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elementary statistics
Elementary Statistics Using Excel Pearson New 5th Edition Mario F Triola - Solutions
Using the computer output and information in Exercise 8.109, determine the value of the following:a. Hypothesized value of population meanb. Sample meanc. Population standard deviationd. Test statistic
The following computer output was used to complete a hypothesis test.TEST OF MU 6.250 VS MU not 6.250 THE ASSUMED SIGMA 1.40 N MEAN STDEV SE MEAN Z P VALUE 78 6.596 1.273 0.1585 2.18 0.029a. State the null and alternative hypotheses.b. If the test is completed using 0.05, what decision
According to the USA Today article “Laptops inching closer to PCs in popularity” (February 6, 2005), the desktop PC era is ending and the age of laptops has begun. A study by researcher Current Analysis found that laptop prices fell to an average of$1211 during the 2004 December holidays. The
One of the best indicators of a baby’s health is his or her weight at birth. In the United States, mothers who live in poverty generally have babies with lower birth weights than those who do not live in poverty. Although the average birth weight for babies born in the United States is
The average size of a home in 2003 was 2320 square feet according to the National Association of Home Builders and reported in USA Today Snapshots(November 27, 2004). The homebuilders of a northeastern city believe that the average size of homes continues to increase each year. To test their claim,
From candy to jewelry to flowers, the average consumer was expected to spend $104.63 for Mother’s Day in 2005, according to the Democrat &Chronicle article “Mom’s getting more this year”(May 7, 2005). Local merchants thought this average was too high for their area. They contracted an
[EX08-120] The National Health and Nutrition Examination Survey (NHANES) indicates that more U.S. adults are becoming either overweight or obese, which is defined as having a body mass index (BMI) of 25 or more. Data from the Centers for Disease Control and Prevention (CDC)indicate that for females
Use a computer or calculator to select 40 random single-digit numbers. Find the sample mean, z, and p-value for testing Ho: 4.5 against a two-tailed alternative. Repeat several times as in Table 8.8. Describe your findings.FYI Use commands for generating integer data on page 101; then continue
Use a computer or calculator to select 36 random numbers from a normal distribution with mean 100 and standard deviation 15. Find the sample mean, z, and p-value for testing a twotailed hypothesis test of 100. Repeat several times as in Table 8.8. Describe your findings.
In the example on page 445, the aircraft builder who is buying the rivets is concerned that the rivets might not meet the mean-strength spec. State the aircraft manufacturer’s null and alternative hypotheses.
Professor Hart does not believe the statement“the mean distance commuted daily by the nonresident students at our college is no more than 9 miles.” State the null and alternative hypotheses he would use to challenge this statement.
Suppose you wanted to test the hypothesis that the mean minimum charge in your area for a home service call by a plumber is at most $85. Explain the conditions that would exist if you make an error in decision by committing a type I error.What about a type II error?
Describe how the null hypothesis in Example 8.21 is a “starting point” for the decision to be made about the mean weight of all female students at the college.
a. What decision is reached when the test statistic falls in the critical region?b. What decision is reached when the test statistic falls in the noncritical region?
Because the size of the type I error can always be made smaller by reducing the size of the critical region, why don’t we always choose critical regions that make extremely small?
Calculate the test statistic z, given Ho: 356, 17, x 354.3, and n 120.
Find the critical region and value(s) for Ha: 19 and 0.01.
Find the critical region and value(s) for Ha: 34 and 0.02.
Determine the critical region and critical values for z that would be used to test the null hypothesis at the given level of significance, as described in each of the following:a. Ho: 20, Ha: ≠ 20, 0.10b. Ho: 24 (), Ha: 24, 0.01c. Ho: 10.5 ( ), Ha: 10.5, 0.05d.
Determine the critical region and the critical values used to test the following null hypotheses:a. Ho: 55 ( ), Ha: 55, 0.02b. Ho: 86 ( ), Ha: 86, 0.01c. Ho: 107, Ha: ≠ 107, 0.05d. Ho: 17.4 (), Ha: 17.4, 0.10
The null hypothesis, Ho: 250, was tested against the alternative hypothesis, Ha: 250. A sample of n 85 resulted in a calculated test statistic of z 1.18. If 22.6, find the value of the sample mean, x. Find the sum of the sample data, x.
Consider the hypothesis test where the hypotheses are Ho: 26.4 and Ha: 26.4. A sample of size 64 is randomly selected and yields a sample mean of 23.6.a. If it is known that 12, how many standard errors below 26.4 is the sample mean, x 23.6?b. If 0.05, would you reject Ho?
There are only two possible decisions as a result of a hypothesis test.a. State the two possible decisions.b. Describe the conditions that will lead to each of the two decisions identified in part a.
The following computer output was used to complete a hypothesis test.TEST OF MU 15.0000 VS MU not 15.0000 THE ASSUMED SIGMA 0.50 N MEAN STDEV SE MEAN Z 30 15.6333 0.4270 0.0913 6.94a. State the null and alternative hypotheses.b. If the test is completed using 0.01, what decision and
The following computer output was used to complete a hypothesis test.TEST OF MU 72.00 VS MU 72.00 THE ASSUMED SIGMA 12.0 N MEAN STDEV SE MEAN Z 36 75.2 11.87 2.00 1.60a. State the null and alternative hypotheses.b. If the test is completed using 0.05, what decision and conclusion are
Using the computer output and information in Exercise 8.147, determine the value of the following:a. Hypothesized value of population meanb. Sample meanc. Population standard deviationd. Test statistic
According to the Democrat & Chronicle article“Millions forfeited in health accounts” (December 26, 2004), an estimated $210 million is forfeited each year because employees do not use all of the money that they contributed to their medical flexible spending accounts. The average amount put into
The National Thoroughbred Racing Association’s figures show that the average age of its 3 million committed fans, those who attend multiple races every year, is now 55 years old. Despite a $30 million a year promotional campaign by the association and its member tracks aimed at younger and female
[EX08-153] The length of major league baseball games are approximately normally distributed and average 2 hours and 50.1 minutes, with a standard deviation of 21.0 minutes. It has been claimed that New York Yankee baseball games last, on the average, longer than the games of the other major league
[EX08-154] The manager at Air Express believes that the weights of packages shipped recently are less than those in the past. Records show that in the past, packages have had a mean weight of 36.5 lb and a standard deviation of 14.2 lb. A random sample of last month’s shipping records yielded the
Do you drink the recommended amount of water each day? Most Americans don’t! On average, Americans drink 4.6 eight-oz servings of water a day.Source: http://www.bottledwater.org/public/summary.htm A sample of 42 education professionals was randomly selected and their water consumption for a
Use a computer or calculator to select 40 random single-digit numbers. Find the sample mean and z. Using 0.05, state the decision for testing Ho: 4.5 against a two-tailed alternative.Repeat it several times as in Table 8.12. Describe your findings after several tries.FYI Use commands for
Use a computer or calculator to select 36 random numbers from a normal distribution with mean 100 and standard deviation 15. Find the sample mean and z for testing a two-tailed hypothesis test of 100. Using 0.05, state the decision. Repeat several times as in Table 8.12. Describe your
A sample of 64 measurements is taken from a continuous population, and the sample mean is found to be 32.0. The standard deviation of the population is known to be 2.4. An interval estimation is to be made of the mean with a level of confidence of 90%. State or calculate the following items.a. xb.
Suppose that a confidence interval is assigned a level of confidence of 1 95%. How is the 95% used in constructing the confidence interval?If 1 was changed to 90%, what effect would this have on the confidence interval?
Are you worried about identity theft? If you do business mostly online, you may be in a safer position as stated in the January 30, 2005, USA Today article, “Odds low for online theft.” In a telephone survey done by the Better Business Bureau and Javelin Strategy & Research, the average loss
[EX08-168] A large order of the no. 9 corks described in Applied Example 6.15 (p. 330) is about to be shipped. The final quality-control inspection includes an estimation of the mean ovality(ovalization; out-of-roundness) of the corks.The diameter of each cork is measured in several places, and the
[EX08-169] This computer output shows a simulated sample of size 25 randomly generated from a normal population with 130 and 10. A confidence interval command was then used to set a 95% confidence interval for .N MEAN STDEV SE MEAN 95.0 PERCENT C.I.25 129.02 10.18 2.00 (125.10, 132.95)a. State
A pharmaceutical company wants to estimate the mean response time for a supplement to reduce blood pressure. How large of a sample should they take to estimate the mean response time to within 1 week at 99% confidence. Assume 3.7 weeks.
An automobile manufacturer wants to estimate the mean gasoline mileage of its new compact model. How many sample runs must be performed to ensure that the estimate is accurate to within 0.3 mpg at 95% confidence? (Assume 1.5.)
The expected mean of a continuous population is 100, and its standard deviation is 12. A sample of 50 measurements gives a sample mean of 96. Using a 0.01 level of significance, a test is to be made to decide between “the population mean is 100” or “the population mean is different from
The expected mean of a continuous population is 200, and its standard deviation is 15. A sample of 80 measurements gives a sample mean of 205. Using a 0.01 level of significance, a test is to be made to decide between “the population mean is 200” or “the population mean is different from
The average weight for a 10-year-old girl in 2002 was 88.0 lb according to the National Center for Health Statistics. This average exceeded the 1966 figure by more than 10 lb. Suppose a random sample of thirty-five 10-year-old girls is taken and the sample mean is 90.5 lb. Assuming that the
With a nationwide average drive time of about 24.3 minutes, Americans now spend more than 100 hours a year commuting to work, according to the U.S. Census Bureau’s American Community Survey. Yes, that’s more than the average 2 weeks of vacation time (80 hours) taken by many workers during a
[EX08-189] This computer output shows a simulated sample of size 28 randomly generated from a normal population with 18 and 4.Computer commands were then used to complete a hypothesis test for 18 against a two-tailed alternative.a. State the alternative hypothesis, the decision, and the
a. Are the assumptions of the confidence interval and hypothesis test methods of this chapter satisfied? Explain.b. Using the sample data and a 95% level of confidence, estimate the mean height of females in the health profession.Use the given population standard deviation of 2.75 inches.c. Test
Design your own study of female heights.Define a specific population that you will sample, describe your sampling plan, collect your data, and answer part b of Exercise 8.1 (p. 396) and parts a,b,c, and g of Exercise 8.199, replacing health profession with your particular population. Discuss the
An unhappy post office customer is frustrated with the waiting time to buy stamps. Upon registering his complaint, he was told, “The average waiting time in the past has been about 4 minutes with a standard deviation of 2 minutes.” The customer collected a sample of n 45 customers and found
State the null (Ho) and the alternative (Ha)hypotheses that would be used to test each of these claims:a. The mean weight of professional football players is more than 245 lb.b. The mean monthly amount of rainfall in Monroe County is less than 4.5 inches.c. The mean weight of the baseball bats used
Determine the level of significance, test statistic, critical region, and critical value(s) that would be used in completing each hypothesis test using 0.05:a. Ho: 43b. Ho: 0.80c. Ho: 95 Ha: 43 Ha: 0.80 Ha: 95(given 6) (given 0.13) (given 12)
Find each value:a. z(0.05)b. z(0.01)c. z(0.12)
In the past, the grapefruits grown in a particular orchard have had a mean diameter of 5.50 inches. and a standard deviation of 0.6 inches. The owner believes this year’s crop is larger than those in the past. He collected a random sample of 100 grapefruits and found a sample mean diameter of
A manufacturer claims that its light bulbs have a mean lifetime of 1520 hours with a standard deviation of 85 hours. A random sample of 40 such bulbs is selected for testing.If the sample produces a mean value of 1498.3 hours, is there sufficient evidence to claim that the mean lifetime is less
Sugar Creek Convenience Stores has commissioned a statistics firm to survey its customers in order to estimate the mean amount spent per customer. From previous records the standard deviation is believed to be $5. In its proposal to Sugar Creek, the statistics firm states that it plans to base
The noise level in a hospital may be a critical factor influencing a patient’s speed of recovery.Suppose for the sake of discussion that a research commission has recommended a maximum mean noise level of 30 decibels(db) with a standard deviation of 10 db. The staff of a hospital intend to sample
The alternative hypothesis is sometimes called the research hypothesis. The conclusion is a statement written about the alternative hypothesis. Explain why these two statements are compatible.
Car Crash Tests Refer to the sample data described in Exercise 9 and construct a 95%confidence interval estimate of the population standard deviation.
Car Crash Tests Data Set 13 in Appendix: Data Sets includes crash test measurements for small cars. The seven chest deceleration measurements have a mean of 42.7 g and a standard deviation of 5.6 g, where g is a force of gravity. Use the sample data to construct a 95% confidence interval estimate
White Blood Cell Counts Data Set 1 in Appendix: Data Sets lists the white blood cell counts (1000 cells/mL) of 40 randomly selected women. The mean of those 40 values is 7.15 and the standard deviation is 2.28. Construct a 90% confidence interval estimate of the mean white blood cell count for the
Wristwatch Accuracy Students of the author collected data measuring the accuracy of wristwatches. The times (sec) below show the discrepancy between the real time and the time indicated on the wristwatch. Negative values correspond to watches that are running ahead of the actual time. The data
Alcohol Consumption In a Gallup poll, 1011 adults were asked if they consume alcoholic beverages, and 64% of them said that they did. Construct a 90% confidence interval estimate of the proportion of all adults who consume alcoholic beverages. Can we safely conclude that the majority of adults
Sample Size You have been hired by a college foundation to conduct a survey of graduates.a. If you want to estimate the percentage of graduates who have made a donation to the college after graduation, how many graduates must you survey if you want 98% confidence that your percentage has a margin
Distributions Identify the distribution (normal, Student t, chi-square) that applies to each of the following situations. (If none of the three distributions is appropriate, then so state.)a. In constructing a confidence interval of m, you have 50 sample values and they appear to be from a
Lefties Yet Again There have been several studies conducted in an attempt to identify ways in which left-handed people are different from those who are right handed. Assume that you want to estimate the mean IQ of all left-handed adults. How many random left-handed adults must be tested in order to
Lefties The author had difficulty finding the percentage of people who write with their left hand. If we want to estimate that percentage based on survey results, how many people must we survey in order to be 99% confident that we are within two percentage points of the population percentage?
Underpaid In a Gallup poll of 557 randomly selected adults, 284 said that they were underpaid.a. Identify the best point estimate of the percentage of all adults who say that they are underpaid.b. Construct a 95% confidence interval estimate of the percentage of all adults who say that they are
Refer to Exercise 7 and assume that the requirements are satisfied. Find the critical values that would be used to construct a 95% confidence interval estimate of s.
Refer to Exercise 7 and assume that the requirements are satisfied. Find the critical value that would be used for constructing a 95% confidence interval estimate of m.
In general, what does “degrees of freedom” refer to? For the sample data described in Exercise 7, find the number of degrees of freedom, assuming that you want to construct a confidence interval estimate of m.
Six human skulls from around 4000 b.c. were measured, and the lengths have a mean of 94.2 mm and a standard deviation of 4.9 mm. If you want to construct a 95% confidence interval estimate of the mean length of all such skulls, what requirements must be satisfied?
Find the sample size required to estimate the mean IQ of students currently taking a statistics course. Assume that we want 99% confidence that the mean from the sample is within two IQ points of the true population mean. Also assume that s = 15.
Find the sample size required to estimate the percentage of college students who own a car.Assume that we want 90% confidence that the proportion from the sample is within three percentage points of the true population percentage.
In a survey of 1023 high school students, 102 chose education for their career choice (based on results from a KeyStat Marketing survey). Find the critical value that would be used for constructing a 90% confidence interval estimate of the population proportion.
Write a brief statement that correctly interprets the confidence interval given in Exercise 2.
Here is a 95% confidence interval estimate of the proportion of female medical school students: 0.449 6 p 6 0.511 (based on data from the Journal of the American Medical Association). What is the best point estimate of the proportion of females in the population of medical school students?
USA Today reported that 40% of people surveyed planned to use accumulated loose change for paying bills. The margin of error was given as {3.1 percentage points. Identify the confidence interval that corresponds to that information.
U.S. Incomes You want to estimate the standard deviation of the population of current annual incomes of adults in the United States. Find the minimum sample size needed to be 99% confident that the sample standard deviation is within 5% of the population standard deviation. Does the population of
Flight Delays You want to estimate the standard deviation of arrival delays for American Airlines flights from Chicago to Miami. Find the minimum sample size needed to be 95% confident that the sample standard deviation is within 5% of the population standard deviation. A histogram of a sample of
McDonald’s Waiting Times You want to estimate s for the population of waiting times at McDonald’s drive-up windows, and you want to be 95% confident that the sample standard deviation is within 20% of s. Find the minimum sample size. Is this sample size practical?
IQ of Statistics Professors You want to estimate s for the population of IQ scores of statistics professors. Find the minimum sample size needed to be 99% confident that the sample standard deviation s is within 1% of s. Is this sample size practical?
Ages of Presidents Refer to Data Set 12 in Appendix: Data Sets and use the ages (years)of the presidents at the times of their inaugurations. Treating the data as a sample, construct a 98% confidence interval estimate of the standard deviation of the population of all such ages.
Penny Weights Refer to Data Set 21 in Appendix: Data Sets and use the weights of the post-1983 pennies to construct a 98% confidence interval estimate of the standard deviation of the weights of all post-1983 pennies.
a. Comparing Waiting Lines The values listed below are waiting times (in minutes) of customers at the Jefferson Valley Bank, where customers enter a single waiting line that feeds three teller windows. Construct a 95% confidence interval for the population standard deviation s.6.5 6.6 6.7 6.8 7.1
Promotion and Age Listed below are ages of applicants who were unsuccessful in winning promotion and ages of applicants who were successful in winning promotion (based on data from “Debating the Use of Statistical Evidence in Allegations of Age Discrimination” by Barry and Boland, American
Highway Speeds Listed below are speeds (mi/h) measured from southbound traffic on I-280 near Cupertino, California (based on data from SigAlert). This simple random sample was obtained at 3:30 p.m. on a weekday. Use the sample data to construct a 95% confidence interval estimate of the population
Mercury in Sushi Listed below are the amounts of mercury (in parts per million, or ppm)found in tuna sushi sampled at different stores in New York City. The study was sponsored by the New York Times, and the stores (in order) are D’Agostino, Eli’s Manhattan, Fairway, Food Emporium, Gourmet
Pulse Rates of Men and Women Data Set 1 in Appendix: Data Sets includes 40 pulse rates of men, and those pulse rates have a mean of 67.3 beats per minute and a standard deviation of 10.3 beats per minute. That data set also includes 40 pulse rates of women, and those pulse rates have a mean of 77.5
Antifreeze A container of car antifreeze is supposed to hold 3785 mL of the liquid.Realizing that fluctuations are inevitable, the quality-control manager of the Taconic Chemical Company wants to be quite sure that the standard deviation is less than 30 mL. Otherwise, some containers would overflow
Chocolate Chip Cookies The mean of the numbers of chocolate chips in a sample of 40 Chips Ahoy regular cookies is 23.95 and the standard deviation is 2.55. Construct a 90%confidence interval estimate of the standard deviation of the numbers of chocolate chips in all such cookies.
Mean Body Temperature Data Set 3 in Appendix: Data Sets includes a sample of 106 body temperatures having has a mean of 98.20oF and a standard deviation of 0.62oF. Construct a 90% confidence interval estimate of the standard deviation of the body temperatures for the entire population.
Earthquake Magnitudes 95% confidence; n = 50, s = 0.587.
Platelet Counts of Women 95% confidence; n = 40, s = 65.2.
Weights of Dollar Coins 99% confidence; n = 20, s = 0.04111 g.
Nicotine in Menthol Cigarettes 99% confidence; n = 25, s = 0.24 mg.
Normality Requirement What is different about the normality requirement for a confidence interval estimate of s and the normality requirement for a confidence interval estimate of m?
Expressing Confidence Intervals Example 2 showed how the statistics of n = 22 and s = 14.3 result in this 95% confidence interval estimate of s: 11.0 6 s 6 20.4. That confidence interval can also be expressed as (11.0, 20.4), but it cannot be expressed as 15.7 { 4.7. Given that 15.7 { 4.7 results
LDL Cholesterol Using the 40 LDL cholesterol levels of women listed in Data Set 1 in Appendix: Data Sets, we get this 95% confidence interval estimate: 916.591 6 s2 6 2252.119, and the units of measurement are (mg/dL)2. Identify the corresponding confidence interval estimate of s and include the
Confidence Interval for Sample of Size n = 1 Based on the article “An Effective Confidence Interval for the Mean with Samples of Size One and Two,” by Wall, Boen, and Tweedie (American Statistician, Vol. 55, No. 2), a 95% confidence interval for m can be found for a sample of size n = 1
Finite Population Correction Factor If a simple random sample of size n is selected without replacement from a finite population of size N, and the sample size is more than 5% of the population size (n 7 0.05N ), better results can be obtained by using the finite population correction factor, which
Outlier Effect If the first value of 3.0 in Exercise 21 is changed to 300, it becomes an outlier. Does this outlier have much of an effect on the confidence interval? How should you handle outliers when they are found in sample data sets that will be used for the construction of confidence
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