Stat 8.3 HW

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 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. 782, 822, 1280, 690, 602, 606 Identify the test statistic.

-1.965

Use the pulse rates in beats per minute​ (bpm) of a random sample of adult females listed in the data set available below to test the claim that the mean is less than 74 bpm. Use a 0.01 significance level. Determine the test statistic.

-1.44

Use the pulse rates in beats per minute​ (bpm) of a random sample of adult females listed in the data set available below to test the claim that the mean is less than 74 bpm. Use a 0.01 significance level. Determine the​ P-value.

0.078

Twelve different video games showing violence were observed. The duration times of violence were​ recorded, with the times​ (seconds) listed below. Assume that these sample data are used with a 0.10 significance level in a test of the claim that the population mean is greater than 90 sec. If we want to construct a confidence interval to be used for testing that​ claim, what confidence level should be used for a confidence​ interval? 91, 14, 612, 47, 0, 58, 190, 44, 172, 0, 2, 53

80%

Listed below are the lead concentrations in μ​g/g measured in different traditional medicines. Use a 0.10 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 μ​g/g. Assume that the sample is a simple random sample. 19, 5, 9.5, 10, 17, 3, 20, 4, 4.5, 4 Determine the test statistic.

-2.07

A data set includes data from student evaluations of courses. The summary statistics are n=85​, x=4.07​, s=0.67. Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25. Determine the test statistic.

-2.48

The display provided from technology available below results from using data for a smartphone​ carrier's data speeds at airports to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. T-Test μ<4.00 t=−3.383863 p=0.000707 x=3.34 Sx=1.379165 n=50 Identify the test statistic.

-3.38

The display provided from technology available below results from using data for a smartphone​ carrier's data speeds at airports to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. T-Test μ<4.00 t=−3.383863 p=0.000707 x=3.34 Sx=1.379165 n=50 Identify the​ P-value.

0.001

A data set includes data from student evaluations of courses. The summary statistics are n=85​, x=4.07​, s=0.67. Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25. Determine the​ P-value.

0.015

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 0.05 significance level. Identify the​ P-value.

0.016

Listed below are the lead concentrations in μ​g/g measured in different traditional medicines. Use a 0.10 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 μ​g/g. Assume that the sample is a simple random sample. 19, 5, 9.5, 10, 17, 3, 20, 4, 4.5, 4 Determine the​ P-value.

0.034

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. 81, 93, 49, 77, 48, 31, 69, 71, 72, 58, 72, 77, 105, 101, 73 Determine the​ P-value.

0.037

A data set includes data from 500 random tornadoes. The display from technology available below results from using the tornado lengths​ (miles) to test the claim that the mean tornado length is greater than 2.4 miles. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. Identify the​ P-value.

0.039

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 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. 782, 822, 1280, 690, 602, 606 Identify the​ P-value.

0.0533

A data set lists earthquake depths. The summary statistics are n=400​, x=6.44 km, s=4.78 km. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 6.00. Assume that a simple random sample has been selected. Determine the​ P-value.

0.067

In a test of the effectiveness of garlic for lowering​ cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes​ (before minus​ after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 0.2 and a standard deviation of 17.5. Use a 0.05 significance level to test the claim that with garlic​ treatment, the mean change in LDL cholesterol is greater than 0. Determine the test statistic.

0.07

In a test of the effectiveness of garlic for lowering​ cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes​ (before minus​ after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 0.2 and a standard deviation of 17.5. Use a 0.05 significance level to test the claim that with garlic​ treatment, the mean change in LDL cholesterol is greater than 0. Determine the​ P-value.

0.472

A data set includes data from 500 random tornadoes. The display from technology available below results from using the tornado lengths​ (miles) to test the claim that the mean tornado length is greater than 2.4 miles. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. Identify the test statistic.

1.76

A data set lists earthquake depths. The summary statistics are n=400​, x=6.44 km, s=4.78 km. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 6.00. Assume that a simple random sample has been selected. Determine the test statistic.

1.84

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. 81, 93, 49, 77, 48, 31, 69, 71, 72, 58, 72, 77, 105, 101, 73 Determine the test statistic.

2.31

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 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. 782, 822, 1280, 690, 602, 606 State the final conclusion that addresses the original claim.

Fail to reject H0. There is insufficient evidence to support the claim that the sample is from a population with a mean less than 1000 hic.

In a test of the effectiveness of garlic for lowering​ cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes​ (before minus​ after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 0.2 and a standard deviation of 17.5. Use a 0.05 significance level to test the claim that with garlic​ treatment, the mean change in LDL cholesterol is greater than 0. State the final conclusion that addresses the original claim.

Fail to reject H0. There is not sufficient evidence to conclude that the mean of the population of changes is greater than 0.

A data set lists earthquake depths. The summary statistics are n=400​, x=6.44 km, s=4.78 km. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 6.00. Assume that a simple random sample has been selected. State the final conclusion that addresses the original claim.

Fail to reject H0. There is not sufficient evidence to conclude that the mean of the population of earthquake depths is 6.00 km is not correct.

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. 81, 93, 49, 77, 48, 31, 69, 71, 72, 58, 72, 77, 105, 101, 73 State the final conclusion that addresses the original claim.

Fail to reject H0. There is not sufficient evidence to conclude that the mean of the population of estimates is 60 seconds is not correct. It appears ​that, as a​group, the students are reasonably good at estimating one minute.

Use the pulse rates in beats per minute​ (bpm) of a random sample of adult females listed in the data set available below to test the claim that the mean is less than 74 bpm. Use a 0.01 significance level. State the final conclusion that addresses the original claim.

Fail to reject H0. There is not sufficient evidence to conclude that the mean of the population of pulse rates for adult females is less than 74 bpm

The display provided from technology available below results from using data for a smartphone​ carrier's data speeds at airports to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. T-Test μ<4.00 t=−3.383863 p=0.000707 x=3.34 Sx=1.379165 n=50 Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

H0: μ=4.00 Mbps H1​: μ<4.00 Mbps

In a test of the effectiveness of garlic for lowering​ cholesterol, 36 subjects were treated with raw garlic. Cholesterol levels were measured before and after the treatment. The changes​ (before minus​ after) in their levels of LDL cholesterol​ (in mg/dL) have a mean of 0.2 and a standard deviation of 17.5. Use a 0.05 significance level to test the claim that with garlic​ treatment, the mean change in LDL cholesterol is greater than 0. What are the null and alternative​ hypotheses?

H0​: μ=0 mg/dL H1​: μ>0 mg/d

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 0.05 significance level. What are the​ hypotheses?

H0​: μ=1.00 in magnitude H1​: μ>1.00 in magnitude

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 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. 782, 822, 1280, 690, 602, 606 What are the​ hypotheses?

H0​: μ=1000 hic H1​: μ<1000 hic

Listed below are the lead concentrations in μ​g/g measured in different traditional medicines. Use a 0.10 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 μ​g/g. Assume that the sample is a simple random sample. 19, 5, 9.5, 10, 17, 3, 20, 4, 4.5, 4 Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

H0​: μ=14 μ​g/g H1​: μ<14 μ​g/g

A data set includes data from 500 random tornadoes. The display from technology available below results from using the tornado lengths​ (miles) to test the claim that the mean tornado length is greater than 2.4 miles. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

H0​: μ=2.4 miles H1​: μ>2.4 miles

A data set includes data from student evaluations of courses. The summary statistics are n=85​, x=4.07​, s=0.67. Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25. What are the null and alternative​ hypotheses?

H0​: μ=4.25 H1​: μ≠4.25

A data set lists earthquake depths. The summary statistics are n=400​, x=6.44 km, s=4.78 km. Use a 0.01 significance level to test the claim of a seismologist that these earthquakes are from a population with a mean equal to 6.00. Assume that a simple random sample has been selected. What are the null and alternative​ hypotheses?

H0​: μ=6.00 km H1​: μ≠6.00 km

A group of students estimated the length of one minute without reference to a watch or​ clock, and the times​ (seconds) are listed below. Use a 0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. 81, 93, 49, 77, 48, 31, 69, 71, 72, 58, 72, 77, 105, 101, 73 Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

H0​: μ=60 seconds H1​: μ≠60 seconds

Use the pulse rates in beats per minute​ (bpm) of a random sample of adult females listed in the data set available below to test the claim that the mean is less than 74 bpm. Use a 0.01 significance level. Assuming all conditions for conducting a hypothesis test are​ met, what are the null and alternative​ hypotheses?

H0​: μ=74 bpm H1​: μ<74 bpm

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

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.

Use technology to find the​ P-value for the hypothesis test described below. The claim is that for 12 AM body​ temperatures, the mean is μ>98.6°F. The sample size is n=3 and the test statistic is t=1.352

P-value = 0.154

Listed below are the lead concentrations in μ​g/g measured in different traditional medicines. Use a 0.10 significance level to test the claim that the mean lead concentration for all such medicines is less than 14 μ​g/g. Assume that the sample is a simple random sample. 19, 5, 9.5, 10, 17, 3, 20, 4, 4.5, 4 State the final conclusion that addresses the original claim.

Reject H0. There is sufficient evidence to conclude that the mean lead concentration for all such medicines is less than 14 μ​g/g.

A data set includes data from student evaluations of courses. The summary statistics are n=85​, x=4.07​, s=0.67. Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25. State the final conclusion that addresses the original claim.

Reject H0. There is sufficient evidence to conclude that the mean of the population of student course evaluations is equal to 4.25 is not correct.

A data set includes data from 500 random tornadoes. The display from technology available below results from using the tornado lengths​ (miles) to test the claim that the mean tornado length is greater than 2.4 miles. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. State the final conclusion that addresses the original claim.

Reject H0. There is sufficient evidence to support the claim that the mean tornado length is greater than 2.4 miles

The display provided from technology available below results from using data for a smartphone​ carrier's data speeds at airports to test the claim that they are from a population having a mean less than 4.00 Mbps. Conduct the hypothesis test using these results. Use a 0.05 significance level. Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. T-Test μ<4.00 t=−3.383863 p=0.000707 x=3.34 Sx=1.379165 n=50 State the final conclusion that addresses the original claim.

Reject H0. There is sufficient evidence to support the claim that the sample is from a population with a mean less than 4.00 Mbps.

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 0.05 significance level. Conclusion for the test

Reject H0. There is sufficient evidence to conclude that the population of earthquakes has a mean magnitude greater than 1.00

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

The Student t distribution has a mean of t=0 and a standard deviation of s=1.

For a hypothesis test of the claim that the mean amount of sleep for adults is less than 9 hours, technology output shows that the hypothesis test has power of 0.4056 of supporting the claim that μ<9 hours of sleep when the actual population mean is 8.0 hours of sleep. Interpret this value of the​ power, then identify the value of β and interpret that value. Interpret this value of the power.

The chance of recognizing that μ<9 hours is not very high when in reality μ=8.0 hours.

Twelve different video games showing violence were observed. The duration times of violence were​ recorded, with the times​ (seconds) listed below. Assume that these sample data are used with a 0.10 significance level in a test of the claim that the population mean is greater than 90 sec. 91, 14, 612, 47, 0, 58, 190, 44, 172, 0, 2, 53 If the confidence interval is found to be 18.2 sec<μ<195.6 ​sec, what should we conclude about the​ claim?

The given confidence interval contains the value of 90 sec, so there is not sufficient evidence to support the claim that the mean is greater than 90 sec.

Eleven different video games showing violence were observed. The duration times of violence (in seconds) were recorded. When using this sample for a t test of the claim that the population mean is greater than 94 sec, what does df​denote, and what is its​value?

The number of degrees of freedom, 10

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

The population​ mean, μ​, is equal to 1.

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

The sample​ mean, x is greater than 30.

For a hypothesis test of the claim that the mean amount of sleep for adults is less than 9 hours, technology output shows that the hypothesis test has power of 0.4056 of supporting the claim that μ<9 hours of sleep when the actual population mean is 8.0 hours of sleep. Interpret this value of the​ power, then identify the value of β and interpret that value. Identify the value of β and interpret that value. Select the correct choice below and fill in the answer box to complete your choice.

The value β=0.5944 indicates that there is a greater than​ 50% chance of failing to recognize that μ<9 hours when in reality μ=8.0 hours.

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 0.01 significance level to test the claim that the sample is from a population with a mean less than 1000 hic. 782, 822, 1280, 690, 602, 606 What do the results suggest about the child booster seats meeting the specified​ requirement?

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.

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

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 strategy for finding​ P-values with the Student t​ distribution?

Use the table in the book to find the​ P-value rounded to at least 4 decimal places.

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 0.05 significance level. Identify the test statistic.

t = 2.22