state Homework ch #8

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. A safety administration conducted crash tests of child booster seats for cars. Listed below are results from those​ tests, with the measurements given in hic​ (standard head injury condition​ units). The safety requirement is that the hic measurement should be less than 1000 hic. Use a 0.05 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. Do the results suggest that all of the child booster seats meet the specified​ requirement?

-- Hw 8.4 (12) H u = 1000 H u < 1000 -------------------- Reject sufficient ---------------------- There is strong evidence that the mean is less than 1000​ hic, but one of the booster seats has a measurement that is greater than 1000 hic. or There is not strong evidence that the mean is less than 1000​ hic, and one of the booster seats has a measurement that is greater than 1000 hic. -

Use technology to find the​ P-value for a​ two-tailed test with n=25 and test statistic

8 post test (13)

In​ statistics, what does df​ denote? If a simple random sample of 25 speeds of cars on California Highway 405 is to be used to test the claim that the sample values are from a population with a mean greater than the posted speed limit of 65​ mi/h, what is the specific value of​ df? Choose the correct answer below.

8 post test (2) df denotes the number of degrees of freedom. For this​ sample, df=24.

What is the null hypothesis and what do you conclude about​ it? Identify the null hypothesis.

H=p (X)

In​ statistics, what does df​ denote? If a simple random sample of 24 speeds of cars on California Highway 405 is to be used to test the claim that the sample values are from a population with a mean greater than the posted speed limit of 65​ mi/h, what is the specific value of​ df?

Hw 8.4 (1) df denotes the number of degrees of freedom. For this​ sample, df=23.

The accompanying data table lists the magnitudes of 50 earthquakes measured on the Richter scale. Test the claim that the population of earthquakes has a mean magnitude greater than 1.00. Use a 0.01 significance level. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, and conclusion for the test. Assume this is a simple random sample.

Hw 8.4 (15) H u = H u > -------------

Which of the following is NOT a requirement for testing a claim about a mean with σ ​known? Choose the correct answer below.

Hw 8.4 (22) If the sample results​ (or more extreme​ results) cannot easily occur when the null hypothesis is​ true, we explain the discrepancy between the assumption and the sample results by concluding that the assumption is​ true, so we do not reject the assumption.

Using a table of critical​ t-values of the t​ distribution, find the range of values for the​ P-value for testing a claim about the mean body temperature of healthy adults for a​ left-tailed test with n=10 and test statistic

Hw 8.4 (3)

Using a table of critical​ t-values of the t​ distribution, find the range of values for the​ P-value for a​ two-tailed test with n=13 and test statistic

Hw 8.4 (4)

Which of the following is NOT a requirement for testing a claim about a standard deviation or​ variance?

Hw 8.5 (12) The population must be skewed to the right.

Which of the following is NOT a property of the​ chi-square distribution?

Hw 8.5 (13) The mean of the​ chi-square distribution is 0.

Is the test​ two-tailed, left-tailed, or​ right-tailed? (becuses it is at 32%)

​Two-tailed test

Identify the type I error and the type II error that correspond to the given hypothesis. The percentage of households with more than 1 pet is equal to 65%. Identify the type I error. Choose the correct answer below. Identify the type II error. Choose the correct answer below.

8 post test (1) Reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65% when that percentage is actually equal to 65%. There is sufficient evidence to support the claim that the new method is effective in increasing the likelihood that a baby will be a boy.

For the given​ claim, complete parts​ (a) and​ (b) below. ​Claim: At most 35​% of Internet users pay bills online. A recent survey of 379 Internet users indicated that 32​% pay their bills online.

8 post test (10) P <= P= P>

In a study of pregnant women and their ability to correctly predict the sex of their​ baby, 57 of the pregnant women had 12 years of education or​ less, and 36.8​% of these women correctly predicted the sex of their baby. Use a 0.05 significance level to test the claim that these women have an ability to predict the sex of their baby equivalent to random guesses. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, and conclusion about the null hypothesis. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution. Do the results suggest that their percentage of correct predictions is different from results expected with random​ guesses?

8 post test (11) H = H not= Reject is is

A survey of 1,586 randomly selected adults showed that 556 of them have heard of a new electronic reader. The accompanying technology display results from a test of the claim that 34​% of adults have heard of the new electronic reader. Use the normal distribution as an approximation to the binomial​ distribution, and assume a 0.01 significance level to complete parts​ (a) through​ (e).

8 post test (12) ​Two-tailed test . Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level, α. here is not sufficient evidence to warrant rejection of the claim that 34​% of adults have heard of the new electronic reader.

In an analysis investigating the usefulness of​ pennies, the cents portions of 82 randomly selected credit card charges from students are​ recorded, and they have a mean of 47.6 cents and a standard deviation of 31.7 cents. If the amounts from 0 cents to 99 cents are all equally​ likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.05 significance level to test the claim that the sample is from a population with a standard deviation equal to 28.866 cents. Complete parts​ (a) through​ (e) below.

8 post test (14) H o = H o not= Do not reject is not ​No, because in that case the underlying population is not normally​ distributed, so the results of standard deviation hypothesis tests are not reliable.

A simple random sample of 55 adults is obtained from a normally distributed​ population, and each​ person's red blood cell count​ (in cells per​ microliter) is measured. The sample mean is 5.31 and the sample standard deviation is 0.52. Use a 0.01 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5.4, which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample​ group?

8 post test (15) H = H < Fail to reject H0. There is not sufficient evidence to support the claim that the sample is from a population with a mean less than 5.4. There is not enough evidence to conclude that the sample is from a population with a mean less than 5.4​, so it is possible that the population has counts that are too high.

Assume that a researcher wants to use sample data to test the claim that the sample is from a population with a standard deviation less than 1.8 min. The researcher will use a 0.05 significance level to test that claim. If the researcher wants to use the confidence interval method of testing​ hypotheses, what level of confidence should be used for the confidence​ interval? Will the conclusion based on the confidence interval be the same as the conclusion based on a hypothesis test that uses the​ P-value method or the critical value​ method?

8 post test (16) Since this is a​ one-tailed test, the researcher should use a confidence level of 0.90. Yes; the confidence interval method and the​ P-value or critical methods always lead to the same conclusion when the tested parameter is the standard deviation.

Make a decision about the given claim. Use only the rare event​ rule, and make subjective estimates to determine whether events are likely. For​ example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20​ flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads​ (because it is easy to get 11 heads in 20 flips by chance with a fair​ coin). ​Claim: The mean IQ score of students in a large statistics class is less than 133. A simple random sample of the students has a mean IQ score of 132.6.

8 post test (17) The sample is not unusual if the claim is true. The sample is not unusual if the claim is false.​ Therefore, there is not sufficient evidence to support the claim.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. In a manual on how to have a number one​ song, it is stated that a song must be no longer than 210 seconds. A simple random sample of 40 current hit songs results in a mean length of 229.4 sec and a standard deviation of 53.01 sec. Use a 0.05 significance level and the accompanying Minitab display to test the claim that the sample is from a population of songs with a mean greater than 210 sec. What do these results suggest about the advice given in the​ manual?

8 post test (18) Reject H0. There is sufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210 sec. The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice.

A 0.01 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selection, the proportion of baby girls is less than 0.5. Assume that sample data consists of 45 girls in 100 ​births, so the sample statistic of 920 results in a z score that is 1 standard deviation below 0. Complete parts​ (a) through​ (h) below. Click here to view page 1 of the Normal table.LOADING... Click here to view page 2 of the Normal table.LOADING...

8 post test (19) Left​-tailed

Workers at a certain soda drink factory collected data on the volumes​ (in ounces) of a simple random sample of 17 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.11 ​oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.96 oz and 12.68 ​oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.18 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.18 oz. Use a 0.05 significance level. Complete parts​ (a) through​ (d) below.

8 post test (20) Reject less than or equal to sufficient

The data table contains waiting times of customers at a​ bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 1.8 ​minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.05. Complete parts​ (a) through​ (d) below. LOADING... Click on the icon to view the data.

8 post test (21) is not not rejected

candy company makes five different colors of candies. Find the sample proportion of candies that are green. Use that result to test the claim that 17​% of the​ company's candies are green. Use the data in the table​ below, the​ P-value method, and a significance level of 0.05.

8 post test (22) Fail to reject the null hypothesis because the​P-value is greater than the significance​level, α. There is not sufficient evidence to warrant rejection of the claim that 17% of the​ company's candies are green.

Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the​ P-value method or the traditional method of testing hypotheses. Company A uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2​ ft, which was the standard deviation for the old production method. If it appears that the standard deviation is​ greater, does the new production method appear to be better or worse than the old​ method? Should the company take any​ action?

8 post test (23)

Consider a flight to be on time if it arrives no later than 15 minutes after the scheduled arrival time. Negative arrival times correspond to flights arriving earlier than their scheduled arrival time. Use the sample data to test the claim that 78.8​% of flights are on time. Use a 0.05 significance level and the​ P-value method to answer the following questions. LOADING... Click on the icon to view the table of arrival delay times.

8 post test (3) H = H not = Fail to reject the null hypothesis because the​P-value is greater than the significance​level, α. There is insufficient evidence to warrant rejection of the claim that 78.8​% of flights are on time.

Assume that the significance level is α=0.1. Use the given information to find the​ P-value and the critical​ value(s). The test statistic of z=−1.82 is obtained when testing the claim that p<0.5.

8 post test (4)

In a recent​ poll, 800 adults were asked to identify their favorite seat when they​ fly, and 474 of them chose a window seat. Use a 0.05 significance level to test the claim that the majority of adults prefer window seats when they fly. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution.

8 post test (5) H p = H p > Reject the null hypothesis because the​P-value is less than or equal to the significance​level, α. There is sufficient evidence to support the claim that the majority of adults prefer window seats when they fly.

Use technology to find the​ P-value for a​ right-tailed test about a mean with n=25 and test statistic

8 post test (6)

Using a table of critical​ t-values of the t​ distribution, find the range of values for the​ P-value for testing a claim about the mean body temperature of healthy adults for a​ left-tailed test with n=11 and test statistic

8 post test (7)

A simple random sample of pulse rates of 20 women from a normally distributed population results in a standard deviation of 12.7 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.01 significance level to test the claim that pulse rates of women have a standard deviation equal to 10 beats per minute. Complete parts​ (a) through​ (d) below.

8 post test (8) H o = H o not = Fail to reject is not

In a recent poll of 740 randomly selected​ adults, 590 said that it is morally wrong to not report all income on tax returns. Use a 0.01 significance level to test the claim that 70​% of adults say that it is morally wrong to not report all income on tax returns. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution.

8 post test (9) H o = H o not= Reject is

Choose the correct answer below.

Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level, α. or Reject the null hypothesis because the​P-value is less than or equal to the significance​level, α.

Decide whether to reject the null hypothesis. Choose the correct answer below.

Fail to reject the null hypothesis because the​ P-value is greater than the significance​ level, α. or Reject the null hypothesis because the​ P-value is less than or equal to the significance​ level, α.

For the given​ claim, complete parts​ (a) and​ (b) below. ​Claim: The mean weight of beauty pageant winners is 121 pounds. A study of 20 randomly selected beauty pageants resulted in a mean winner weight of 117 pounds.

HW 8.2 (1)

Assume that the significance level is α=0.05. Use the given statement and find the​ P-value and critical​ value(s). The test statistic of z=−1.53 is obtained when testing the claim that p=13.

Hw 8.2 (10)

Assume that the significance level is α=0.01. Use the given information to find the​ P-value and the critical​ value(s). With H1: p≠25​, the test statistic is z=−1.02.

Hw 8.2 (11)

Assume a significance level of α=0.05 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: The proportion of male golfers is less than 0.2. The hypothesis test results in a​ P-value of 0.097. a) Assume a significance level of α=0.05 and use the given information to complete parts​ (a) and​ (b) below. Original​ claim: The proportion of male golfers is less than 0.2. The hypothesis test results in a​ P-value of 0.097. a. State a conclusion about the null hypothesis.​ (Reject H0 or fail to reject H0​.) Choose the correct answer below. b) Without using technical​ terms, state a final conclusion that addresses the original claim. Which of the following is the correct​ conclusion?

Hw 8.2 (12) a) Fail to reject H0 because the​P-value is greater than α. b) There is not sufficient evidence to support the claim that the proportion of male golfers is less than 0.2.

A 0.01 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selection, the proportion of baby girls is greater than 0.5. Assume that sample data consists of 55 girls in 100 ​births, so the sample statistic of 1120 results in a z score that is 1 standard deviation above 0. Complete parts​ (a) through​ (h) below. a) Identify the null hypothesis and the alternative hypothesis. Choose the correct answer below. c) What is the sampling distribution of the sample​ statistic? d) Is the test​ two-tailed, left-tailed, or​ right-tailed?

Hw 8.2 (13) a) H p= (x) H p> (x) c) Normal distribution d) Right​-tailed

Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of settled medical malpractice suits is 0.21. a) Which of the following is a type I​ error? b) Which of the following is a type II​ error?

Hw 8.2 (14) a) Reject the claim that the proportion of settled malpractice suits is 0.21 when the proportion is actually 0.21. b) Fail to reject the claim that the proportion of settled malpractice suits is 0.21 when the proportion is actually different from 0.21.

Identify the type I error and the type II error that correspond to the given hypothesis. The percentage of households with more than 1 pet is equal to 65%. a) Identify the type I error. Choose the correct answer below. b) Identify the type II error. Choose the correct answer below.

Hw 8.2 (15) a) Reject the null hypothesis that the percentage of households with more than 1 pet is equal to 65% when that percentage is actually equal to 65%. b) Fail to reject the null hypothesis that the percentage of high school students who graduate is equal to 55% when that percentage is actually greater than 55%.

A​ _____________ is a procedure for testing a claim about a property of a population.

Hw 8.2 (16) hypothesis test

The​ _____________ states that​ if, under a given​ assumption, the probability of a particular observed event is extremely​ small, we conclude that the assumption is probably not correct.

Hw 8.2 (17) rare event rule

The​ _________ hypothesis is a statement that the value of a population parameter is equal to some claimed value.

Hw 8.2 (18) null

The​ ___________ is a value used in making a decision about the null hypothesis and is found by converting the sample statistic to a score with the assumption that the null hypothesis is true.

Hw 8.2 (19) test statistic

For the given​ claim, complete parts​ (a) and​ (b) below. ​Claim: High school teachers have incomes with a standard deviation that is less than ​$17,750. A recent study of 150 high school teacher incomes showed a standard deviation of ​$13,750.

Hw 8.2 (2)

Which of the following is NOT true about​ P-values in hypothesis​ testing? Choose the correct answer below.

Hw 8.2 (20) The​ P-value separates the critical region from the values that do not lead to rejection of the null hypothesis.

Which of the following is NOT true about the tails in a​ distribution? Choose the correct answer below.

Hw 8.2 (21) The inequality symbol in the alternative hypothesis points away from the critical region.

Which of the following is NOT a criterion for making a decision in a hypothesis​ test?

Hw 8.2 (22) If the​ P-value is less than​ 0.05, the decision is to reject the null hypothesis.​ Otherwise, we fail to reject the null hypothesis.

Which of the following is NOT a true statement about error in hypothesis​ testing?

Hw 8.2 (23) A type I error is making the mistake of rejecting the null hypothesis when it is actually false.

The​ _________ of a hypothesis test is the probability ​(1−β​) of rejecting a false null hypothesis.

Hw 8.2 (24) power

For the given​ claim, complete parts​ (a) and​ (b) below. ​Claim: At least 27​% of Internet users pay bills online. A recent survey of 343 Internet users indicated that 30​% pay their bills online.

Hw 8.2 (3)

Make a decision about the given claim. Do not use any formal procedures and exact calculations. Use only the rare event rule. ​Claim: A coin favors heads when​ tossed, and there are 19 heads in 22 tosses.

Hw 8.2 (4) There does appear to be sufficient evidence to support the claim because there are substantially more heads than tails.

Make a decision about the given claim. Use only the rare event​ rule, and make subjective estimates to determine whether events are likely. For​ example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20​ flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads​ (because it is easy to get 11 heads in 20 flips by chance with a fair​ coin).

Hw 8.2 (5) The sample is not unusual if the claim is true. The sample is not unusual if the claim is false.​ Therefore, there is not sufficient evidence to support the claim.

The claim is that the proportion of peas with yellow pods is equal to 0.25​ (or 25%). The sample statistics from one experiment include 540 peas with 155 of them having yellow pods. Find the value of the test statistic.

Hw 8.2 (6)

The claim is that the proportion of adults who smoked a cigarette in the past week is less than 0.25​, and the sample statistics include n=1339 subjects with 308 saying that they smoked a cigarette in the past week. Find the value of the test statistic.

Hw 8.2 (7)

The claim is that the IQ scores of statistics professors are normally​ distributed, with a mean greater than 126. A sample of 15 professors had a mean IQ score of 129 with a standard deviation of 9. Find the value of the test statistic. The value of the test statistic is

Hw 8.2 (8)

Assume that the significance level is α=0.01. Use the given information to find the​ P-value and the critical​ value(s). The test statistic of z=1.45 is obtained when testing the claim that p>0.3.

Hw 8.2 (9)

In a Harris​ poll, adults were asked if they are in favor of abolishing the penny. Among the​ responses, 1200 answered​ "no," 456 answered​ "yes," and 359 had no opinion. What is the sample proportion of yes​ responses, and what notation is used to represent​ it?

Hw 8.3 (1) The symbol p is used to represent a sample proportion.

Trials in an experiment with a polygraph include 96 results that include 22 cases of wrong results and 74 cases of correct results. Use a 0.05 significance level to test the claim that such polygraph results are correct less than 80​% of the time. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution. Identify the conclusion about the null hypothesis and the final conclusion that addresses the original claim. ▼ Reject Fail to reject H0. There ▼ is notis sufficient evidence to support the claim that the polygraph results are correct less than 80​% of the time.

Hw 8.3 (10) H p = (x) H p < (x) Fail to reject is not

A recent broadcast of a television show had a 15 ​share, meaning that among 5000 monitored households with TV sets in​ use, 15​% of them were tuned to this program. Use a 0.01 significance level to test the claim of an advertiser that among the households with TV sets in​ use, less than 25​% were tuned into the program. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution. Reject H0. There is sufficient evidence to support the claim that less than 25​% of the TV sets in use were tuned to the program.

Hw 8.3 (11) H p = 0.25 H p < 0.25 Reject is

A survey of 61,646 people included several questions about office relationships. Of the​ respondents, 25.5​% reported that bosses scream at employees. Use a 0.05 significance level to test the claim that more than 1/4 of people say that bosses scream at employees. How is the conclusion affected after learning that the survey is an online survey in which Internet users chose whether to​ respond? Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution. Reject H0. There is sufficient evidence to support the claim that more than 1/4 of people say that bosses scream at employees. If the sample is a voluntary response​sample, the conclusion might not be valid

Hw 8.3 (12) H p = 0.25 H p > 0.25 Reject is might not be

In a recent court case it was found that during a period of 11 years 884 people were selected for grand jury duty and 42​% of them were from the same ethnicity. Among the people eligible for grand jury​ duty, 80.4​% were of this ethnicity. Use a 0.05 significance level to test the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution. What is the conclusion on the null​ hypothesis?

Hw 8.3 (13) H p = 0.804 H p < 0.804 Reject the null hypothesis because the​P-value is less than or equal to the significance​level, α. There is sufficient evidence to support the claim that the selection process is biased against allowing this ethnicity to sit on the grand jury. The jury selection process appears to be unfair.

A recent sports game set a record for the number of television viewers. The game had a share of 78​%, meaning that among the television sets in use at the time of the​ game, 78​% were tuned to the game. The sample size is 24,149 households. Use a 0.05 significance level to test the claim that more than 74​% of television sets in use were tuned to the sports game. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution. What is the conclusion on the null​ hypothesis? What is the final​ conclusion?

Hw 8.3 (14) H p = 0.74 H p > 0.74 Reject the null hypothesis because the​P-value is less than or equal to the significance​level, α. There is sufficient evidence to support the claim that more than 74​% of television sets in use were tuned to the sports game.

A candy company makes five different colors of candies. Find the sample proportion of candies that are green. Use that result to test the claim that 16​% of the​ company's candies are green. Use the data in the table​ below, the​ P-value method, and a significance level of 0.01.

Hw 8.3 (15) H p = 0.16 H p not = 0.16

Which of the following is NOT a requirement of testing a claim about a population proportion using the normal approximation​ method?

Hw 8.3 (16) The lowercase​ symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim.

Which of the following is NOT true when testing a claim about a​ proportion? Choose the correct answer below.

Hw 8.3 (17) A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

Which of the following is NOT true of using the binomial probability distribution to test claims about a​ proportion? Choose the correct answer below.

Hw 8.3 (18) One requirement of this method is that np≥5 and nq≥5.

A certain drug is used to treat asthma. In a clinical trial of the​ drug, 30 of 273 treated subjects experienced headaches​ (based on data from the​ manufacturer). The accompanying calculator display shows results from a test of the claim that less than 8​% of treated subjects experienced headaches. Use the normal distribution as an approximation to the binomial distribution and assume a 0.05 significance level to complete parts​ (a) through​ (e) below.

Hw 8.3 (2)

A survey of 1,682 randomly selected adults showed that 586 of them have heard of a new electronic reader. The accompanying technology display results from a test of the claim that 37​% of adults have heard of the new electronic reader. Use the normal distribution as an approximation to the binomial​ distribution, and assume a 0.01 significance level to complete parts​ (a) through​ (e).

Hw 8.3 (3)

A genetic experiment involving peas yielded one sample of offspring consisting of 409 green peas and 145 yellow peas. Use a 0.01 significance level to test the claim that under the same​ circumstances, 24​% of offspring peas will be yellow. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution. What is the conclusion about the null​ hypothesis? What is the final​ conclusion?

Hw 8.3 (4) H p=(x) H p not = (x) Fail to reject the null hypothesis because the​P-value is greater than the significance​level, α. There is not sufficient evidence to warrant rejection of the claim that 25​% of offspring peas will be yellow.

In​ 1997, a survey of 800 households showed that 147 of them use​ e-mail. Use those sample results to test the claim that more than​ 15% of households use​ e-mail. Use a 0.05 significance level. Use this information to answer the following questions. a) Which of the following is the hypothesis test to be​ conducted? d) What is the​ conclusion? e) Is the conclusion valid​ today? Why or why​ not?

Hw 8.3 (5) a) H p = (x) H p > (x) d) There is sufficient evidence to support the claim that more than​ 15% of households use​ e-mail. e) ​No, the conclusion is not valid today because the population characteristics of the use of​ e-mail are changing rapidly.

A clinical trial was conducted using a new method designed to increase the probability of conceiving a girl. As of this​ writing, 945 babies were born to parents using the new​ method, and 862 of them were girls. Use a 0.01 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a girl. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution. a) What is the conclusion about the null​ hypothesis? b) What is the final​ conclusion?

Hw 8.3 (6) H p = (x) H p > (x) a) Reject the null hypothesis because the​P-value is less than or equal to the significance​level, α. b) There is sufficient evidence to support the claim that the new method is effective in increasing the likelihood that a baby will be a girl.

A clinical trial was conducted using a new method designed to increase the probability of conceiving a boy. As of this​ writing, 300 babies were born to parents using the new​ method, and 239 of them were boys. Use a 0.05 significance level to test the claim that the new method is effective in increasing the likelihood that a baby will be a boy. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, conclusion about the null​ hypothesis, and final conclusion that addresses the original claim. Use the​ P-value method and the normal distribution as an approximation to the binomial distribution. a) What is the conclusion on the null​ hypothesis? b) What is the final​ conclusion? Identify the conclusion about the null hypothesis. Do the results suggest that their percentage of correct predictions is different from results expected with random​ guesses?

Hw 8.3 (7) H p = (x) H p > (x) a) Reject the null hypothesis because the​P-value is less than or equal to the significance​level, α. b) There is sufficient evidence to support the claim that the new method is effective in increasing the likelihood that a baby will be a boy. Fail to reject is not is not

In a study of pregnant women and their ability to correctly predict the sex of their​ baby, 56 of the pregnant women had 12 years of education or​ less, and 44.6​% of these women correctly predicted the sex of their baby. Use a 0.01 significance level to test the claim that these women have an ability to predict the sex of their baby equivalent to random guesses. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, and conclusion about the null hypothesis. Use the​ P-value method. Use the normal distribution as an approximation of the binomial distribution. Do the results suggest that their percentage of correct predictions is different from results expected with random​ guesses?

Hw 8.3 (8)

When testing gas pumps for​ accuracy, fuel-quality enforcement specialists tested pumps and found that 1308 of them were not pumping accurately​ (within 3.3 oz when 5 gal is​ pumped), and 5647 pumps were accurate. Use a 0.01 significance level to test the claim of an industry representative that less than​ 20% of the pumps are inaccurate. Use the​ P-value method and use the normal distribution as an approximation to the binomial distribution. Because the​ P-value is less than the significance​ level, reject the null hypothesis. There is sufficient evidence support the claim that less than​ 20% of the pumps are inaccurate.

Hw 8.3 (9) H p = (x) H p < (x) less than reject sufficient

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100 mm cigarettes is​ obtained, and the tar content of each cigarette is measured. The sample has a mean of 19.2 mg and a standard deviation of 3.41 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 ​mg, which is the mean for unfiltered king size cigarettes. What do the results​ suggest, if​ anything, about the effectiveness of the​ filters?

Hw 8.4 (10) H p = 21.1 H p < 21.1 a) Reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. --------------------------- b) The results suggest that the filters are effective.

For the following​ claim, find the null and alternative​ hypotheses, test​ statistic, critical​ value, and draw a conclusion. Assume that a simple random sample has been selected from a normally distributed population. Answer parts ​a-d. ​Claim: The mean IQ score of statistics professors is less than 116. Sample​ data: n=14​, x=113​, s=11. The significance level is α=0.05.

Hw 8.4 (11) Fail to reject the null hypothesis and do not support the claim that μ>128.

Assume that a simple random sample has been selected and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. Listed below are brain volumes in cm3 of unrelated subjects used in a study. Use a 0.01 significance level to test the claim that the population of brain volumes has a mean equal to 1099.4 cm3.

Hw 8.4 (13) H u = H u not = -------- Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the population of brain volumes has a mean equal to 1099.4 cm3. to reject H0. There is insufficient evidence to warrant rejection of the claim that the population of brain volumes has a mean equal to 1099.4 cm3. H0. There is insufficient evidence to warrant rejection of the claim that the population of brain volumes has a mean equal to 1099.4 cm3.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, critical​ value(s), and state the final conclusion that addresses the original claim. A simple random sample of pages from a dictionary is obtained. Listed below are the numbers of words defined on those pages. Given that this dictionary has 1459 pages with defined​ words, the claim that there are more than​ 70,000 defined words is the same as the claim that the mean number of defined words on a page is greater than 48.0. Use a 0.10 level significance level to test this claim. What does the result suggest about the claim that there are more than​ 70,000 defined words in the​ dictionary?

Hw 8.4 (14) H u = H u not = or H u = H u > ------------------- There is sufficient evidence to support the claim that there are more than​ 70,000 words in the dictionary. or There is not sufficient evidence to support the claim that there are more than​ 70,000 words in the dictionary.

The accompanying data table lists the weights of male college students in kilograms. Test the claim that male college students have a mean weight that is less than the 84 kg mean weight of males in the general population. Use a 0.01 significance level. Identify the null​ hypothesis, alternative​ hypothesis, test​ statistic, P-value, and conclusion for the test. Assume this is a simple random sample.

Hw 8.4 (16) H p = 84 H p < 84

Which of the following is not a requirement for testing a claim about a population with σ not​ known?

Hw 8.4 (17) The population​ mean, μ​, is equal to 1.

Which of the following is not a characteristic of the t​ test?

Hw 8.4 (18) The Student t distribution has a mean of t=0 and a standard deviation of s=1.

Which of the following is not a strategy for finding​ P-values with the Student t​ distribution? Choose the correct answer below.

Hw 8.4 (19) Use the table in the book to find the​ P-value rounded to at least 4 decimal places.

Use technology to find the​ P-value for a​ right-tailed test about a mean with n=18 and test statistic t=2.067.

Hw 8.4 (2)

Which of the following is not true when using the confidence interval method for testing a claim about μ when σ is​ unknown? Choose the correct answer below.

Hw 8.4 (20) The​ P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results.

Which of the following is NOT a requirement for testing a claim about a population mean with σ ​known? Choose the correct answer below.

Hw 8.4 (21) The sample​ mean, x is greater than 30.

Use technology to find the​ P-value for a​ two-tailed test with n=26 and test statistic

Hw 8.4 (5)

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. In a manual on how to have a number one​ song, it is stated that a song must be no longer than 210 seconds. A simple random sample of 40 current hit songs results in a mean length of 243.6 sec and a standard deviation of 54.92 sec. Use a 0.05 significance level and the accompanying Minitab display to test the claim that the sample is from a population of songs with a mean greater than 210 sec. What do these results suggest about the advice given in the​ manual? State the final conclusion that addresses the original claim. Choose the correct answer below. What do the results suggest about the advice given in the​ manual?

Hw 8.4 (6) H p = 210 H p > 210 Reject H0. There is sufficient evidence to support the claim that the sample is from a population of songs with a mean length greater than 210 sec. The results suggest that the advice of writing a song that must be no longer than 210 seconds is not sound advice.

A simple random sample of 42 adults is obtained from a normally distributed​ population, and each​ person's red blood cell count​ (in cells per​ microliter) is measured. The sample mean is 5.32 and the sample standard deviation is 0.52. Use a 0.01 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5.4, which is a value often used for the upper limit of the range of normal values. What do the results suggest about the sample​ group? State the final conclusion that addresses the original claim. Choose the correct answer below.

Hw 8.4 (7) H p = 5.4 H p < 5.4 Fail to reject H0. There is not sufficient evidence to support the claim that the sample is from a population with a mean less than 5.4. There is not enough evidence to conclude that the sample is from a population with a mean less than 5.4​, so it is possible that the population has counts that are too high.

Assume that a simple random sample has been selected and test the given claim. Use the​ P-value method for testing hypotheses. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. The ages of actresses when they won an acting award is summarized by the statistics n=78​, x=35.6 ​years, and s=11.1 years. Use a 0.05 significance level to test the claim that the mean age of actresses when they win an acting award is 34 years. State the final conclusion that addresses the original claim. Choose the correct answer below.

Hw 8.4 (8) H u = 34 H u not = 34 Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the mean age of actresses when they win an acting award is 33 years.

Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. A coin mint has a specification that a particular coin has a mean weight of 2.5 g. A sample of 39 coins was collected. Those coins have a mean weight of 2.49443 g and a standard deviation of 0.01356 g. Use a 0.05 significance level to test the claim that this sample is from a population with a mean weight equal to 2.5 g. Do the coins appear to conform to the specifications of the coin​ mint?

Hw 8.4 (9) H p = 2.5 H p not = 2.5 ---------------------------------------------------- Reject H0. There is sufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5 g. or Fail to reject H0. There is insufficient evidence to warrant rejection of the claim that the sample is from a population with a mean weight equal to 2.5 g. ------------------------------------------ Yes, since the coins do not seem to come from a population with a mean weight different from 2.5 g. or No, since the coins seem to come from a population with a mean weight different from 2.5 g.

Assume that a researcher wants to use sample data to test the claim that the sample is from a population with a standard deviation less than 1.8 min. The researcher will use a 0.05 significance level to test that claim. If the researcher wants to use the confidence interval method of testing​ hypotheses, what level of confidence should be used for the confidence​ interval? Will the conclusion based on the confidence interval be the same as the conclusion based on a hypothesis test that uses the​ P-value method or the critical value​ method? If the researcher wants to use the confidence interval method of testing​ hypotheses, what level of confidence should be used for the confidence​ interval? Will the conclusion based on the confidence interval be the same as the conclusion based on a hypothesis test that uses the​ P-value method or the critical value​ method?

Hw 8.5 (1) a) Since this is a​ one-tailed test, the researcher should use a confidence level of 0.90. b ​Yes; the confidence interval method and the​ P-value or critical methods always lead to the same conclusion when the tested parameter is the standard deviation.

Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the​ P-value method or the traditional method of testing hypotheses. Company A uses a new production method to manufacture aircraft altiTest the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the​ P-value method or the traditional method of testing hypotheses. Company A uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2​ ft, which was the standard deviation for the old production method. If it appears that the standard deviation is​ greater, does the new production method appear to be better or worse than the old​ method? Should the company take any​ action?meters. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2​ ft, which was the standard deviation for the old production method. If it appears that the standard deviation is​ greater, does the new production method appear to be better or worse than the old​ method? Should the company take any​ action?

Hw 8.5 (10) H o = H o> b) greater than reject sufficient e) greater worse more should

The data table contains waiting times of customers at a​ bank, where customers enter a single waiting line that feeds three teller windows. Test the claim that the standard deviation of waiting times is less than 2.2 ​minutes, which is the standard deviation of waiting times at the same bank when separate waiting lines are used at each teller window. Use a significance level of 0.05. Complete parts​ (a) through​ (d) below.

Hw 8.5 (11) H o = H o <

Which of the following is NOT true when testing a claim about a standard deviation or​ variance?

Hw 8.5 (14) The​ P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results.

Workers at a certain soda drink factory collected data on the volumes​ (in ounces) of a simple random sample of 25 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard deviation of 0.11 ​oz, and they appear to be from a normally distributed population. If the workers want the filling process to work so that almost all cans have volumes between 11.98 oz and 12.70 ​oz, the range rule of thumb can be used to estimate that the standard deviation should be less than 0.18 oz. Use the sample data to test the claim that the population of volumes has a standard deviation less than 0.18 oz. Use a 0.05 significance level. Complete parts​ (a) through​ (d) below.

Hw 8.5 (2) H o = 0.17 H o < 0.17

Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 4​%. A​ mutual-fund rating agency randomly selects 29 months and determines the rate of return for a certain fund. The standard deviation of the rate of return is computed to be 3.56​%. Is there sufficient evidence to conclude that the fund has moderate risk at the α=0.01 level of​ significance? A normal probability plot indicates that the monthly rates of return are normally distributed.

Hw 8.5 (3) o = 0.04 o < 0.04

The piston diameter of a certain hand pump is 0.6 inch. The manager determines that the diameters are normally​ distributed, with a mean of 0.6 inch and a standard deviation of 0.006 inch. After recalibrating the production​ machine, the manager randomly selects 26 pistons and determines that the standard deviation is 0.0053 inch. Is there significant evidence for the manager to conclude that the standard deviation has decreased at the α=0.10 level of​ significance?

Hw 8.5 (4)

A simple random sample of 49 men from a normally distributed population results in a standard deviation of 7.4 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of men have a standard deviation equal to 10 beats per minute. Complete parts​ (a) through​ (d) below. d. State the conclusion. Reject H0​, because the​ P-value is less than or equal to the level of significance. There is sufficient evidence to warrant rejection of the claim that the standard deviation of​ men's pulse rates is equal to 10 beats per minute.

Hw 8.5 (5) a) H o = H o not = d) Reject less than or equal to sufficient

A simple random sample of pulse rates of 40 women from a normally distributed population results in a standard deviation of 11.9 beats per minute. The normal range of pulse rates of adults is typically given as 60 to 100 beats per minute. If the range rule of thumb is applied to that normal​ range, the result is a standard deviation of 10 beats per minute. Use the sample results with a 0.05 significance level to test the claim that pulse rates of women have a standard deviation equal to 10 beats per minute. Complete parts​ (a) through​ (d) below.

Hw 8.5 (6) H o = H o not = Fail to reject is not

A simple random sample of 29 filtered​ 100-mm cigarettes is obtained from a normally distributed​ population, and the tar content of each cigarette is measured. The sample has a standard deviation of 0.20 mg. Use a 0.05 significance level to test the claim that the tar content of filtered​ 100-mm cigarettes has a standard deviation different from 0.30 ​mg, which is the standard deviation for unfiltered​ king-size cigarettes. Complete parts​ (a) through​ (d) below.

Hw 8.5 (7) H o = H o not =

In an analysis investigating the usefulness of​ pennies, the cents portions of 80 randomly selected credit card charges from students are​ recorded, and they have a mean of 47.6 cents and a standard deviation of 31.9 cents. If the amounts from 0 cents to 99 cents are all equally​ likely, the mean is expected to be 49.5 cents and the population standard deviation is expected to be 28.866 cents. Use a 0.01 significance level to test the claim that the sample is from a population with a standard deviation equal to 28.866 cents. Complete parts​ (a) through​ (e) below.

Hw 8.5 (8) H o = H o not = d.) Do not reject is not e) No, because in that case the underlying population is not normally​ distributed, so the results of standard deviation hypothesis tests are not reliable.

Data show that men between the ages of 20 and 29 in a general population have a mean height of 69.3​ inches, with a standard deviation of 2.5 inches. A baseball analyst wonders whether the standard deviation of heights of​ major-league baseball players is less than 2.5 inches. The heights​ (in inches) of 20 randomly selected players are shown in the table. LOADING... Click the icon to view the data table.

Hw 8.5 (9) o = o <

What is the final​ conclusion?

There is not sufficient evidence to support the claim that less than 8​% of treated subjects experienced headaches. or There is sufficient evidence to support the claim that less than 11​% of treated subjects experienced headaches.

What is the final​ conclusion?

There is not sufficient evidence to warrant rejection of the claim that 32​% of adults have heard of the new electronic reader. or There is sufficient evidence to warrant rejection of the claim that 33​% of adults have heard of the new electronic reader.