A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?
ProTutor11Question 1 of 40 | 2.5 Points |
A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?
[removed] A. Greater than or equal to 0.10 | ||
[removed] B. Less than or equal to 0.05 | ||
[removed] C. Less than or equal to 0.10 | ||
[removed] D. Greater than or equal to 0.05 | ||
Question 2 of 40 | 2.5 Points | |
A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand. State the null hypothesis and the alternative hypothesis for a test of significance.
[removed] A. H_{0}: p = 0.001 H_{a}: p > 0.001 | ||
[removed] B. H_{0}: p = 0.001 H_{a}: p < 0.001 | ||
[removed] C. H_{0}: p > 0.001 H_{a}: p = 0.001 | ||
[removed] D. H_{0}: p < 0.001 H_{a}: p = 0.001 | ||
Question 3 of 40 | 2.5 Points | |
The owner of a football team claims that the average attendance at home games is over 4000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.
[removed] A. All games played by the team in question in which the attendance is over 4000 | ||
[removed] B. All future home games to be played by the team in question | ||
[removed] C. All home games played by the team in question | ||
[removed] D. None of the populations given are appropriate | ||
Question 4 of 40 | 2.5 Points | |
A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 35 such cases from court files and finds that months. Assume that the population standard deviation is 7 months. Test the null hypothesis that µ = 18.7 at the 0.05 significance level.
[removed] A. Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported. | ||
[removed] B. Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported. | ||
[removed] C. Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported. | ||
[removed] D. Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported. | ||
Question 5 of 40 | 2.5 Points | |
without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.
[removed] A. is less than 1 standard deviation above the claimed mean. | ||
[removed] B. is more than 4 standard deviations above the claimed mean. | ||
[removed] C. is less than 1 standard deviation above the claimed mean. | ||
[removed] D. is more than 4 standard deviations above the claimed mean. | ||
Question 6 of 40 | 2.5 Points | |
A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to rejection of the null hypothesis.
[removed] A. Conclusion: Support the claim that the mean is equal to 16 ounces. | ||
[removed] B. Conclusion: Support the claim that the mean is greater than 16 ounces. | ||
[removed] C. Conclusion: Support the claim that the mean is not equal to 16 ounces. | ||
[removed] D. Conclusion: Support the claim that the mean is less than 16 ounces. | ||
Question 7 of 40 | 2.5 Points | |
A study of a brand of “in the shell peanuts” gives the following results:
A significant event at the 0.01 level is a fan getting a bag with how many peanuts?
[removed] A. 30 peanuts | |
[removed] B. 25 or 30 peanuts | |
[removed] C. 25 or 55 peanuts | |
[removed] D. 25 peanuts |
Question 8 of 40 | 2.5 Points |
In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient evidence to conclude that the mean call duration, µ, is different from the 1990 mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that s = 4.8 minutes.
[removed] A. With a z of -1.2 there is sufficient evidence to conclude that the mean | |
[removed] B. With a P-value of 0.2302 there is not sufficient evidence to conclude | |
[removed] C. With a P-value of 0.2302 there is sufficient evidence to conclude that | |
[removed] D. With a z of –1.2 there is not sufficient evidence to conclude that the |
Question 9 of 40 | 2.5 Points |
If a fan purchased a bag with 30 peanuts, what is the lowest level at which this would be a significant event?
[removed] A. 0.05 | ||
[removed] B. 0.025 | ||
[removed] C. 0.01 | ||
[removed] D. It is not significant at any of the levels given | ||
Question 10 of 40 | 2.5 Points | |
In the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:
H_{0} : µ = 8.0 hours
H_{a} : µ > 8.0 hours
Explain the meaning of a Type II error.
[removed] A. Concluding that µ > 8.0 hours when in fact µ > 8.0 hours | ||
[removed] B. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ > | ||
[removed] C. Concluding that µ > 8.0 hours | ||
[removed] D. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ = 8.0 hours | ||
Question 11 of 40 | 2.5 Points | |
A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was greater than 9.4 minutes, which is the average for the state. Determine the conclusion of the hypothesis test assuming that the results of the sampling do not lead to rejection of the null hypothesis.
[removed] A. Conclusion: Support the claim that the mean is less than 9.4 minutes. | |||||||||||||
[removed] B. Conclusion: Support the claim that the mean is greater than 9.4 minutes. | |||||||||||||
[removed] C. Conclusion: Support the claim that the mean is equal to 9.4 minutes. | |||||||||||||
[removed] D. Conclusion: Do not support the claim that the mean is greater than 9.4 minutes.
A right-tailed test is conducted at the 5% significance level. Which of the following z-scores is the smallest one in absolute value that leads to rejection of the null hypothesis?
| |||||||||||||
Question 13 of 40 | 2.5 Points | ||||||||||||
A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 15.94 ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16-ounce bottles, µ, is less than 16.1 ounces? Perform the appropriate hypothesis test using a significance level of 0.10. Assume that s = 0.9 ounces.
[removed] A. The z of -1.49 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz. | ||
[removed] B. The z of -1.49 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz. | ||
[removed] C. The z of -0.1778 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz. | ||
[removed] D. The z of -0.1778 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz. | ||
Question 14 of 40 | 2.5 Points | |
A psychologist claims that more than 29 percent of the professional population suffers from problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in non-technical terms.
[removed] A. There is sufficient evidence to support the claim that the true proportion is less than 29 percent. | ||
[removed] B. There is not sufficient evidence to support the claim that the true proportion is greater than 29 percent. | ||
[removed] C. There is sufficient evidence to support the claim that the true proportion is equal to 29 percent. | ||
[removed] D. There is sufficient evidence to support the claim that the true proportion is greater than 29 percent. | ||
Question 15 of 40 | 2.5 Points | |
In 1990, the average duration of long-distance telephone calls originating in one town was 9.3 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.3 minutes. Formulate the null and alternative hypotheses for the study described.
[removed] A. H_{o}: µ = 9.3 minutes H_{a}: µ < 9.3 minutes | ||
[removed] B. H_{o}: µ = 9.3 minutes H_{a}: µ > 9.3 minutes | ||
[removed] C. H_{o}: µ = 9.3 minutes H_{a}: µ ¹9.3 minutes | ||
[removed] D. H_{o}: µ ¹9.3 minutes H_{a}: µ = 9.3 minutes | ||
Question 16 of 40 | 2.5 Points | |
A psychologist claims that more than 19 percent of the population suffers from professional problems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.
[removed] A. The population is all shy workers. | ||
[removed] B. The population cannot be identified from the description of the study. | ||
[removed] C. The population is all American workers. | ||
[removed] D. The population is all American professional workers (doctors, lawyers, CPA’s, and the like.. | ||
Question 17 of 40 | 2.5 Points | |
A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis?
[removed] A. 97.5% | ||
[removed] B. 5% | ||
[removed] C. 2.5% | ||
[removed] D. 95% | ||
Question 18 of 40 | 2.5 Points | |
A consumer advocacy group claims that the mean amount of juice in a 16
ounce bottled drink is not 16 ounces, as stated by the bottler.
Determine the null and alternative hypotheses for the test described.
[removed] A. H_{0}: µ = 16 ounces H_{a}: µ < 16 ounces | ||
[removed] B. H_{0}: µ ¹16 ounces H_{a}: µ = 16 ounces | ||
[removed] C. H_{0}: µ = 16 ounces H_{a}: µ > 16 ounces | ||
[removed] D. H_{0}: µ = 16 ounces H_{a}: µ ¹16 ounces | ||
Question 19 of 40 | 2.5 Points | |
The principal of a middle school claims that annual incomes of the families of the seventh-graders at his school vary more than the annual incomes of the families of the seventh-graders at a neighboring school, which have variation described by s= $13,700. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.
[removed] A. The current seventh graders at the principal’s school | ||
[removed] B. Seventh graders’ families at the school with a standard deviation of $13,700 | ||
[removed] C. All of the families of the class of seventh graders at the principal’s school | ||
[removed] D. All seventh graders’ families | ||
Question 20 of 40 | 2.5 Points | |
A two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis?
[removed] A. Greater than or equal to .010 | ||
[removed] B. Greater than or equal to 0.05 | ||
[removed] C. Less than or equal to 0.10 | ||
[removed] D. Less than or equal to 0.05 | ||
Question 21 of 40 | 2.5 Points | |
The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 25 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3?
[removed] A. Smaller. E increases as the square root of the sample size gets larger. | ||
[removed] B. Smaller. E decreases as the square root of the sample size gets larger. | ||
[removed] C. Larger. E decreases as the square root of the sample size gets larger. | ||
[removed] D. Larger. E increases as the square root of the sample size gets larger. | ||
Question 22 of 40 | 2.5 Points | |
The following data were analyzed using one-way analysis of variance.
A | B | C |
34 | 27 | 19 |
26 | 23 | 21 |
31 | 29 | 22 |
28 | 21 | 12 |
Which one of the following statements is correct?
[removed] A. The purpose of the analysis is to determine whether the groups A, B, and C are independent. | ||
[removed] B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal. | ||
[removed] C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal. | ||
[removed] D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal. | ||
Question 23 of 40 | 2.5 Points | |
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.
The critical value of X^{2 }for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X^{2} statistic is 4.613, state your conclusion about the relationship between gender and colorblindness.
[removed] A. Reject H_{0}. There is not sufficient evidence to support the claim that gender and colorblindness are related. | ||
[removed] B. Reject H_{0}. There is sufficient evidence to support the claim that gender and colorblindness are related. | ||
[removed] C. Do not Reject H_{0}. There is sufficient evidence to support the claim that gender and colorblindness are related. | ||
[removed] D. Do not Reject H_{0}. There is not sufficient evidence to support the claim that gender and colorblindness are related. | ||
Question 24 of 40 | 2.5 Points | |
Which of the following statements is true?
[removed] A. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population. | ||
[removed] B. The t distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population. | ||
[removed] C. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population. | ||
[removed] D. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population. | ||
Question 25 of 40 | 2.5 Points | |
The following data were analyzed using one-way analysis of variance.
A | B | C |
34 | 27 | 19 |
26 | 23 | 31 |
31 | 29 | 22 |
28 | 21 | 22 |
Which one of the following statements is correct?
[removed] A. The purpose of the analysis is to determine whether the groups A, B, and C are independent. | ||
[removed] B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal. | ||
[removed] C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal. | ||
[removed] D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal. | ||
Question 26 of 40 | 2.5 Points | |
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
| Colorblind | Not Colorblind | Total |
Male | 7 | 53 | 60 |
Female | 1 | 39 | 40 |
Total | 8 | 92 | 100 |
Find the value of the X^{2} statistic for the data above.
[removed] A. 1.325 | ||
[removed] B. 1.318 | ||
[removed] C. 1.286 | ||
[removed] D. 1.264 | ||
Question 27 of 40 | 2.5 Points | |
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.
The critical value of X^{2} for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X^{2 }statistic is 3.179, state your conclusion about the relationship between gender and colorblindness.
[removed] A. Do not reject H_{0}. | ||
[removed] B. Reject H_{0}. | ||
[removed] C. There is sufficient evidence to support the claim that gender and colorblindness are not related. | ||
[removed] D. There is not sufficient evidence to accept or reject H_{0}. | ||
Question 28 of 40 | 2.5 Points | |
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
| Colorblind | Not Colorblind | Total |
Male | 8 | 52 | 60 |
Female | 2 | 38 | 40 |
Total | 10 | 90 | 100 |
Find the value of the X^{2 }statistic for the data above.
[removed] A. 1.463 | ||
[removed] B. 1.852 | ||
[removed] C. 1.947 | ||
[removed] D. 1.949 | ||
Question 29 of 40 | 2.5 Points | |
A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4. What is the margin of error?
[removed] A. 4.6 | ||
[removed] B. 4.4 | ||
[removed] C. 4.2 | ||
[removed] D. 5.6 | ||
Question 30 of 40 | 2.5 Points | |
A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed.
Data from this test had a sample mean of 171.6 yards with a sample standard deviation of 2.4 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below.
| Area in one tail | |
| 0.025 | 0.05 |
| Area in two tails | |
Degrees of | 0.05 | 0.10 |
6 | 2.447 | 1.943 |
7 | 2.365 | 1.895 |
8 | 2.306 | 1.860 |
9 | 2.262 | 1.833 |
[removed] A. Accept the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 170 yards. | ||
[removed] B. Accept the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 170 yards. | ||
[removed] C. Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 170 yards. | ||
[removed] D. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 170 yards. | ||
Question 31 of 40 | 2.5 Points | |
A large test statistic F tells us that the sample means __________ the data within the individual samples, which would be unlikely if the population’s means really were equal (as the null hypothesis claims).
[removed] A. differ more than | ||
[removed] B. differ less than | ||
[removed] C. are equal to | ||
[removed] D. do not vary with | ||
Question 32 of 40 | 2.5 Points | |
A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 8, the sample mean x̄ is 22, and the sample standard deviation s is 6.3, what is the margin of error? Show your answer to 2 decimal places.
[removed] A. df = 7; E = 3.3445.38 = 5.6566 | ||
[removed] B. df = 8; E = 3.3445.38 = 5.6566 | ||
[removed] C. df = 6; E = 2.3656.38 = 5.769 | ||
[removed] D. df = 7; E = 2.3656.38 = 5.869 | ||
Question 33 of 40 | 2.5 Points | |
A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 8 times at the required speed.
Data from this test resulted in a sample mean of 163.2 yards with a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below to solve this problem.
| Area in one tail | |
| 0.025 | 0.05 |
| Area in two tails | |
Degrees of | 0.05 | 0.10 |
6 | 2.447 | 1.943 |
7 | 2.365 | 1.895 |
8 | 2.306 | 1.860 |
9 | 2.262 | 1.833 |
[removed] A. Do not reject the null hypothesis. The data do not provide sufficient | ||
[removed] B. Reject the null hypothesis. The data does provide sufficient evidence that the average distance is greater than 160 yards. | ||
[removed] C. t= 1.2334; Critical value = 1.992 | ||
[removed] D. Insufficient information to answer this question. | ||
Question 34 of 40 | 2.5 Points | |
A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 8 times at the required speed. State the null and alternative hypotheses for this test.
[removed] A. H_{0}: µ = 160; H_{a}: µ > 150 | ||
[removed] B. H_{0}: µ = 150; H_{a}: µ > 150 | ||
[removed] C. H_{0}: µ = 160; H_{a}: µ > 160 | ||
[removed] D. H_{0}: µ = 140; H_{a}: µ > 160 | ||
Question 35 of 40 | 2.5 Points | |
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
| Colorblind | Not Colorblind | Total |
Male | 7 | 53 | 60 |
Female | 1 | 39 | 40 |
Total | 8 | 92 | 100 |
If gender and colorblindness are independent, find the expected values corresponding to the male combinations of gender and colorblindness.
[removed] A. Colorblind Male 4.8; Not Colorblind Male 55.2 | ||
[removed] B. Colorblind Male 6.8; Not Colorblind Male 53.2 | ||
[removed] C. Colorblind Male 4.8; Not Colorblind Male 55.4 | ||
[removed] D. Colorblind Male 4.8; Not Colorblind Male 56.2 | ||
Question 36 of 40 | 2.5 Points | |
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
| Colorblind | Not Colorblind | Total |
Male | 8 | 52 | 60 |
Female | 2 | 38 | 40 |
Total | 10 | 90 | 100 |
State the null and alternative hypothesis for the test associated with this data.
[removed] A. H_{0}: Colorblindness and gender are dependent characteristics. | ||
[removed] B. H_{0}: Colorblindness and gender are dependent characteristics. | ||
[removed] C. H_{0}: Colorblindness and gender are independent characteristics. | ||
[removed] D. H_{0}: Colorblindness and gender are independent characteristics. | ||
Question 37 of 40 | 2.5 Points | |
A golfer wished to find a ball that would travel more than 180 yards when hit with his 5-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 7 times at the required speed. State the null and alternative hypotheses for this test.
[removed] A. H_{0}: µ = 180; H_{a}: µ > 180 | ||
[removed] B. H_{0}: µ > 180; H_{a}: µ > 180 | ||
[removed] C. H_{0}: µ < 180; H_{a}: µ > 180 | ||
[removed] D. H_{0}: µ = 180; H_{a}: µ < 180 | ||
Question 38 of 40 | 2.5 Points | |
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
| Colorblind | Not Colorblind | Total |
Male | 7 | 53 | 60 |
Female | 1 | 39 | 40 |
Total | 8 | 92 | 100 |
If gender and colorblindness are independent, find the expected values corresponding to the female combinations of gender and colorblindness.
[removed] A. Colorblind Female 4.8; Not Colorblind Female 55.2 | ||
[removed] B. Colorblind Female 3.2; Not Colorblind Female 36.8 | ||
[removed] C. Colorblind Female 4.8; Not Colorblind Female 35.2 | ||
[removed] D. Colorblind Female 3.8; Not Colorblind Female 36.2 | ||
Question 39 of 40 | 2.5 Points | |
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.
The critical value of X^{2} for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X^{2} statistic is 3.427, state your conclusion about the relationship between gender and colorblindness.
[removed] A. Do not reject H_{0}. There is not sufficient evidence to support the claim that gender and colorblindness are related. | ||
[removed] B. Do not reject H_{0}. There is sufficient evidence to support the claim that gender and colorblindness are related. | ||
[removed] C. Reject H_{0}. There is not sufficient evidence to support the claim that gender and colorblindness are related. | ||
[removed] D. Reject H_{0}. There is sufficient evidence to support the claim that gender and colorblindness are related. | ||
Question 40 of 40 | 2.5 Points | |
A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 25.2. What is the margin of error?
[removed] A. 3.9 | |
[removed] B. 4.8 | |
[removed] C. 4.9 | |
[removed] D. 3.7 |
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