ownership per household.a. Replacing the category “five or more” with exactly “five,” find the mean
The number of ships to arrive at a harbor on any given day is a random variable represented by x. The probability distribution for x is as follows:Find the mean and standard deviation of the number
[EX05-034] In a USA Snapshot (June 12, 2002), the U.S. Census Bureau describes the number of vehicles per household in the United States as follows.a. Replacing the category “3 or more” with

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