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elementary statistics

Questions and Answers of Elementary Statistics

A test is made of H0 : μ = 15 versus H1: μ > 15.The sample mean is x̄ = 16.5, the sample size is n = 50, and the population standard deviation is σ = 5.a. Find the value of the test statistic
A test is made of H0 : μ = 125 versus H1: μ < 125.The sample mean is x̄ = 123, the sample size is n = 100, and the population standard deviation is σ = 20.a. Find the value of the test statistic
A test is made of H0 : μ = 100 versus H1: μ ≠ 100.The sample mean is x̄ = 97, the sample size is n = 75, and the population standard deviation is σ = 8.a. Find the value of the test statistic
Which provides stronger evidence against H0: a P-value of 0.05 or a P-value of 0.50?
A test is made of H0 : μ = 30 versus H1: μ < 30.The test statistic is z = −1.28. Find and interpret the P-value.
A test is made of H0 : μ = 6 versus H1: μ ≠ 6.a. The test statistic is z = 0.75. Find and interpret the P-value.b. The test statistic is z = −2.20. Find and interpret the P-value.c. Which
If P = 0.02, which is the best conclusion?i. The probability that H0 is true is 0.02.ii. If H0 is true, the probability of obtaining a test statistic more extreme than the one actually observed is
A hypothesis test is performed with a significance level of α = 0.05.a. If the P-value is 0.08, is H0 rejected?b. If the P-value is 0.08, are the results statistically significant at the 0.05
For each of the following P-values, state whether H0 will be rejected at the 0.10 level.a. P = 0.12b. P = 0.07c. P = 0.05d. P = 0.20
For each of the following P-values, state whether the result is statistically significant at the 0.10 level.a. P = 0.08b. P = 0.15c. P = 0.01d. P = 0.50
A social scientist suspects that the mean number of years of education μ for adults in a certain large city is greater than 12 years. She will test the null hypothesis H0 : μ =12 against the
The following display from a TI-84 Plus calculator presents the results of a hypothesis test for a population mean.a. What are the null and alternate hypotheses?b. What is the value of the test
The following output from MINITAB presents the results of a hypothesis test for a population mean.a. What are the null and alternate hypotheses?b. What is the value of the test statistic?c. What is
A 95% confidence interval for μ is computed to be (1.75, 3.25). For each of the following hypotheses, state whether H0 will be rejected at the 0.05 level.a. H0 : μ = 3 versus H1: μ ≠ 3b. H0 : μ
You want to test H0 : μ = 4 versus H1: μ ≠ 4, so you compute a 95% confidence interval for μ. The 95% confidence interval is 5.1 < μ < 7.2.a. Do you reject H0 at the α = 0.05 level?b. Your
A hypothesis test is performed at a significance level α = 0.05. What is the probability of a Type I error?
Charlie will perform a hypothesis test at the α = 0.05 level. Felice will perform the same test at the α = 0.01 level.a. If H0 is true, who has a greater probability of making a Type I error?b. If
A test was made of the hypotheses H0 : μ = 15 versus H1: μ > 15.Four statisticians wrote summaries of the results. For each summary, state whether it contains enough information. If there is not
A certain type of calculator battery has a mean lifetime of 100 hours and a standard deviation of σ = 10 hours. A company has developed a new battery and claims it has a longer mean life. A random
The ______________ is the probability, assuming H0 is true, of observing a value for the test statistic that is as extreme as or more extreme than the value actually observed.In Exercises 23–28,
The smaller the P-value is, the stronger the evidence against the ______________ hypothesis becomes.In Exercises 23–28, fill in each blank with the appropriate word or phrase.
When using the critical value method, the region that contains the unusual values is called the _______________ region.In Exercises 23–28, fill in each blank with the appropriate word or phrase.
If we decrease the value of the significance level α, we _______________ the probability of a Type I error.In Exercises 23–28, fill in each blank with the appropriate word or phrase.
If we decrease the value of the significance level α, we ________________ the probability of a Type II error.In Exercises 23–28, fill in each blank with the appropriate word or phrase.
When results are statistically significant, they do not necessarily have _______________ significance.In Exercises 23–28, fill in each blank with the appropriate word or phrase.
The smaller the P-value, the stronger the evidence against H0.In Exercises 29–34, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
If the P-value is less than the significance level, we reject H0.In Exercises 29–34, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
The probability of a Type II error is α, the significance level.In Exercises 29–34, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
If the P-value is very small, we can be sure that the results have practical significance.In Exercises 29–34, determine whether the statement is true or false. If the statement is false, rewrite it
The P-value represents the probability that H0 is true.In Exercises 29–34, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
When presenting the results of a hypothesis test, one should report the P-value or the value of the test statistic.In Exercises 29–34, determine whether the statement is true or false. If the
A test is made of H0: μ = 50 versus H1: μ > 50.A sample of size n = 75 is drawn, and x̄ = 56.The population standard deviation is σ = 20.a. Compute the value of the test statistic z.b. Is H0
A test is made of H0: μ = 14 versus H1: μ ≠ 14.A sample of size n = 48 is drawn, and x̄ = 12.The population standard deviation is σ = 6.a. Compute the value of the test statistic z.b. Is H0
A test is made of H0: μ = 130 versus H1: μ ≠ 130.A sample of size n = 63 is drawn, and x̄ = 135.The population standard deviation is σ = 40.a. Compute the value of the test statistic z.b. Is H0
A test is made of H0: μ = 5 versus H1: μ < 5.A sample of size n = 87 is drawn, and x̄ = 4.5. The population standard deviation is σ = 25.a. Compute the value of the test statistic z.b. Is H0
A test of the hypothesis H0: μ = 65 versus H1: μ ≠ 65 was performed. The P-value was 0.035. Fill in the blank: Ifμ = 65, then the probability of observing a test statistic as extreme as or more
A test of the hypothesis H0: μ = 150 versus H1: μ < 150 was performed. The P-value was 0.28. Fill in the blank: If μ = 150, then the probability of observing a test statistic as extreme as or more
True or false: If P = 0.02, thena. The result is statistically significant at the α = 0.05 level.b. The result is statistically significant at the α = 0.01 level.c. The null hypothesis is rejected
True or false: If P = 0.08, thena. The result is statistically significant at the α = 0.05 level.b. The result is statistically significant at the α = 0.10 level.c. The null hypothesis is rejected
A test of H0: μ = 17 versus H1: μ < 17 is performed using a significance level of α = 0.01. The value of the test statistic is z = −2.68.a. Is H0 rejected?b. If the true value of μ is 17, is
A test of H0: μ = 50 versus H1: μ ≠ 50 is performed using a significance level of α = 0.01. The value of the test statistic is z = 1.23.a. Is H0 rejected?b. If the true value of μ is 50, is the
A test of H0: μ = 0 versus H1: μ ≠ 0 is performed using a significance level of α = 0.05. The P-value is 0.15.a. Is H0 rejected?b. If the true value of μ is 1, is the result a Type I error, a
A test of H0: μ = 6 versus H1: μ > 6 is performed using a significance level of α = 0.01. The P-value is 0.002.a. Is H0 rejected?b. If the true value of μ is 8, is the result a Type I error, a
If H0 is rejected at the α = 0.05 level, which of the following is the best conclusion?i. H0 is also rejected at the α = 0.01 level.ii. H0 is not rejected at the α = 0.01 level.iii. We cannot
If H0 is rejected at the α = 0.01 level, which of the following is the best conclusion?i. H0 is also rejected at the α = 0.05 level.ii. H0 is not rejected at the α = 0.05 level.iii. We cannot
If P = 0.03, which of the following is the best conclusion?i. If H0 is true, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.03.ii. The
If P = 0.25, which of the following is the best conclusion?i. The probability that H0 is true is 0.25.ii. If H0 is false, the probability of obtaining a test statistic as extreme as or more extreme
A study conducted in 2015 by the technology company Rovi (now TiVo) showed that the mean time spent per day browsing the video streaming service Netflix for something to watch was 19.3 minutes.
A random sample of 60 second graders in a certain school district are given a standardized mathematics skills test. The sample mean score is x̄ = 52.Assume the standard deviation of test scores is
Are older men shorter than younger men?According to the National Health Statistics Reports, the mean height for U.S. men is 69.4 inches. In a sample of 300 men between the ages of 60 and 69, the mean
Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology (NIST)in Washington, D.C. Suppose that
One of the measurements used to determine the health of a person’s lungs is the amount of air a person can exhale under force in one second. This is called the forced expiratory volume in one
Are children heavier now than they were in the past? The National Health and Nutrition Examination Survey (NHANES) published in 2004 reported that the mean weight of six-year-old girls in the United
Data from the National Association of Realtors indicate that the mean price of a home in Denver, Colorado, in December 2016 was 366.5 thousand dollars. A random sample of 50 homes sold in 2017 had a
The College Board reports that in 2016 the mean score on the math SAT was 510 and the population standard deviation was σ = 103.A random sample of 20 students who took the test in 2017 had a mean
Environmental Protection Agency standards require that the amount of lead in drinking water be less than 15 micrograms per liter. Twelve samples of water from a particular source have the following
The mean GPA at a certain university is 2.80. Following are GPAs for a random sample of 16 business students from this university.a. Following is a boxplot of the data. Is it reasonable to assume
The age in years was recorded for a sample of books in a college library. The following display from a TI-84 Plus calculator presents the results of a hypothesis test regarding the mean age of books
The number of characters was determined for a sample of text messages sent by a certain student. The following display from a TI-84 Plus calculator presents the results of a hypothesis test regarding
A zoologist recorded the weight, in grams, for a sample of white-fronted Amazon parrots. The following MINITAB output presents the results of a hypothesis test regarding the mean weight of this
A sample of students at a certain college was drawn, and the age of each, in years, was determined. The following MINITAB output presents the results of a hypothesis test regarding the mean age of
A new method of teaching arithmetic to elementary school students was evaluated. The students who were taught by the new method were given a standardized test with a maximum score of 100 points. They
A new method of postoperative treatment was evaluated for patients undergoing a certain surgical procedure. Under the old method, the mean length of hospital stay was 6.3 days. The sample mean for
A math teacher has developed a new program to help high school students prepare for the math SAT. A sample of 100 students enroll in the program. They take a math SAT exam before the program starts
doctor has developed a new diet to help people lose weight. A random sample of 500 people went on the diet for six weeks. The mean number of pounds lost was x̄ = 0.5.Assume the standard deviation is
A test was made of the hypotheses H0: μ = 70 versus H1: μ ≠ 70.A report of the results stated:‘‘P < 0.05, so we reject H0 at the α = 0.05 level.’’ Is there any additional information
A test was made of the hypotheses H0: μ = 10 versus H1: μ > 10.A report of the results stated:‘‘The critical value was 1.645. Since z > 1.645, we reject H0 at the α = 0.05 level.’’ Is
Cindy computes a 95% confidence interval for μ and obtains (94.6, 98.3). Luis performs a test of the hypotheses H0: μ = 100 versus H1: μ ≠ 100 and obtains a P-value of 0.12. Explain why they
A sample of size n = 100 is used to test H0: μ = 20 versus H1: μ > 20.The value of μ will not have practical significance unless μ > 25.The population standard deviation is σ = 10.The value of
A simple random sample of 200 third graders in a large school district was chosen to participate in an after-school program to improve reading skills. After completing the program, the children were
In a preliminary study, a simple random sample of 100 computer chips was tested, and 17 of them were found to be defective. Now another sample will be drawn in order to construct a 95% confidence
A pollster is going to sample a number of voters in a large city and construct a 98% confidence interval for the proportion who support the incumbent candidate for mayor. Find a sample size so that
A pollster is planning to draw a simple random sample of 500 people in Colorado (population 5.5 million). He will then conduct a similar poll in Texas (population 27.9 million). He wants to have
A marketing firm in New York City (population 8.6 million) plans to draw a simple random sample of 1000 people to estimate the proportion who have heard about a new product. The firm then plans to
In a simple random sample of 15 seniors from a certain college, 8 of them had found jobs. Use the small-sample method to construct a 95% confidence interval for the proportion of seniors at that
If p̂ is the sample proportion and n is the sample size, then is the ____________________ .In Exercises 7 and 8, fill in each blank with the appropriate word or phrase. p(1 - p) n
To estimate the necessary sample size when no value of p̂ is available, we use p̂ = ______________ .In Exercises 7 and 8, fill in each blank with the appropriate word or phrase.
If we estimate the necessary sample size and no value for p̂ is available, the estimated sample size will be larger than if a value for p̂ were available.In Exercises 9 and 10, determine whether
The margin of error does not depend on the sample size.In Exercises 9 and 10, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
x = 146, n = 762, confidence level 95%In Exercises 11–14, find the point estimate, the standard error, and the margin of error for the given confidence levels and values of x and n.
x = 46, n = 97, confidence level 99%In Exercises 11–14, find the point estimate, the standard error, and the margin of error for the given confidence levels and values of x and n.
x = 236, n = 474, confidence level 90%In Exercises 11–14, find the point estimate, the standard error, and the margin of error for the given confidence levels and values of x and n.
x = 29, n = 80, confidence level 92%In Exercises 11–14, find the point estimate, the standard error, and the margin of error for the given confidence levels and values of x and n.
x = 28, n = 64, confidence level 93%In Exercises 15–18, use the given data to construct a confidence interval of the requested level.
x = 52, n = 71, confidence level 97%In Exercises 15–18, use the given data to construct a confidence interval of the requested level.
x = 125, n = 317, confidence level 95%In Exercises 15–18, use the given data to construct a confidence interval of the requested level.
x = 178, n = 531, confidence level 90%In Exercises 15–18, use the given data to construct a confidence interval of the requested level.
Among 238 cell phone owners aged 18–24 surveyed by the Pew Research Center, 102 said their phone was an Android phone.a. Find a point estimate for the proportion of cell phone owners aged 18–24
According to the U.S. Census Bureau, 43% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 162 were college graduates.a. Find a point estimate for the
Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. In a sample of 427 people aged 65 and over, 104 of them
An Internet service provider sampled 540 customers and found that 75 of them experienced an interruption in high-speed service during the previous month.a. Find a point estimate for the population
The General Social Survey asked 1294 people whether they performed any volunteer work during the past year. A total of 517 people said they did.a. Find a point estimate for the proportion of people
A college admissions officer sampled 120 entering freshmen and found that 42 of them scored more than 550 on the math SAT.a. Find a point estimate for the proportion of all entering freshmen at this
In the computer game League of Legends, some of the strikes are critical strikes, which do more damage.Assume that the probability of a critical strike is the same for every attack, and that attacks
In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead.a. Construct a 90% confidence interval for the proportion of water specimens that contain
A sociologist wants to construct a 95% confidence interval for the proportion of children aged 8–12 living in New York who own a cell phone.a. A survey by the National Consumers League estimated
An educator wants to construct a 98%confidence interval for the proportion of elementary schoolchildren in Colorado who are proficient in reading.a. The results of a recent statewide test suggested
A medical researcher wants to construct a 99% confidence interval for the proportion of knee replacement surgeries that result in complications.a. An article in the Journal of Bone and Joint Surgery
A pollster wants to construct a 95%confidence interval for the proportion of adults who believe that economic conditions are getting better.a. A Gallup poll estimates this proportion to be 0.34.
A sociologist sampled 200 people who work in computer-related jobs, and found that 42 of them have changed jobs in the past 6 months.a. Construct a 95% confidence interval for the proportion of those

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