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business statistics

Questions and Answers of Business Statistics

Find the proportions p̂ and q̂ for each.a. n = 52, X = 32b. n = 80, X = 66c. n = 36, X = 12d. n = 42, X = 7e. n = 160, X = 50
When one is computing the F test value, what condition is placed on the variance that is in the numerator?
Classify each as independent or dependent samples.a. Heights of identical twinsb. Test scores of the same students in English and psychologc. The effectiveness of two different brands of aspirin on
Explain the difference between testing a single mean and testing the difference between two means.
Suppose a statistician chose to test a hypothesis at α = 0.01. The critical value for a right-tailed test is +2.33. If the test value were 1.97, what would the decision be? What would happen if,
Approximately 70% of the U.S. population recycles. According to a green survey of a random sample of 250 college students, 204 said that they recycled. At α = 0.01, is there sufficient evidence to
To see whether people are keeping their car tires inflated to the correct level of 35 pounds per square inch (psi), a tire company manager selects a random sample of 36 tires and checks the pressure.
A medical college dean read that the average number of applications a potential medical school student sends is 7.8. She thinks that the mean is higher. So she selects a random sample of 35
Room and board fees for a random sample of independent religious colleges are shown.Estimate the standard deviation in costs based on s ‰ˆ R/4. Is there sufficient evidence to conclude that
The standard deviation of fuel consumption of a manufacturer’s sport utility vehicle is hypothesized to be 3.3 miles per gallon. A random sample of 18 vehicles has a standard deviation of 2.8 miles
The director of a medical hospital feels that her surgeons perform fewer operations per year than the national average of 211. She selected a random sample of 15 surgeons and found that the mean
A random sample of second-round golf scores from a major tournament is listed below. At Î± = 0.10, is there sufficient evidence to conclude that the population variance exceeds 9? 75 69
The average length of prison term in the United States for white collar crime is 34.9 months. A random sample of 40 prison terms indicated a mean stay of 28.5 months with a standard deviation of 8.9
The amounts of vitamin C (in milligrams) for 100 g (3.57 ounces) of various randomly selected fruits and vegetables are listed. Is there sufficient evidence to conclude that the standard deviation
Of men aged 65 and over 20.5% are still in the U.S. labor force. A random sample of 120 retired male teachers indicated that 38 were still working. Use both a confidence interval and a hypothesis
For each conjecture, state the null and alternative hypotheses.a. The average age of first-year medical school students is at least 27 years.b. The average experience (in seasons) for an NBA player
A person read that the average number of hours an adult sleeps on Friday night to Saturday morning was 7.2 hours. The researcher feels that college students do not sleep 7.2 hours on average. The
In a previous study conducted several years ago, a man owned on average 15 dress shirts. The standard deviation of the population is 3. A researcher wishes to see if that average has changed. He
A manufacturer of cigarettes wishes to test the claim that the variance of the nicotine content of the cigarettes the company manufactures is equal to 0.638 milligram. The variance of a random sample
For each conjecture, state the null and alternative hypotheses.a. The average weight of dogs is 15.6 pounds.b. The average distance a person lives away from a toxic waste site is greater than 10.8
An automobile owner found that 20 years ago, 76% of Americans said that they would prefer to purchase an American automobile. He believes that the number is much less than 76% today. He selected a
An obstetrician read that a newborn baby loses on average 7 ounces in the first two days of his or her life. He feels that in the hospital where he works, the average weight loss of a newborn baby is
The National Novel Writing Association states that the average novel is at least 50,000 words. A particularly ambitious writing club at a college-preparatory high school had randomly selected members
The average number of miles a person drives per day is 24. A researcher wishes to see if people over age 60 drive less than 24 miles per day. She selects a random sample of 49 drivers over the age of
In hypothesis testing, why can’t the hypothesis be proved true?
A corrections officer read that 58% of runaways are female. He believes that the percentage is higher than 58. He selected a random sample of 90 runaways and found that 63 were female. At α = 0.05,
How can the power of a test be increased?
A researcher knew that before cell phones, a person made on average 2.8 calls per day. He believes that the number of calls made per day today is higher. He selects a random sample of 30 individuals
A random sample of the distances in miles 8 shoppers travel to their nearest supermarkets is shown. Test the claim at Î± = 0.10 that the standard deviation of the distance shoppers
It has been reported that one in four medical doctors received their degrees from foreign schools. A hospital researcher believes that the percentage is less than 25%. A random survey of 100 medical
When should a one-tailed test be used? A two-tailed test?
How is the power of a test related to the type II error?
The average cost for teeth straightening with metal braces is approximately $5400. A nationwide franchise thinks that its cost is below that figure. A random sample of 28 patients across the country
Explain what is meant by a significant difference.
A magazine article reported that 11% of adults buy takeout food every day. A fast-food restaurant owner surveyed 200 customers and found that 32 said that they purchased takeout food every day. At α
A researcher found that a cigarette smoker smokes on average 31 cigarettes a day. She feels that this average is too high. She selected a random sample of 10 smokers and found that the mean number of
What symbols are used to represent the probabilities of type I and type II errors?
According to the National Association of Home Builders, the average cost of building a home in the Northeast is $117.91 per square foot. A random sample of 36 new homes indicated that the mean cost
A random sample of $1 Trifecta tickets at a local racetrack paid the following amounts (in dollars and cents). Is there sufficient evidence to conclude that the average Trifecta winnings exceed $50?
What symbols are used to represent the null hypothesis and the alternative hypothesis?
Forty-six percent of people believe that there is life on other planets in the universe. A scientist does not agree with this finding. He surveyed 120 randomly selected individuals and found 48
A researcher wishes to see if the average number of sick days a worker takes per year is greater than 5. A random sample of 32 workers at a large department store had a mean of 5.6. The standard
Test the claim that the standard deviation of the ages of psychologists in Pennsylvania is 8.6 at α = 0.05. A random sample of 12 psychologists had a standard deviation of 9.3.
A shopper in a grocery store purchases 22 items on average. A store manager believes that the mean is greater than 22. She surveyed a randomly selected group of 36 customers and found that the mean
What are the mean and the standard deviation of a proportion?
According to a public service website, 69.4% of white collar criminals get prison time. A randomly selected sample of 165 white collar criminals revealed that 120 were serving or had served prison
Find the critical value (or values) for the t test for each.a. n = 15, α = 0.05, right-tailedb. n = 23, α = 0.005, left-tailedc. n = 28, α = 0.01, two-tailedd. n = 17, α = 0.02, two-tailed
What is meant by a statistical test?
When you are testing hypotheses by using proportions, what are the necessary requirements?
Find the critical value (or values) for the t test for each.a. n = 12, α = 0.01, left-tailedb. n = 16, α = 0.05, right-tailedc. n = 7, α = 0.10, two-tailedd. n = 11, α = 0.025, right-tailede. n =
Why is a proportion considered a binomial variable?
What are the degrees of freedom for the t test?
Many people believe that the average number of Facebook friends is 338. The population standard deviation is 43.2. A random sample of 50 high school students in a particular county revealed that the
According to the almanac, the mean age for a woman giving birth for the first time is 25.2 years. A random sample of ages of 35 professional women giving birth for the first time had a mean of 28.7
Using Table G, find the critical value(s) for each. Indicate the noncritical region or regions, and state the null and alternative hypotheses. Use σ2 = 225.a. α = 0.10, n = 14, two-tailedb. α =
The average lifetime of circulated $1 bills is 18 months. A researcher believes that the average lifetime is not 18 months. He researched the lifetime of 50 $1 bills and found the average lifetime
If the variance of the water temperature in a lake is 28°, how many days should the researcher select to measure the temperature to estimate the true mean within 3° with 99% confidence?
According to the World Almanac, 35.2% of men ages 18 to 44 meets the U.S. Fitness Guidelines. How large a sample is necessary to estimate the true proportion of men that are fit in this age group
The speeds in miles per hour of eight randomly selected qualifiers for the Indianapolis 500 (in 2012) are listed below. Estimate the mean qualifying speed with 95% confidence.Assume that all
The American Heart Association recommends a daily cholesterol intake of less than 300 mg. Here are the cholesterol amounts in a random sample of single servings of grilled meats. Estimate the
Estimate the standard deviation in calories for these randomly selected standard-size candy bars with 95% confidence. (The number of calories is listed for each.) Assume the variable is normally
A recent survey of 349 people ages 18 to 29 found that 86% of them own a smartphone. Find the 99% confidence interval of the population proportion.
What distribution must be used when computing confidence intervals for variances and standard deviations?
For a group of 12 men subjected to a stress test situation, the average heart rate was 109 beats per minute. The standard deviation was 4. Find the 99% confidence interval of the population
It is desired to estimate the mean GPA of each undergraduate class at a large university. How large a sample is necessary to estimate the GPA within 0.25 at the 99% confidence level? The population
A pizza shop owner wishes to find the 95% confidence interval of the true mean cost of a large cheese pizza. How large should the sample be if she wishes to be accurate to within $0.15? A previous
A researcher wishes to estimate the average number of minutes per day a person spends on the Internet. How large a sample must she select if she wishes to be 90% confident that the population mean is
How large a sample is needed to estimate the population mean for the amount of money a person spends on Christmas presents within $2 and be 95% confident? The standard deviation of the population is
A random sample of 36 drivers used on average 749 gallons of gasoline per year. If the standard deviation of the population is 32 gallons, find the 95% confidence interval of the mean for all
The number of grams of carbohydrates in various commercially prepared 7-inch subs is recorded below. The population standard deviation is 6.46. Estimate the mean number of carbs in all similarly
According to a study, 96% of adults ages 18–29 had internet access at home in 2015. A researcher wanted to estimate the proportion of undergraduate college students (18 to 29 years) with access, so
At a large company, the Director of Research found that the average work time lost by employees due to accidents was 98 hours per year. She used a random sample of 18 employees. The standard
For a random sample of 60 overweight men, the mean of the number of pounds that they were overweight was 30. The standard deviation of the population is 4.2 pounds.a. Find the best point estimate of
A person recently read that 84% of cat owners are women. How large a sample should the person take if she wishes to be 90% confident that her proportion is within 3% of the true population proportion?
A medical researcher surveyed 11 hospitals and found that the standard deviation for the cost for removing a person’s gall bladder was $53. Assume the variable is normally distributed. Based on
A survey of 50 students in grades 4 through 12 found 68% have classroom Wi-Fi access. Find the 99% confidence interval of the population proportion.
A sample of 8 adult elephants had an average weight of 12,300 pounds. The standard deviation for the sample was 22 pounds. Find the 95% confidence interval of the population mean for the weights of
A random sample of 50 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.21 per car. The population standard deviation is $5.92. Estimate the mean bill for all
Since 1975 the average fuel efficiency of U.S. cars and light trucks (SUVs) has increased from 13.5 to 25.8 mpg, an increase of over 90%! A random sample of 40 cars from a large community got a mean
In 1960, 67.6% of the U.S. population (aged 14 and over) was married. A random sample of 600 Americans in 2014 indicated that 316 were married. Estimate the true proportion of married Americans with
The standard deviation of a sample of 15 automobile repairs at a local garage was $120.82. Assume the variable is normally distributed. Find the 90% confidence of the true variance and standard
The number of calories per candy bar for a random sample of standard-size candy bars is shown below. Estimate the mean number of calories per candy bar with 98% confidence.Assume that all variables
What is necessary to determine the sample size?
In a recent survey of 1000 adults ages 18 to 40, 34% said they had no credit cards. Find the 95% confidence interval of the population proportion.
A manufacturer of pacemakers wants the standard deviation of the lifetimes of the batteries to be less than 1.8 months. A sample of 20 batteries had a standard deviation of 1.6 months. Assume the
Research by Steelcase found the average worker get interrupted every 11 minutes and takes 23 minutes to get back on task. From a random sample of 200 workers, 168 said they are interrupted every 11
The prices (in dollars) for a particular model of digital camera with 18.0 megapixels and a f/3.5−5.6 zoom lens are shown here for 10 randomly selected online retailers. Estimate the true mean
What statistic best estimates μ?
A random sample of 15 registered nurses in a large hospital showed that they worked on average 44.2 hours per week. The standard deviation of the sample was 2.6. Estimate the mean of the population
What are three properties of a good estimator?
A survey of 100 Americans found that 68% said they find it hard to buy holiday gifts that convey their true feelings. Find the 90% confidence interval of the population proportion.
When should the t distribution be used to find a confidence interval for the mean?
In 2014, six percent of the cars sold had a manual transmission. A random sample of college students who owned cars revealed the following: out of 122 cars, 26 had manual transmissions. Estimate the
A researcher wishes to estimate within 2 points the average systolic blood pressure of female college students. If she wishes to be 90% confident, how large a sample should she select if the
A survey of 1000 U.S. adults found that 33% of people said that they would get no work done on Cyber Monday since they would spend all day shopping online. Find the 95% confidence interval of the
What assumption must be made when computing confidence intervals for variances and standard deviations?
Find p̂ and q̂ for each situation.a. n = 60 and X = 35b. n = 95 and X = 43c. 68%d. 55%e. 12%
A survey of 49 individuals found that the average number of times a person blinks his or her eyes is 25 times per minute. Based on this survey, find the 90% confidence of the population mean number
In each case, find p̂ and q̂.a. n = 80 and X = 40b. n = 200 and X = 90c. n = 130 and X = 60d. 25%e. 42%
What is meant by the 95% confidence interval of the mean?

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