Questions and Answers of Essential Statistics

A result is significant at the 0.01 level. Explain why it must also be significant at the 0.05 level.
What’s the news? The Pew Research Center reported that 23% of 18- to 29-year-olds watch a cable news channel regularly. The director of media relations at a large university wants to know whether
How much rent? A housing official in a certain city claims that the mean monthly rent for apartments in the city is more than $1000. To verify this claim, a simple random sample of 40 renters in the
Crackers: Boxes of crackers are filled by a machine. The weights of a random sample of 25 boxes of crackers have standard deviation s = 5 grams. Assume the weights are normally distributed. Can you
How many TV sets? A survey organization sampled 60 households in a community and found that the sample mean number of TV sets per household was 3.1. The population standard deviation is ???? = 1.5.
Interpret calculator display: The following TI-84 Plus display presents the results of a hypothesis test.a. Is this a test for a mean, a proportion, or a standard deviation?b. What are the null and
Interpret computer output: The following output from MINITAB presents the results of a hypothesis test.a. What are the null and alternate hypotheses?b. What is the value of the test statistic?c. What
Can you conclude that the population standard deviation is greater than 2? Use the ???? = 0.01 level of significance.
Sugar content: The sugar content in milligrams of a syrup used to pack canned fruit is measured for 8 batches of syrup.The measurements are normally distributed, and the sample standard deviation is
Job satisfaction: The General Social Survey sampled 762 employed people and asked them how satisfied they were with their jobs. Of the 762 people sampled, 386 said that they were completely satisfied
Household size: For the past several years, the mean number of people in a household has been declining. A social scientist believes that in a certain large city, the mean number of people per
If the test is made at the ???? = 0.05 level with the same sample size, would the power be greater than or less than in Exercise 5? Explain.
More power: Refer to Exercise
Find the power of the test against the alternative ????1 = 110.
Power: A test of H0: ???? = 100 versus H1: ???? > 100 will be made at a significance level of ???? = 0.01. The population standard deviation is ???? = 50 and the sample size is n =
Playing the market: The Russell 2000 is a group of 2000 small-company stocks. On a recent day, a random sample of 35 of these stocks had a mean price of $26.89, with a standard deviation of $23.41. A
Facebook: A popular blog reports that 60% of college students log in to Facebook on a daily basis. The Dean of Students at a certain university thinks that the proportion may be different at her
Scoring runs: In 2012, the mean number of runs scored by both teams in a Major League Baseball game was 8.62.Following are the numbers of runs scored in a sample of 24 games in 2013.a. Construct a
What’s the conclusion? A hypothesis test is performed, and P = 0.02. Which of the following is the best conclusion?i. H0 is rejected at the 0.05 level.ii. H0 is rejected at the 0.01 level.iii. H1
Find the power of the test against the alternative ????1 = 55.
A test of H0: ???? = 50 versus H1: ???? > 50 will be made at a significance level of ???? = 0.05. The population standard deviation is ???? = 10 and the sample size is n =
Use the ???? = 0.05 level.
Test H0: ???? = 15 versus H1: ????
A random sample of size 20 from a normal population has sample standard deviation s =
True or false: We can perform a test for a standard deviation only when the population is almost exactly normal.
In a test of H0: ???? = 5 versus H1: ???? > 5, the value of the test statistic is t = 2.96. There are 17 degrees of freedom. Do you reject H0 at the ???? = 0.05 level?
The result of a hypothesis test is reported as follows: ‘‘We reject H0 at the ???? = 0.05 level.’’ What additional information should be included?
True or false: When we reject H0, we are certain that H1 is true.
For testing H0: ???? = 3 versus H1: ???? < 3, a P-value of 0.024 is obtained.a. If the significance level is ???? = 0.05, would you conclude that ???? < 3? Explain.b. If the significance level is
In a random sample of 500 people who took their driver’s test, 445 passed. Let p be the population proportion who pass. A test will be made of H0: p = 0.85 versus H1: p > 0.85.a. Compute the value
True or false: We never conclude that H0 is true.
The population standard deviation is unknown. Find the critical value of the test statistic if the significance level is ???? = 0.05.
A test will be made of H0: ???? = 4 versus H1: ???? > 4, using a sample of size
A sample of size 8 is drawn from a normal population with mean ????, and the population standard deviation is unknown.a. Is it appropriate to perform a z-test? Explain.b. Is it appropriate to perform
A null hypothesis is rejected at the ???? = 0.05 level. True or false:a. The P-value is greater than 0.05.b. The P-value is less than or equal to 0.05.c. The result is statistically significant at
True or false: If P = 0.03, thena. The result is statistically significant at the ???? = 0.05 level.b. The result is statistically significant at the ???? = 0.01 level.c. The null hypothesis is
A hypothesis test results in a P-value of 0.008. Which is the best conclusion?i. H0 is definitely false.ii. H0 is definitely true.iii. H0 is plausible.iv. H0 might be true, but it’s very
Fill in the blank: A test of the hypotheses H0: ???? = 65 versus H1: ???? ≠ 65 was performed. The P-value was 0.035. Fill in the blank: If ???? = 65, then the probability of observing a test
It is stated in the text that there are many different t distributions. Explain how this is so.
When constructing a confidence interval for ????, how do you decide whether to use the t distribution or the normal distribution? Are there any circumstances when it is acceptable to use either
In a survey of 5050 U.S. adults, 29% would consider traveling abroad for medical care because of medical costs. The survey’s margin of error was plus or minus 2%.Source: The Gallup Poll
According to a survey of 1000 American adults, 55% of Americans do not have a will specifying the handling of their estate. The survey’s margin of error was plus or minus 3%.Source: FindLaw.com
Explain the difference between confidence and probability.In Exercises 4 and 5, express the following survey results in terms of confidence intervals for p:
What factors can you think of that may affect the width of a confidence interval? In what way does each factor affect the width?
When constructing a confidence interval for ???? when ???? is known, we assume that we have a simple random sample, that ????is known, and that either the sample size is large or the population is
Don’t construct a confidence interval: A meteorology student examines precipitation records for a certain city and discovers that of the last 365 days, it rained on 46 of them. Explain why these
Waist size: According to the National Health Statistics Reports, a sample of 783 men aged 20–29 years had a mean waist size of 36.9 inches with a standard deviation of 8.8 inches.a. Construct a 95%
Leaking tanks: Leakage from underground fuel tanks has been a source of water pollution. In a random sample of 107 gasoline stations, 18 were found to have at least one leaking underground tank.a.
Sleep time: In a sample of 87 young adults, the average time per day spent in bed asleep was 7.06 hours. Assume the population standard deviation is 1.11 hours.a. Construct a 99% confidence interval
Testing math skills: In order to test the effectiveness of a program to improve mathematical skills, a simple random sample of 45 fifth graders was chosen to participate in the program. The students
Super Bowl: A simple random sample of 140 residents in a certain town was polled the week after the Super Bowl, and 75 of them said they had watched the game on television.a. Construct a 95%
Assume the population is normal. Construct a 95% confidence interval for the population standard deviation ????.
Cost of repairs: Refer to Exercise
Cost of repairs: A sample of eight repair records for a certain fiber-optic component was drawn, and the cost of each repair, in dollars, was recorded, with the following results:30 35 19 23 27 22 26
Defective electronics: A simple random sample of 200 electronic components was tested, and 17 of them were found to be defective.a. Construct a 99% confidence interval for the proportion of
Contaminated water: Polychlorinated biphenyls (PCBs) are a group of synthetic oil-like chemicals that were at one time widely used as insulation in electrical equipment and were discharged into
Would it be appropriate to use these data to construct a confidence interval for ???? using the methods of Section 8.4? Explain.
More repairs: Refer to Exercise
More repairs: A sample of six records for repairs of a component showed the following costs:93 97 27 79 81 87a. Construct a 90% confidence interval for the mean cost of a repair for this type of
Cost of environmental restoration: In a survey of 189 Scottish voters, 61 said they would be willing to pay additional taxes in order to restore the Affric forest.a. Assuming that the 189 voters who
Does this confidence interval contradict this claim? Explain.c. How large would the sample need to be so that a 95% confidence interval would have a margin of error of 1.0?Source: Journal of
Drill lifetime: A sample of 50 drills had a mean lifetime of 12.68 holes drilled when drilling a low-carbon steel. Assume the population standard deviation is 6.83.a. Construct a 95% confidence
Build more parking? A survey is to be conducted in which a random sample of residents in a certain city will be asked whether they favor or oppose the building of a new parking structure downtown.
How large a sample is needed so that a 99% confidence interval will have margin of error of 0.08, assuming no estimate of ̂p is available?
Refer to Exercise
How large a sample is needed so that a 99% confidence interval will have margin of error of 0.08, using the sample proportion for ̂p?
Refer to Exercise
In a survey of 802 U.S. adult drivers, 265 state that traffic is getting worse in their community. Construct a 99%confidence interval for the proportion of adult drivers who think that traffic is
What sample size is necessary so that a 95% confidence interval will have a margin of error of 1 hour?
Refer to Exercise
Suppose that a 95% confidence interval is to be constructed for the mean time.a. What is the critical value?b. What is the margin of error?c. Construct the 95% confidence interval.
Refer to Exercise
The amount of time that a certain cell phone will keep a charge is known to be normally distributed with standard deviation???? = 16 hours. A sample of 40 cell phones had a mean time of 141 hours.
Find the critical values for a 98% confidence interval using the chi-square distribution with 18 degrees of freedom.
Find the critical value z????∕2 needed to construct a confidence interval for a population proportion with confidence level 92%.
Construct a 90% confidence interval for the population standard deviation ???? if a sample of size 6 has standard deviation s = 22.
A person selects a random sample of 15 credit cards and determines the annual interest rate, in percent, of each. The sample mean is 12.42 with a sample standard deviation of 1.3. Construct a 95%
A cookie manufacturer wants to estimate the length of time that her boxes of cookies spend in the store before they are bought. She visits a sample of 15 supermarkets and determines the number of
Construct a 95% confidence interval for the population standard deviation ???? if a sample of size 20 has standard deviation s = 10.
An owner of a fleet of taxis wants to estimate the mean gas mileage, in miles per gallon, of the cars in the fleet. A random sample of 40 cars is followed for one month, and the sample mean gas
Find the critical value t????∕2 needed to construct a 90% confidence interval for a population mean with sample size 27.
Define the following terms:a. Point estimateb. Confidence intervalc. Confidence level
Describe the effect, if any, that the size of a sample has in assessing the normality of a population.
Explain how to decide when it is appropriate to use the normal approximation to the binomial distribution.
Consider the formula for the standard deviation of the sampling distribution of ̂p given byWhat happens to the standard deviation as n gets larger and larger? Explain what this means in terms of the
Which is more likely to be closer to 75:i. The exam grade of a randomly selected student in the class?ii. The mean exam grade of a sample of 10 students?Explain.
Suppose that in a large class, the instructor announces that the average grade on an exam is
Describe the information you must know to find the value corresponding to a given proportion of the area under a normal curve.
Describe the information you must know to compute the area under the normal curve over a given interval.
Explain why P(a < X
Is it normal? Is it reasonable to treat the following sample as though it comes from an approximately normal population?Explain.8.8 11.2 11.6 6.3 9.3 1.5 14.6 7.5 5.2 9.0 4.3 9.9 7.8 13.1
Is it normal? Is it reasonable to treat the following sample as though it comes from an approximately normal population?Explain.2.6 4.2 1.5 2.0 0.6 0.7 6.6 2.2 9.7 1.8 4.2 4.4 0.6
Defective rods: A grinding machine used to manufacture steel rods produces rods, 5% of which are defective. When a customer orders 1000 rods, a package of 1060 rods is shipped, with a guarantee that
Side effects: A new medical procedure produces side effects in 25% of the patients who receive it. In a clinical trial, 60 people undergo the procedure. What is the probability that 20 or fewer
It’s all politics: A politician in a close election race claims that 52% of the voters support him. A poll is taken in which 200 voters are sampled, and 44% of them support the politician.a. If the
Facebook: Eighty percent of the students at a particular large university have logged on to Facebook at least once in the past week. A sample of 95 students is asked about their Internet habits.a.
Elementary school: In a certain elementary school, 52% of the students are girls. A sample of 65 students is drawn.a. What is the probability that more than 60% of them are girls?b. Would it be
Safe delivery: A certain delivery truck can safely carry a load of 3400 pounds. The cartons that will be loaded onto the truck have a mean weight of 80 pounds with a standard deviation of 20 pounds.
Pay your taxes: Among all the state income tax forms filed in a particular state, the mean income tax paid was ???? = $2000 and the standard deviation was ???? = $500. As part of a study of the
More lightbulbs: Someone claims to have developed a new lightbulb whose mean lifetime is 1800 hours with a standard deviation of 100 hours. A sample of 100 of these bulbs is tested. The sample mean

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