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elementary statistics
Elementary Statistics Picturing The World 5th Edition Ron Larson, Betsy Farber - Solutions
Describe the difference between the variance between samples MSB and the variance within samples MSw.
Explain how to determine the values of d.f.y and d.f.p when performing a two-sample F-test.
In addition to the variables used in the Case Study, what other variables do you think are important to consider when studying the distribution of U.S. consumers' attitudes about healthy fast food?
Compare the distribution of responses by males with the national distribution. What can you conclude?
Compare the distribution of responses by females with the national distribution. What can you conclude?
At a 0.01, perform a chi-square indepen- dence test to determine whether the variables response and gender are independent. What can you conclude? In Exercises 4 and 5, perform a chi-square goodness-of-fit test to compare the national distribution of responses with the distribution of each gender.
Assuming the variables gender and response are independent, did female respondents or male respondents exceed the expected number of "neither agree nor disagree" responses? =
Assuming the variables gender and response are independent, did female respondents or male respondents exceed the expected number of "somewhat agree" responses?
What conclusions can you make from the bar graph you constructed in Exercise 38?
Use your results from Exercise 35 to construct a bar graph that shows the percentages of U.S. adults ages 25 and over based on employment status. Each category of employment status will have four bars, representing the four levels of educational attainment mentioned in the contingency table.
What percent of U.S. adults ages 25 and over who are not high school graduates are unemployed?
What percent of U.S. adults ages 25 and over who have a degree are not in the labor force?
Calculate the conditional relative frequencies in the contingency table based on the column totals.
What percent of U.S. adults ages 25 and over who are not in the labor force have some college education, but no degree?
What percent of U.S. adults ages 25 and over who are employed have a degree?
Calculate the conditional relative frequencies in the contingency table based on the row totals.
Explain why you cannot perform the chi-square independence test on these data. Conditional Relative Frequencies In Exercises 32-39, use the contingency table from Exercises 29-31, and the following information. Relative frequencies can also be calculated based on the row totals (by dividing each
What percent of U.S. adults ages 25 and over (a) have a degree and are unemployed? (b) have some college education, but no degree, and are not in the labor force? (c) are employed and high school graduates? (d) are not in the labor force? (e) are high school graduates?
Rewrite the contingency table using relative frequencies.
If the test statistic for the chi-square independence test is large, you will, in most cases, reject the null hypothesis.
If the two variables of the chi-square test for independence are dependent, then you can expect little difference between the observed frequencies and the expected frequencies.
Explain why the chi-square independence test is always a right-tailed test. True or False? In Exercises 5 and 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
Explain how the chi-square test for independence and the chi-square goodness-of-fit test are similar. How are they different?
Stock Price The equation used to predict the stock price (in dollars) at the end of the year for McDonald's Corporation is -475.91x1 - 1.99x2 where x is the total revenue (in billions of dollars) and x2 is the shareholders' equity (in billions of dollars). Use the multiple regression equation to
Construct a 95% prediction interval for the average annual salary of public school classroom teachers when the average annual salary of public school principals is $85,750. Interpret the results.
Find the standard error of estimates, and interpret the result.
Find the coefficient of determination r and interpret the result.
Use the regression equation to predict the average annual salary of public school classroom teachers when the average annual salary of public school principals is $90,500.
Find the equation of the regression line for the data. Draw the regression line on the scatter plot.
Test the level of significance of the correlation coefficient r. Use a = 0.05.
Calculate the correlation coefficient r. What can you conclude?
Construct a scatter plot for the data. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation? Explain.
The coefficient of determination is the ratio of which two types of variations? What does measure? What does measure?
Describe the unexplained variation about a regression line in words and in symbols.
Describe the explained variation about a regression line in words and in symbols.
Describe the total variation about a regression line in words and in symbols.
The point a regression line always passes througha. b. yic. bd. (x, y)e. mf. y
The mean of the y-values
y-intercept
Slope
The y-value for a point on the regression line corresponding to x
The y-value of a data point corresponding to x
Why is it not appropriate to use a regression line to predict y-values for x-values that are not in (or close to) the range of x-values found in the data? In Exercises 7-12, match the description in the left column with its symbol(s) in the right column.
Given a set of data and a corresponding regression line, describe all values of x that provide meaningful predictions for y.
In your own words, what does it mean to say “correlation does not imply causation”?
Explain how to decide whether a sample correlation coefficient indicates that the population correlation coefficient is significant.
What does the sample correlation coefficient r measure? Which value indicates a stronger correlation: or Explain your reasoning.
Two variables have a negative linear correlation. Does the dependent variable increase or decrease as the independent variable increases?
Two variables have a positive linear correlation. Does the dependent variable increase or decrease as the independent variable increases?
A tourist agency in Kansas claims the mean daily cost of meals and lodging for a family of 4 traveling in the state is $201. You work for a consumer protection advocate and want to test this claim. In a random sample of 35 families of 4 traveling in Kansas, the mean daily cost of meals and lodging
A government agency reports that the mean amount of earnings for full-time workers ages 25 to 34 with a master's degree is $62,569. In a random sample of 15 full-time workers ages 25 to 34 with a master's degree, the mean amount of earnings is $59,231 and the standard deviation is $5945. Is there
A state school administrator says that the standard deviation of SAT critical reading test scores is112.A random sample of 19 SAT critical reading test scores has a standard deviation of143.At a = 0.10, test the administrator's claim. What can you conclude? Assume the population is normally
A maker of microwave ovens advertises that no more than 10% of its microwaves need repair during the first 5 years of use. In a random sample of 57 microwaves that are 5 years old, 13% needed repairs. At a = 0.04, can you reject the maker's claim that no more than 10% of its microwaves need repair
A hat company states that the mean hat size for a male is at least 7.25. A random sample of 12 hat sizes has a mean of 7.15 and a standard deviation of 0.27. At a = 0.05, can you reject the company's claim that the mean hat size for a male is at least 7.25? Assume the population is normally
A research service estimates that the mean annual consumption of vegetables and melons by people in the United States is at least 170 pounds per person. A random sample of 360 people in the United States has a mean consumption. of vegetables and melons of 168.5 pounds per year and a standard
In Exercise 62, is there enough evidence to reject the restaurant's claim at the a = 0.05 level? Explain.
A restaurant claims that the standard deviation of the lengths of serving times is 3 minutes. A random sample of 27 serving times has a standard deviation of 3.9 minutes. At a 0.01, is there enough evidence to reject the restaurant's claim?
A bolt manufacturer makes a type of bolt to be used in airtight containers. The manufacturer needs to be sure that all of its bolts are very similar in width, so it sets an upper tolerance limit for the variance of bolt width at 0.01. A random sample of the widths of 28 bolts has a variance of
Claim: # 0.035; a = 0.01. Sample statistics: s = 0.026, n = 16 In Exercises 61 and 62, test the claim about the population variance or standard deviation. Interpret your decision in the context of the original claim. For each claim, assume the population is normally distributed.
Claim: = 1.25; a = 0.05. Sample statistics: s = 1.03, n = 6
Claim: o = 60; a = 0.025. Sample statistics: s = 72.7, n = 15 =>
Claim: > 2; a = 0.10. Sample statistics: s = 2.95, n = 18
Left-tailed test, n = 6, a = 0.05 In Exercises 57-60, use a x-test to test the claim about the population variance o or standard deviation or at the given level of significance a and using the given sample statistics. For each claim, assume the population is normally distributed.
Right-tailed test, n = 51, a = 0.10
Two-tailed test, n = 14, a = 0.01
Right-tailed test, n = = 20, = 0.05
The Western blot assay is a blood test for the presence of HIV. It has been found that this test sometimes gives false positive results for HIV. A medical researcher claims that the rate of false positives is 2%. A recent study of 300 randomly selected U.S. blood donors who do not have HIV found
A polling agency reports that over 16% of U.S. adults are without health care coverage. In a random survey of 1420 U.S. adults, 256 said they did not have health care coverage. At a = 0.02, is there enough evidence to support the agency's claim? (Source: The Gallup Poll)
Claim: p 0.80; a = 0.10. Sample statistics: p = 0.85, n = 43 = 0.01. Sample statistics: p = 0.29, n = 60 In Exercises 51 and 52, test the claim about the population proportion p. Interpret your decision in the context of the original claim. If convenient, use technology.
Claim: p + 0.24; a = 0.02. Sample statistics: p = 0.32, n = 50
Claim: p 0.34; a
Claim: p 0.04; =
Claim: p=0.65; a
Claim: p
Claim: p < 0.70; a = 0.01. Sample statistics: p = 0.50, n = 68 = 0.08. Sample statistics: p = 0.07, n = 75 0.03. Sample statistics: p = 0.76, n = 116 0.10. Sample statistics: p = 0.03, n = 30
When testing a claim about a population mean or a population standard deviation, a requirement is that the sample is from a population that is normally distributed. How is this requirement different between the two tests?
Can a critical value for the -test be negative? Explain.
Explain how to find critical values in a - sampling distribution.
Writing You are testing a claim and incorrectly use the normal sampling distribution instead of the t-sampling distribution. Does this make it more or less likely to reject the null hypothesis? Is this result the same no matter whether the test is left-tailed, right-tailed, or two-tailed? Explain
Private Law School An education publication claims that the average in-state tuition for one year of law school at a private institution is more than $35,000. A random sample of 50 private law schools has a mean in-state tuition of $34,967 and a standard deviation of $5933 for one year. At test the
Gas Mileage A car company says that the mean gas mileage for its luxury sedan is at least 23 miles per gallon (mpg). You believe the claim is incorrect and find that a random sample of 5 cars has a mean gas mileage of 22 mpg and a standard deviation of 4 mpg. At test the company’s claim. Assume
Using Different Values of c and n In Exercise 35, you believe that Ho is not valid. Which of the following allows you to reject Ho? Explain your reasoning. (a) Use the same values but decrease a from 0.05 to 0.01. (b) Use the same values but increase a from 0.05 to 0.10. (c) Use the same values but
Credit Card Balances To test the claim that the mean credit card debt for individuals is greater than $5000, you do some research and find that a random sample of 6 cardholders has a mean credit card balance of $5434 with a standard deviation of $625. You conduct a statistical experiment where Ho
Claim:
Claim: 31.5, s = 4.7, n = 12
Claim: 73.6, s = 3.2, n = 26
Faculty Classroom Hours The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is
Class Size You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is fewer than 32 students.You want to test this claim.You randomly select 18 classes taught by full-time faculty and determine the class size of each. The results are
Lodging Cost A travel association claims that the mean daily lodging cost for two adults traveling together on vacation in San Francisco is at least $240. A random sample of 24 such groups of adults has a mean daily lodging cost of $233 and a standard deviation of $12.50. Is there enough evidence
Meal Cost A travel association claims that the mean daily meal cost for two adults traveling together on vacation in San Francisco is $105. A random sample of 20 such groups of adults has a mean daily meal cost of $110 and a standard deviation of $8.50. Is there enough evidence to reject the claim
Oil Changes A repair shop believes that people travel more than 3500 miles between oil changes. A random sample of 8 cars getting an oil change has a mean distance of 3375 miles since having an oil change with a standard deviation of 225 miles. At a = 0.05, do you have enough evidence to support
Speed Limit A county is considering raising the speed limit on a road because they claim that the mean speed of vehicles is greater than 45 miles per hour. A random sample of 25 vehicles has a mean speed of 48 miles per hour and a standard deviation of 5.4 miles per hour. At a = 0.10, do you have
Annual Pay An employment information service claims the mean annual salary for full-time female workers over age 25 and without a high school diploma is more than $18,500. The annual salaries for a random sample of 12 full-time female workers without a high school diploma are listed. At a = 0.10,
Annual Pay An employment information service claims the mean annual salary for full-time male workers over age 25 and without a high school diploma is $26,000. The annual salaries for a random sample of 10 full-time male workers without a high school diploma are listed. At a = 0.05, test the claim
Waste Generated As part of your work for an environmental awareness group, you want to test a claim that the mean amount of waste generated by adults in the United States is more than 4 pounds per day. In a random sample of 22 adults in the United States, you find that the mean waste generated per
Waste Recycled An environmentalist estimates that the mean amount of waste recycled by adults in the United States is more than 1 pound per person per day. You want to test this claim. You find that the mean waste recycled per person per day for a random sample of 13 adults in the United States is
The conventional "normal" body temperature was established by Carl Wunderlich over 100 years ago. What were possible sources of error in Wunderlich's sampling procedure?
Use the sample of 130 temperatures to form a 99% confidence interval for the mean body temperature of adult humans.
Test the hypothesis that the mean temperature of women is 98.6F. What can you conclude at a level of significance of a = 0.01?
Test the hypothesis that the mean temperature of men is 98.6F. What can you conclude at a level of significance of a = 0.01?
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