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statistics
elementary statistics a step by step approach
Elementary Statistics A Step By Step Approach 9th Edition Allan G. Bluman - Solutions
For the following exercises where applicable:a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.Use the traditional method of hypothesis testing unless otherwise specified. Assume all variables are
For Exercises perform each of the following steps.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Find the test value.d. Make the decision.e. Summarize the results.The average movie ticket in 2010 cost $7.89.A random sample of 15 movie tickets from the suburbs of a
For the following exercises where applicable:a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.Use the traditional method of hypothesis testing unless otherwise specified. Assume all variables are
The degrees of freedom for the t test are________ .
To test the claim that the mean is greater than 87, you would use a(n) _______-tailed test.
For Exercises assume that the variables are normally or approximately normally distributed. Use the traditional method of hypothesis testing unless otherwise specified.Healthier diets generally involve lower sodium amounts. The American Heart Association recommends less than 2300 mg of sodium
The average cost of a speeding ticket plus court fees is approximately $150. A random sample of 38 speeding ticket court cases showed that the mean cost was $152.59. At the 0.01 level of significance, is that greater than $150? The population standard deviation is $10.78.For Exercises perform each
Using the z table (Table E), find the critical value (or values) for each.a. a = 0.02, left-tailed testb. a = 0.05, right-tailed testc. a = 0.01, two-tailed testd. a = 0.04, left-tailed teste. a = 0.02, right-tailed test
For Exercises assume that the variables are normally or approximately normally distributed. Use the traditional method of hypothesis testing unless otherwise specified.A researcher claims that the standard deviation of the number of deaths annually from tornadoes in the United States is less than
The average height of an NBA player is 6.698 feet. A random sample of 30 players’ heights from a major college basketball program found the mean height was 6.75 feet with a standard deviation of 5.5 inches. At α = 0.05, is there sufficient evidence to conclude that the mean height differs from
Rejecting the null hypothesis when it is true is called a(n) _______ error.
About 30% of all burglaries are through an open or unlocked door or window. A random sample of 130 burglaries indicated that 85 were not via an open or unlocked door or window. At the 0.05 level of significance, can it be concluded that this differs from the stated proportion?For Exercises perform
For the t test, one uses _______ instead of σ.a. nb. sc. χ2d. t
When should a one-tailed test be used? A two-tailed test?
For Exercises perform each of the following steps.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.In 2008, 17% of U.S. homes were protected by a home security system. A random sample of 220 homes
The degrees of freedom for the chi-square test for variances or standard deviations area. 1b. nc. n - 1d. None of the above
Explain what is meant by a significant difference.
Consider the distribution of monthly Social Security (OASDI) payments. Assume a normal distribution with a standard deviation of $120. Ifone-fourth of the payments are above $1255.94, what is the mean monthly payment?
If you wish to test the claim that the mean of the population is 100, the appropriate null hypothesis isa. X̅ = 100b. µ ≥ 100c. µ ≤ 100d. µ = 100
For Exercises perform each of the following steps.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.According to the National Association of Home Builders, the average cost of building a home in the
Using the data obtained in Exercise 5, test the hypothesis H0 : σ ≥ 150. Use α = 0.05. Assume the variable is normally distributed.Data From in Exercise 5Using the data from Data Set XIII, select a sample of 10 hospitals, and test H0 : µ = 250 and H1 : µ < 250 for
For Exercises perform each of the following steps.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.According to a professional polling company, an unbelievably low percentage—36%—of Americans
For Exercises perform each of the following steps.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Find the test value.d. Make the decision.e. Summarize the results.The average strawberry has approximately 200 seeds. A very patient student selected a random sample of
When the value of a is increased, the probability of committing a type I error isa. Decreasedb. Increasedc. The samed. None of the above
Using Table F, find the P-value interval for each test value.a. t = 3.025, n = 24, right-tailedb. t = - 1.145, n = 5, left-tailedc. t = 2.179, n = 13, two-tailedd. t = 0.665, n = 10, right-tailed
Using the data from Data Set XIII, select a sample of 10 hospitals, and test H0 : µ = 250 and H1 : µ < 250 for the number of beds. Use α = 0.05. Assume the variable is normally distributed.Data from in data set XIII Data Set XIII Hospital Data* Number of
Use the data collected in data project 6 of Chapter 7 for this exercise. Test the claim that the mean BMI for a student is more than 25.Data from in Project 6Have each student compute his or her body mass index (BMI) (703 times weight in pounds, divided by the square of the height in inches). Find
For Exercises perform each of the following steps.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.In 2009, 45.6% of motor vehicle accidents involved no improper driving. In an area comprised of six
Select a sample of 20 individuals and test the hypothesis H0 : σ2 = 225 for IQ level. Use α = 0.05. Assume the variable is normally distributed.Data from data bank appendix B Data Bank 882882&ID
Determine whether each statement is true or false. If the statement is false, explain why.The chi-square test for variances is always one-tailed.
For Exercises assume that the variables are normally or approximately normally distributed. Use the traditional method of hypothesis testing unless otherwise specified.Test the claim that the standard deviation of the number of aircraft stolen each year in the United States is less than 15 if a
Use the most recent results of the Presidential primary elections for both parties. Determine what percentage of voters in your state voted for the eventual Democratic nominee for President and what percentage voted for the eventual Republican nominee. Test the claim that a majority of your state
What are the mean and the standard deviation of a proportion?
Determine whether each statement is true or false. If the statement is false, explain why.The values of a chi-square test cannot be negative.
Select a random sample of at least 30 individuals, and using the z test for proportions, test one or more of the following hypotheses. Use α = 0.05.a. For educational level, H0 : p = 0.50 for level 2.b. For smoking status, H0 : p = 0.20 for level 1.c. For exercise
For Exercises perform each of the following steps.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.A researcher estimates that the average revenue of the largest businesses in the United States is
Explain the difference between a one-tailed and a two-tailed test.
Using Table G, find the P-value interval for each χ2 test value.a. χ2 = 13.974, n = 28, two-tailedb. χ2 = 10.571, n = 19, left-tailedc. χ2 = 12.144, n = 6, two-tailedd. χ2 = 8.201, n = 23, two-tailed
Use the data collected in data project 4 of Chapter 7 for this exercise. Test the claim that the mean body temperature is less than 98.6 degrees Fahrenheit.Data from in Project 4Use your class as the sample. Have each student take her or his temperature on a day when he or she is
Determine whether each statement is true or false. If the statement is false, explain why.The test value separates the critical region from the noncritical region.
For Exercises perform each of the following steps.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.Many people believe that the average number of Facebook friends is 130. The population standard
What is meant by a statistical test?
Use your last month’s itemized cell phone bill for your data. Determine the percentage of your text messages that were outgoing. Test the claim that a majority of your text messages were outgoing. Determine the mean, median, and standard deviation for the length of a call. Test the claim that the
The power of a test (1 – b) can be calculated when a specific value of the mean is hypothesized in the alternative hypothesis; for example, let H0 : µ = 50 and let H1 : µ = 52. To find the power of a test, it is necessary to find the value of β. This can be done by the following
Determine whether each statement is true or false. If the statement is false, explain why.When you are conducting the t test, the population must be approximately normally distributed.
What are the degrees of freedom for the t test?
For Exercises perform each of the following steps.a. State the hypotheses and identify the claim.b. Find the critical value(s).c. Compute the test value.d. Make the decision.e. Summarize the results.The average depth of the Hudson Bay is 305 feet. Climatologists were interested in seeing if warming
Select a random sample of 15 individuals and test one or more of the hypotheses in Exercise 1 by using the t test. Use α = 0.05.Data from in Exercise 1From the Data Bank, select a random sample of at least 30 individuals, and test one or more of the following hypotheses by using the z test. Use α
From the Data Bank, select a random sample of at least 30 individuals, and test one or more of the following hypotheses by using the z test. Use α = 0.05.a. For serum cholesterol, H0 : µ = 220 milligram percent (mg%). Use σ = 5.b. For systolic pressure, H0 : µ = 120 millimeters of
Using Table G, find the critical value(s) for each. Show the critical and noncritical regions, and state the appropriate null and alternative hypotheses. Use σ2 = 225.a. α = 0.01, n = 17, right-tailedb. α = 0.025, n = 20, left-tailedc. α = 0.01, n = 13, two-tailedd. α = 0.025, n = 29,
Use the most recent NFL season for your data. For each team, find the quarterback rating for the number one quarterback. Test the claim that the mean quarterback rating for a number one quarterback is more than 80.
Give three examples of proportions.
Determine whether each statement is true or false. If the statement is false, explain why.No error is committed when the null hypothesis is rejected when it is false.
Use the Dow Jones Industrial stocks in data project 1 of Chapter 7 as your data set. Find the gain or loss for each stock over the last quarter. Test the claim that the mean is that the stocks broke even (no gain or loss indicates a mean of 0).Data from in Project 1Use 30 stocks classified as the
A random sample of 20 automobiles has a pollution by-product release standard deviation of 2.3 ounces when 1 gallon of gasoline is used. Find the 90% confidence interval of the population standard deviation. Assume the variable is normally distributed.
Find the 90% confidence interval for the variance and standard deviation for the time it takes a state police inspector to check a truck for safety if a random sample of 27 trucks has a standard deviation of 6.8 minutes. Assume the variable is normally distributed.
A random sample of 25 novels has a standard deviation of 9 pages. Find the 95% confidence interval of the population standard deviation. Assume the variable is normally distributed.
A nutritionist wishes to determine, within 3%, the true proportion of adults who do not eat any lunch. If he wishes to be 95% confident that his estimate contains the population proportion, how large a sample will be necessary? A previous study found that 15% of the 125 people surveyed said they
A survey of 90 randomly selected families showed that 40 owned at least one television set. Find the 95% confidence interval of the true proportion of families who own at least one television set.
How large a sample is needed to estimate the population mean monthly gasoline expenditure within $10 with 95% confidence? The population standard deviation is $59.50.
In a study of 150 randomly selected accidents that required treatment in an emergency room, 36% involved children under 6 years of age. Find the 90% confidence interval of the true proportion of accidents that involve children under the age of 6.
A political analyst found that 43% of 300 randomly selected Republican voters feel that the federal government has too much power. Find the 95%confidence interval of the population proportion of Republican voters who feel this way.
A researcher wishes to estimate within $300 the true average amount of money a county spends on road repairs each year. If she wants to be 90% confident, how large a sample is necessary? The standard deviation is known to be $900.
A university dean wishes to estimate the average number of hours that freshmen study each week. The standard deviation from a previous study is 2.6 hours. How large a sample must be selected if he wants to be 99% confident of finding whether the true mean differs from the sample mean by 0.5 hour?
For a certain urban area, it was found that in a random sample of 4 months, an average of 31 burglaries occurred each month. The standard deviation was 4. Assume the variable is normally distributed. Find the 90% confidence interval of the true mean number of burglaries each month.
In a hospital, a random sample of 8 weeks was selected, and it was found that an average of 438 patients were treated in the emergency room each week. The standard deviation was 16. Find the 99% confidence interval of the true mean. Assume the variable is normally distributed.
In a study of 10 randomly selected insurance sales representatives from a certain large city, the average age of the group was 48.6 years and the standard deviation was 4.1 years. Assume the variable is normally distributed. Find the 95% confidence interval of the population mean age of all
According to a study, 76% of adults ages 18–29 years had broadband Internet access at home in 2011. A researcher wanted to estimate the proportion of undergraduate college students (18–23 years) with access, so she randomly sampled 180 undergraduates and found that 157 had access. Estimate the
The average weight of 40 randomly selected minivans was 4150 pounds. The population standard deviation was 480 pounds. Find a point estimate of the population mean. Find the 99% confidence interval of the true mean weight of the minivans.
In 2008, 17% of American homes were protected by a home security system. A marketing firm wanted to estimate the proportion of protected homes today. It chose a random sample of 200 homes and discovered that 53 had home security systems. Estimate the true proportion of homes with security systems
An irate patient complained that the cost of a doctor’s visit was too high. She randomly surveyed 20 other patients and found that the mean amount of money they spent on each doctor’s visit was $44.80. The standard deviation of the sample was $3.53. Find a point estimate of the population mean.
An irate student complained that the cost of textbooks was too high. He randomly surveyed 36 other students and found that the mean amount of money spent for texts was $121.60. If the standard deviation of the population was $6.36, find the best point estimate and the 90% confidence interval of the
The three confidence levels used most often are the______%,______ %, and________ %.
It is believed that slightly over 60% of Americans own pets. How large a sample is necessary to estimate the true proportion within 0.02 with 90% confidence?
The statement “The average height of an adult male is 5 feet 10 inches” is an example of a(n)________ estimate.
The maximum likely difference between the point estimate of a parameter and the actual value of the parameter is called the_____.
In 1960, 67.6% of the U.S. population (aged 14 and over) was married. A random sample of 600 Americans in 2011 indicated that 312 were married. Estimate the true proportion of married Americans with 99% confidence. Assume the variable is normally distributed.
What is necessary to determine the sample size?
Select a random sample of 20 of the record high temperatures in the United States, found in Data Set I in Appendix B. Find the proportion of temperatures below 110°. Construct a 95% confidence interval for this proportion. Then find the true proportion of temperatures below 110°, using all the
A good estimator should be______ ,__________ , and_______.
A random sample of state gasoline taxes (in cents) is shown here for 12 states. Use the data to estimate the true population mean gasoline tax with 90%confidence. Does your interval contain the national average of 44.7 cents?38.4 40.9 67 32.5
Find each.a. za/2 for the 99% confidence intervalb. za/2 for the 98% confidence intervalc. za/2 for the 95% confidence intervald. za/2 for the 90% confidence intervale. za/2 for the 94% confidence interval
From Data Set VI in Appendix B, select a sample of 20 values and find the 90% confidence interval of the mean of the number of acres. Find the mean of all the values, and determine if the confidence interval contains the mean.Data from in Data SET VI Appendix B Data Set VI Acreage of U.S. National
When the population standard deviation is unknown and the sample size is less than 30, what table value should be used in computing a confidence interval for a mean?a. zb. tc. Chi-squared. None of the above
Have each student compute his or her body mass index (BMI) (703 times weight in pounds, divided by the square of the height in inches). Find the mean and standard deviation for the data set. Compute a 95% confidence interval for the mean BMI of a student. A BMI score over 30 is considered obese.
The best point estimate of the population mean isa. The sample meanb. The sample medianc. The sample moded. The sample midrange
Select five political polls and note the margin of error, sample size, and percentage favoring the candidate for each. For each poll, determine the level of confidence that must have been used to obtain the margin of error given, knowing the percentage favoring the candidate and number of
The predicted high temperatures for a day in late May for a random sample of U.S. cities are listed here. Estimate the mean population high temperature with 90% confidence.For Exercises assume that all variables are approximately normally distributed. 60 73 103 67 89 76 88 86 79 72 88 87
When a 99% confidence interval is calculated instead of a 95% confidence interval with n being the same, the margin of error will bea. Smallerb. Larger c. The samed. It cannot be determined.
The lengths (in minutes) of a random selection of popular children’s animated films are listed below. Estimate the true mean length of all children’s animated films with 95% confidence. Assume the variable is normally distributed.93 83 76 92
From Data Set III in Appendix B, select a sample of 30 values and construct the 95 and 99% confidence intervals of the mean length in miles of major North American rivers. Find the mean of all the values, and determine if the confidence intervals contain the mean.Data from in Data SET III Appendix
In 1980 more than 35% of cars purchased had a manual transmission (i.e. stick shift). By 2007 the proportion had decreased to 7.7%. A random sample of college students who owned cars revealed the following: out of 122 cars, 26 had stick shifts. Estimate the proportion of college students who drive
What is meant by the 95% confidence interval of the mean?
Use your class as the sample. Have each student take her or his temperature on a day when he or she is healthy. Compute the mean and standard deviation for the sample. Create a 95% confidence interval for the mean temperature. Does the confidence interval obtained support the long-held belief that
Determine whether each statement is true or false. If the statement is false, explain why.To determine the sample size needed to estimate a parameter, you must know the margin of error.
When should the t distribution be used to find a confidence interval for the mean?
Fifty-six percent of respondents to an online poll said that they were Perry Como fans. If 982 randomly selected people responded to this poll, what is the true proportion of all local residents who are Perry Como fans? Estimate at the 95% confidence level.
Use the data collected in data project 3 of Chapter 2 regarding song lengths. Select a specific genre, and compute the percentage of songs in the sample that are of that genre. Create a 95% confidence interval for the true percentage. Use the entire music library, and find the population percentage
Determine whether each statement is true or false. If the statement is false, explain why.An estimator is consistent if as the sample size decreases, the value of the estimator approaches the value of the parameter estimated.
Repeat Exercise 1, using a proportion. For example, construct a confidence interval for the proportion of individuals who did not complete high school.Data from in Exercise 1From the Data Bank choose a variable, find the mean, and construct the 95 and 99% confidence intervals of the population
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