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elementary statistics

Questions and Answers of Elementary Statistics

When testing a hypothesis for a proportion, we assume that the items in the population are divided into two categories.In Exercises 7 and 8, determine whether the statement is true or false. If the
When testing a hypothesis for a proportion, the alternate hypothesis is always two-tailed.In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false, rewrite it
In a simple random sample of size 80, there were 54 individuals in the category of interest.a. Compute the sample proportion ̂p.b. Are the assumptions for a hypothesis test satisfied?Explain.c. It
In a simple random sample of size 60, there were 38 individuals in the category of interest.a. Compute the sample proportion ̂p.b. Are the assumptions for a hypothesis test satisfied?Explain.c. It
In a simple random sample of size 75, there were 42 individuals in the category of interest.a. Compute the sample proportion ̂p.b. Are the assumptions for a hypothesis test satisfied?Explain.c. It
In a simple random sample of size 150, there were 90 individuals in the category of interest.a. Compute the sample proportion ̂p.b. Are the assumptions for a hypothesis test satisfied?Explain.c. It
According to Secure List, 71.8% of all email sent is spam. A system manager at a large corporation believes that the percentage at his company may be 80%. He examines a random sample of 500 emails
A poll conducted by the General Social Survey asked a random sample of 1325 adults in the United States how much confidence they had in banks and other financial institutions. A total of 149 adults
A marketing manager for a cell phone company claims that more than 55% of children aged 8–12 have cell phones. In a survey of 802 children aged 8–12 by the National Consumers League, 449 of them
The Gallup Poll asked 1015 U.S. adults whether they believed that people should pay sales tax on items purchased over the Internet. Of these, 437 said they supported such a tax. Does the survey
In a survey of 444 HIV-positive smokers, 170 reported that they had used a nicotine patch to try to quit smoking. Can you conclude that less than half of HIV-positive smokers have used a nicotine
A poll taken by the Software Usability Research Laboratory surveyed 341 video gamers, and 110 of them said that they prefer playing games on a console, rather than a computer or hand-held device. An
A Harris poll taken surveyed 2016 adults and found that 423 of them had one or more tattoos. Can you conclude that the percentage of adults who have a tattoo is less than 25%? Use the α = 0.01 level
Vertical banded gastroplasty is a surgical procedure that reduces the volume of the stomach in order to produce weight loss. In a recent study, 82 patients with Type 2 diabetes underwent this
An article in Forbes magazine reported that 73%of Fortune 500 companies have Twitter accounts. A economist thinks the percentage is higher at technology companies. She samples 70 technology companies
A Pew poll surveyed 1802 Internet users and found that 829 of them had posted a photo or video online. Can you conclude that less than half of Internet users have posted photos or videos online? Use
Which do patients value more when choosing a doctor: interpersonal skills or technical ability? In a recent study, 304 people were asked to choose a physician based on two hypothetical descriptions.
A telecommunications company provided its cable TV subscribers with free access to a new sports channel for a period of one month. It then chose a sample of 400 television viewers and asked them
In a recent poll, people were asked whether they supported an increase in the sales tax. The following display from a TI-84 Plus calculator presents the results of a hypothesis test regarding the
A sample of mothers was asked how old they were when their first child was born. The following display from a TI-84 Plus calculator presents the results of a hypothesis test regarding the proportion
A sample of college students was asked whether they had a job outside of school. The following MINITAB output presents the results of a hypothesis test regarding the proportion of college students
A sample of adults was asked whether they were interested in economic issues. The following MINITAB output presents the results of a hypothesis test regarding the proportion who said they were
A simple random sample of 500 students at a certain college were surveyed and asked whether they were satisfied with college life. Two hundred eighty of them replied that they were satisfied. The
A simple random sample of 1500 voters were surveyed and asked whether they were planning to vote for the incumbent mayor for re-election. Seven hundred ninety-eight of them replied that they were
A few weeks before election day, a TV station broadcast a debate between the two leading candidates for governor. Viewers were invited to send a tweet to indicate which candidate they plan to vote
Over the past 100 days, the price of a certain stock went up on 60 days and went down on 40 days. Explain why these data should not be used to test the claim that this stock price goes down on less
When np0 < 10 or n(1 − p0) < 10, we cannot use the normal approximation, but we can use the binomial distribution to perform what is known as an exact test. Let p be the probability that a given
A random sample of size 20 from a normal distribution has standard deviation s = 50.Test H0 : σ = 45 versus H1: σ > 45 at the α = 0.05 level. Do you reject H0?
A random sample of size 12 from a normal distribution has standard deviation s = 7.Test H0 : σ = 15 versus H1: σ < 15 at the α = 0.01 level. Do you reject H0?
A random sample of size 28 from a normal distribution has standard deviation s = 5.Test H0 : σ = 3 versus H1: σ ≠ 3 at the α = 0.01 level. Do you reject H0?
A random sample of size 5 from a normal distribution has standard deviation s = 28.Test H0 : σ = 40 versus H1: σ ≠ 40 at the α = 0.05 level. Do you reject H0?
To test a hypothesis about a standard deviation using a sample of size 15, we use a chi-square distribution with ___________________ degrees of freedom.In Exercises 5 and 6, fill in each blank with
The method described for testing hypotheses about standard deviations should be used only when the distribution of the population is almost exactly ___________________ .In Exercises 5 and 6, fill in
When a test for a standard deviation is performed, it does not matter whether the population is normal, so long as the sample is large.In Exercises 7 and 8, determine whether the statement is true or
Hypothesis tests for a standard deviation may be either one- or two-tailed.In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false, rewrite it as a true
A random sample of size 11 from a normal distribution has standard deviation s = 98.Test H0: σ = 70 versus H1: σ > 70.Use the α = 0.05 level of significance.
A random sample of size 29 from a normal distribution has standard deviation s = 49.Test H0: σ = 55 versus H1: σ < 55.Use the α = 0.01 level of significance.
A random sample of size 24 from a normal distribution has standard deviation s = 29.Test H0: σ = 35 versus H1: σ < 35.Use the α = 0.01 level of significance.
A random sample of size 13 from a normal distribution has standard deviation s = 83.Test H0: σ = 60 versus H1: σ > 60.Use the α = 0.05 level of significance.
A random sample of size 25 from a normal distribution has standard deviation s = 51.Test H0: σ = 30 versus H1: σ ≠ 30.Use the α = 0.05 level of significance.
A random sample of size 8 from a normal distribution has standard deviation s = 75.Test H0: σ = 50 versus H1: σ ≠ 50.Use the α = 0.01 level of significance.
A sample of 25 one-year-old girls had a mean weight of 24.1 pounds with a standard deviation of 4.3 pounds.Assume that the population of weights is normally distributed.A pediatrician claims that the
The General Social Survey asked a large number of people how much time they spent watching TV each day. The mean number of hours was 3.09 with a standard deviation of 2.87. Assume that in a sample of
Scores on an IQ test are normally distributed.A sample of 25 IQ scores had standard deviation s = 8.The developer of the test claims that the population standard deviation is σ = 15.Do these data
Scores on the math SAT are normally distributed.A sample of 20 SAT scores had standard deviation s = 87.Someone says that the scoring system for the SAT is designed so that the population standard
A machine that fills beverage cans is supposed to put 12 ounces of beverage in each can. The standard deviation of the amount in each can is 0.1 ounce.The machine is moved to a new location. To
One of the ways in which doctors try to determine how long a single dose of pain reliever will provide relief is to measure the drug’s half-life, which is the length of time it takes for one-half
A sample of size 101 from a normal population has sample standard deviation s = 40.Use Table A.4 to find the exact critical values X2 0.025 and X2 0.975 to test H0: σ = 30 versus H1: σ ≠ 30.Can
Refer to Exercise 21.Use the normal approximation to estimate the critical values X2 0.025 and X2 0.975. Using these critical values, can you reject H0 at theα = 0.05 level?A sample of size 101 from
Refer to Exercise 21.Use the more accurate normal approximation to estimate the critical values X2 0.025 and X2 0.975. Using these critical values, can you reject H0 at theα = 0.05 level?A more
A test is made of H0 : μ = 25 versus H1: μ < 25.The value of the test statistic is z = −1.84.a. Find the critical value and the critical region for a significance level ofα = 0.05.b. Do you
A test is made of H0 : μ = 7.5 versus H1: μ > 7.5. The value of the test statistic is z = 2.71.a. Find the critical value and the critical region for a significance level ofα = 0.05.b. Do you
A test is made of H0 : μ = 12 versus H1: μ ≠ 12.The value of the test statistic is z = 1.78.a. Find the critical value and the critical region for a significance level ofα = 0.05.b. Do you
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

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