Question
MATH221 Statistics for Decision Making
Week 6 Homework  
Question 1A consumer analyst reports that the mean life of a certain type of alkaline battery is more than 63 months. Write the null and alternative hypotheses and note which is the claim.
Homework Help:
6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)
  Ho: μ ≤ 63, Ha: μ < 63 (claim)   Ho: μ = 63 (claim), Ha: μ ≥ 63   Ho: μ ≤ 63, Ha: μ > 63 (claim)
  Ho: μ > 63 (claim), Ha: μ ≤ 63
Question 2A business claims that the mean time that customers wait for service is at most 5.9 minutes. Write the null and alternative hypotheses and note which is the claim.
Homework Help:
6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)
  Ho: μ > 5.9 (claim), Ha: μ > 5.9
  Ho: μ ≥ 5.9, Ha: μ ≤ 5.9 (claim)
  Ho: μ ≤ 5.9 (claim), Ha: μ > 5.9
  Ho: μ > 5.9, Ha: μ ≤ 5.9 (claim)
Question 3An amusement park claims that the average daily attendance is at least 20,000. Write the null and alternative hypotheses and note which is the claim.
Homework Help:
6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)
  Ho: μ > 20000 (claim), Ha: μ = 20000
  Ho: μ ≤ 20000, Ha: μ > 20000 (claim)
  Ho: μ ≥ 20000 (claim), Ha: μ < 20000   Ho: μ = 20000, Ha: μ ≤ 20000 (claim)  Question 4A transportation organization claims that the mean travel time between two destinations is about 23 minutes. Write the null and alternative hypotheses and note which is the claim. Homework Help: 6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)   Ho: μ > 23, Ha: μ ≤ 23 (claim)
  Ho: μ ≠ 23, Ha: μ = 23 (claim)
  Ho: μ = 23 (claim), Ha: μ ≠ 23
  Ho: μ = 23 (claim), Ha: μ ≤ 23
Question 5If the null hypothesis is not rejected when it is false, this is called __________.
Homework Help:
6DB. Type I and type II errors (Links to an external site.) (DOCX)
  the Empirical Rule
  an alternative hypothesis
  a type I error
  a type II error
Question 6A scientist claims that the mean gestation period for a fox is more than 48.9 weeks. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted?
Homework Help:
6VA. Overview of hypothesis testing: hypotheses, conclusions, implications for claim (Links to an external site.)(4:32)
6DC. Connecting reject/fail to reject decision and implication for claim (Links to an external site.) (DOCX)
  There is enough evidence to support the scientist’s claim that the gestation period is more than 48.9 weeks
  There is not enough evidence to support the scientist’s claim that the gestation period is 48.9 weeks
  The evidence indicates that the gestation period is less than 48.9 weeks
  There is enough evidence to support the scientist’s claim that the gestation period is 48.9 weeks
Question 7A marketing organization claims that less than 15% of its employees are paid minimum wage. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted?
Homework Help:
6VA. Overview of hypothesis testing: hypotheses, conclusions, implications for claim (Links to an external site.)(4:32)
6DC. Connecting reject/fail to reject decision and implication for claim (Links to an external site.) (DOCX)
  There is not sufficient evidence to support the claim that less than 15% of the employees are paid minimum wage
  There is sufficient evidence to support the claim that less than 15% of the employees are paid minimum wage
  There is sufficient evidence to support the claim that 15% of the employees are paid minimum wage
  There is not sufficient evidence to support the claim that more than 15% of the employees are paid minimum wage
Question 8A sprinkler manufacturer claims that the average activating temperatures is at least 131 degrees. To test this claim, you randomly select a sample of 32 systems and find the mean activation temperature to be 133 degrees. Assume the population standard deviation is 3.3 degrees. Find the standardized test statistic and the corresponding p-value.
Homework Help:
6VB. Hypothesis testing with spreadsheet to find test statistic and p-value (Links to an external site.) (2:58)
  z-test statistic = -3.43, p-value = 0.0003
  z-test statistic = 3.43, p-value = 0.0006
  z-test statistic = -3.43, p-value = 0.0006
  z-test statistic = 3.43, p-value = 0.0003
Question 9A consumer group claims that the mean acceleration time from 0 to 60 miles per hour for a sedan is 7.9 seconds. A random sample of 33 sedans has a mean acceleration time from 0 to 60 miles per hour of 7.6 seconds. Assume the population standard deviation is 2.3 seconds. Find the standardized test statistic and the corresponding p-value.
Homework Help:
6VB. Hypothesis testing with spreadsheet to find test statistic and p-value (Links to an external site.) (2:58)
  z-test statistic = -0.749, p-value = 0.227
  z-test statistic = -0.749, p-value = 0.454
  z-test statistic = -0.749, p-value = 0.227
  z-test statistic = 0.749, p-value = 0.454
Question 10A consumer research organization states that the mean caffeine content per 12-ounce bottle of a population of caffeinated soft drinks is 37.8 milligrams. You find a random sample of 48 12-ounce bottles of caffeinated soft drinks that has a mean caffeine content of 35.2 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, do you support or reject the organization’s claim using the test statistic?
Homework Help:
6VC. Determining when to reject or fail to reject, both methods (Links to an external site.) (4:00)
6VE. Second sample hypothesis testing from word problem to implications for claim, with test statistic (Links to an external site.) (3:26)
6DD. Determining when to reject or fail to reject, both methods (Links to an external site.) (DOCX)
  Claim is null, fail to reject the null and support claim as test statistic (-1.44) is not in the rejection region defined by the critical value (-1.96)
  Claim is alternative, fail to reject the null and support claim as test statistic (-1.44) is not in the rejection region defined by the critical value (-1.64)
  Claim is alternative, reject the null and reject claim as test statistic (-1.44) is in the rejection region defined by the critical value (-1.64)
  Claim is null, reject the null and reject claim as test statistic (-1.44) is in the rejection region defined by the critical value (-1.96)
Question 11A computer manufacturer estimates that its cheapest screens will last less than 2.8 years. A random sample of 61 of these screens has a mean life of 2.6 years. The population is normally distributed with a population standard deviation of 0.88 years. At α=0.02, what type of test is this and can you support the organization’s claim using the test statistic?
Homework Help:
6VC. Determining when to reject or fail to reject, both methods (Links to an external site.) (4:00)
6VE. Second sample hypothesis testing from word problem to implications for claim, with test statistic (Links to an external site.) (3:26)
6DD. Determining when to reject or fail to reject, both methods (Links to an external site.) (DOCX)
  Claim is null, fail to reject the null and cannot support claim as test statistic (-1.78) is not in the rejection region defined by the critical value (-2.05)
  Claim is alternative, reject the null and support claim as test statistic (-1.78) is not in the rejection region defined by the critical value (-2.05)
  Claim is alternative, fail to reject the null and cannot support claim as test statistic (-1.78) is not in the rejection region defined by the critical value (-2.05)
  Claim is null, reject the null and cannot support claim as test statistic (-1.78) is not in the rejection region defined by the critical value (-2.05)
Question 12A pharmaceutical company claims that the average cold lasts an average of 8.4 days. They are using this as a basis to test new medicines designed to shorten the length of colds. A random sample of 106 people with colds, finds that on average their colds last 8.5 days. The population is normally distributed with a population standard deviation of 0.9 days. At α=0.02, what type of test is this and can you support the company’s claim using the p-value?
Homework Help:
6VC. Determining when to reject or fail to reject, both methods (Links to an external site.) (4:00)
6VE. Second sample hypothesis testing from word problem to implications for claim, with test statistic (Links to an external site.) (3:26)
6DD. Determining when to reject or fail to reject, both methods (Links to an external site.) (DOCX)
  Claim is null, fail to reject the null and support claim as the p-value (0.253) is greater than alpha (0.02)
  Claim is null, reject the null and cannot support claim as the p-value (0.253) is less than alpha (0.02)
  Claim is alternative, reject the null and support claim as the p-value (0.126) is greater than alpha (0.02)
  Claim is alternative, fail to reject the null and support claim as the p-value (0.126) is less than alpha (0.02)
Question 13A business receives supplies of copper tubing where the supplier has said that the average length is 26.70 inches so that they will fit into the business’ machines. A random sample of 48 copper tubes finds they have an average length of 26.77 inches. The population standard deviation is assumed to be 0.20 inches. At α=0.05, should the business reject the supplier’s claim?
Homework Help:
6VD. Sample hypothesis testing from word problem to implications for claim, with p-values (Links to an external site.) (3:15)
  Yes, since pα, we fail to reject the null and the null is the claim
  Yes, since p>α, we fail to reject the null and the null is the claim
  No, since p>α, we reject the null and the null is the claim
Question 14The company’s cleaning service states that they spend more than 46 minutes each time the cleaning service is there. The company times the length of 37 randomly selected cleaning visits and finds the average is 46.5 minutes. Assuming a population standard deviation of 5.2 minutes, can the company support the cleaning service’s claim at α=0.10?
Homework Help:
6VD. Sample hypothesis testing from word problem to implications for claim, with p-values (Links to an external site.) (3:15)
  Yes, since pα, we fail to reject the null. The claim is the alternative, so the claim is not supported
Question 15A customer service phone line claims that the wait times before a call is answered by a service representative is less than 3.3 minutes. In a random sample of 62 calls, the average wait time before a representative answers is 3.26 minutes. The population standard deviation is assumed to be 0.29 minutes. Can the claim be supported at α=0.08?
Homework Help:
6VE. Second sample hypothesis testing from word problem to implications for claim, with test statistic (Links to an external site.) (3:26)
  No, since test statistic is not in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is not supported
  Yes, since test statistic is in the rejection region defined by the critical value, reject the null. The claim is the alternative, so the claim is supported
  No, since test statistic is not in the rejection region defined by the critical value, fail to reject the null. The claim is the alternative, so the claim is not supported
  Yes, since test statistic is in the rejection region defined by the critical value, fail to reject the null. The claim is the alternative, so the claim is supported
Question 16In a hypothesis test, the claim is μ≤40 while the sample of 27 has a mean of 41 and a sample standard deviation of 5.9 from a normally distributed data set. In this hypothesis test, would a z test statistic be used or a t test statistic and why?
Homework Help:
6DE. When to use z and when to use t distribution (Links to an external site.) (DOCX)
  t test statistic would be used as the standard deviation is less than 10
  z test statistic would be used as the population standard deviation is known
  t test statistic would be used as the data are normally distributed with an unknown population standard deviation
  z test statistic would be used as the mean is greater than 30
Question 17A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sample of eight professors finds that the mean time in their offices is 6.2 hours each week. With a sample standard deviation of 0.49 hours from a normally distributed data set, can the university’s claim be supported at α=0.05?
Homework Help:
6VE. Second sample hypothesis testing from word problem to implications for claim, with test statistic (Links to an external site.) (3:26)
6VF. Third sample hypothesis testing from word problem to implications for claim, with t distribution, test statistic and p-value (Links to an external site.) (4:03)
6DE. When to use z and when to use t distribution (Links to an external site.) (DOCX)
  No, since the test statistic is in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported
  No, since the test statistic is not in the rejection region defined by the critical value, the null is rejected. The claim is the null, so is not supported
  Yes, since the test statistic is not in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported
  Yes, since the test statistic is in the rejection region defined by the critical value, the null is not rejected. The claim is the null, so is supported
Question 18A credit reporting agency claims that the mean credit card debt in a town is greater than $3500. A random sample of the credit card debt of 28 residents in that town has a mean credit card debt of $3590 and a standard deviation of $391. At α=0.10, can the credit agency’s claim be supported, assuming this is a normally distributed data set?
Homework Help:
6VD. Sample hypothesis testing from word problem to implications for claim, with p-values (Links to an external site.) (3:15)
6VF. Third sample hypothesis testing from word problem to implications for claim, with t distribution, test statistic and p-value (Links to an external site.) (4:03)
6DE. When to use z and when to use t distribution (Links to an external site.) (DOCX)
  No, since p of 0.12 is greater than 0.10, reject the null. Claim is null, so is not supported
  Yes, since p-value of 0.12 is greater than 0.10, fail to reject the null. Claim is null, so is supported
  Yes, since p-value of 0.12 is less than 0.55, reject the null. Claim is alternative, so is supported
  No, since p-value of 0.12 is greater than 0.10, fail to reject the null. Claim is alternative, so is not supported
Question 19A car company claims that its cars achieve an average gas mileage of at least 26 miles per gallon. A random sample of eight cars form this company have an average gas mileage of 25.6 miles per gallon and a standard deviation of 1 mile per gallon. At α=0.06, can the company’s claim be supported, assuming this is a normally distributed data set?
Homework Help:
6VE. Second sample hypothesis testing from word problem to implications for claim, with test statistic (Links to an external site.) (3:26)
6VF. Third sample hypothesis testing from word problem to implications for claim, with t distribution, test statistic and p-value (Links to an external site.) (4:03)
6DE. When to use z and when to use t distribution (Links to an external site.) (DOCX)
  No, since the test statistic of -1.13 is close to the critical value of -1.24, the null is not rejected. The claim is the null, so is supported
  No, since the test statistic of -1.13 is in the rejection region defined by the critical value of -1.77, the null is rejected. The claim is the null, so is not supported
  Yes, since the test statistic of -1.13 is not in the rejection region defined by the critical value of -1.77, the null is not rejected. The claim is the null, so is supported
  Yes, since the test statistic of -1.13 is not in the rejection region defined by the critical value of -1.55, the null is rejected. The claim is the null, so is supported
 Question 20A researcher wants to determine if extra homework problems help 8th grade students learn algebra. An 8th grade class is divided into pairs and one student from each pair has extra homework problems and the other in the pair does not. After 2 weeks, the entire class takes an algebra test and the results of the two groups are compared. To be a valid matched pair test, what should the researcher consider in creating the two groups?
Homework Help:
6DF. Paired sample experiment structure requirements and assumptions (Links to an external site.) (DOCX)
  That each pair of students has similar ages at the time of the testing
  That the group without extra homework problems receives different instruction
  That each pair of students has similar IQs or abilities in mathematics
  That the group with the extra homework problems has fewer after school activities