MATH 221 Week 6 Quiz 2

MATH 221 Week 6 Quiz 2 | Devry University

Week 6: Homework

Question 1

A consumer analyst reports that the mean life of a certain type of alkaline battery is no more than 36 months. Write the null and alternative hypotheses and note which is the claim.

6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)  

·         Ho: μ = 36, Ha: μ > 36 (claim)  

·         Ho: μ = 36 (claim), Ha: μ > 36  

·         Ho: μ > 36, Ha: μ = 36 (claim)  

·         Ho: μ = 36 (claim), Ha: μ ≥ 36

 

 Question 2

An 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.

6DA. Theory and basics of writing hypotheses (Links to an external site.) (DOCX)  

·         Ho: μ = 20000, Ha: μ > 20000 (claim)  

·         Ho: μ = 20000, Ha: μ ≤ 20000 (claim)  

·         Ho: μ > 20000 (claim), Ha: μ = 20000  

·         Ho: μ = 20000 (claim), Ha: μ < 20000

 

Question 3

If the null hypothesis is rejected when it is false, this is called __________.

6DB. Type I and type II errors (Links to an external site.) (DOCX)  

·         a type II error    

·         the correct decision  

·         an alternative hypothesis  

·         a type I error

 

 Question 4

A scientist claims that the mean gestation period for a fox is less than 50.3 weeks. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted?

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 less than 50.3 weeks  

·         There is not enough evidence to support the scientist’s claim that the gestation period is 50.3 weeks  

·         There is not enough evidence to support the scientist’s claim that the gestation period is more than 50.3 weeks  

·         The evidence indicates that the gestation period is more than 50.3 weeks

 

 Question 5

A marketing organization claims that 10% 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?

·         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 sufficient evidence to support the claim that 10% of the employees are paid minimum wage  

·         There is not sufficient evidence to support the claim that less than 10% of the employees are paid minimum wage    

·         There is not sufficient evidence to support the claim that 10% of the employees are paid minimum wage

 

  Question 6

A sprinkler manufacturer claims that the average activating temperatures is at least 135 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.

6VB. Hypothesis testing with spreadsheet to find test statistic and p-value (Links to an external site.) (1:57) 

·         z-test statistic = -3.43, p-value = 0.0006  

·         z-test statistic = 3.43, p-value = 0.0003   

·         z-test statistic = -3.43, p-value = 0.0003  

·         z-test statistic = 3.43, p-value = 0.0006

 

 Question 7

A 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 32.8 milligrams. Assume the population standard deviation is 12.5 milligrams. At α=0.05, what type of test is this and can you reject the organization’s claim using the p-value?

Homework Help:

6VC. Hypothesis test example, population standard deviation (Links to an external site.) (3:35)

6DD. Determining when to reject or fail to reject, both methods (Links to an external site.) (DOCX)

  

·         The p-value is 0.0056, it is less than α=0.05, we reject the null, the null is claim, the claim is not supported. 

·         The p-value is 0.003, it is less than α=0.05, we reject the null, the null is claim, the claim is not supported.  

·         The p-value is 0.06, it is greater than α=0.05, we fail to reject the null, the null is claim, the claim is supported.  

·         The p-value is 0.997, it is greater than α=0.05, we fail to reject the null, the null is claim, the claim is supported.

 

 Question 8

A computer manufacturer estimates that its cheapest screens will last less than 2.6 years. A random sample of 61 of these screens has a mean life of 2.4 years. The population is normally distributed with a population standard deviation of 0.88 years. At α=0.02, can you support the organization's claim?

6VC. Hypothesis test example, population standard deviation (Links to an external site.) (3:35)

6DD. Determining when to reject or fail to reject, both methods (Links to an external site.) (DOCX)  

·         No, the claim is not supported. The p-value is 0.001, it is less than α = 0.02, we reject the null. The null is the claim and is not supported.    

·         Yes, the claim can be supported. The p-value is 0.04, it is greater than α = 0.02, we fail to reject the null, the claim is the null and is supported.  

·         No, the claim is not supported. The p-value is 0.96, it is less than α = 0.02, we reject the null. The null is the claim and is not supported.    

·         Yes, the claim can be supported. The p-value is 0.08, it is greater than α = 0.02, we fail to reject the null, the claim is the null and is supported.

 

 Question 9

A 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 26.75 inches. The population standard deviation is assumed to be 0.15 inches. At α=0.05, should the business reject the supplier’s claim?

6VC. Hypothesis test example, population standard deviation (Links to an external site.) (3:35)  

·         No, since p>α, we reject the null and the null is the claim 

·         Yes, since p<α, we reject the null and the null is the claim 

·         No, since p>α, 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

 

Question 10

The 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 48.2 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:

6VC. Hypothesis test example, population standard deviation (Links to an external site.) (3:35)  

·         Yes, since p<α, we reject the null. The claim is the alternative, so the claim is supported 

·         No, since p>α, we fail to reject the null. The claim is the alternative, so the claim is not supported  

·         No, since p>α, we reject the null. The claim is the alternative, so the claim is supported  

·         Yes, since p<α, we fail to reject the null. The claim is the alternative, so the claim is not supported

 

Question 11

A 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 3.24 minutes with a standard deviation of 0.40 minutes. Can the claim be supported at α=0.08?

6VD. Hypothesis test example, sample standard deviation (Links to an external site.) (5:12)

  

·         Yes, since the p-value (0.12) is less than alpha, reject the null. The claim is the alternative, so the claim is supported

 

·         No, since the p-value (0.12) is less than alpha, fail to reject the null. The claim is the alternative, so the claim is not supported  

·         No, since the p-value (0.12) greater than alpha, fail to reject the null. The claim is the alternative, so the claim is not supported  

·         Yes, since the p-value (0.24) is greater than alpha, reject the null. The claim is the alternative, so the claim is supported

 

 Question 12

In 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?

6DE. When to use z and when to use t distribution (Links to an external site.) (DOCX)  

·         z test statistic would be used as the mean is greater than 30    

·         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 population standard deviation is known  

·         t test statistic would be used as the standard deviation is less than 10

 

 Question 13

A 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:

6VD. Hypothesis test example, sample standard deviation (Links to an external site.) (5:12)

6DE. When to use z and when to use t distribution (Links to an external site.) (DOCX)  

·         Yes, since the p-value is less than alpha, the null is not rejected. The claim is the null, so is supported  

·         No, since the p-value is less than alpha, the null is rejected. The claim is the null, so is not supported  

·         Yes, since the p-value is greater than alpha, the null is not rejected. The claim is the null, so is supported    

·         No, since the p-value is greater than alpha, the null is rejected. The claim is the null, so is not supported

 

Question 14

A 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 20 residents in that town has a mean credit card debt of $3619 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?

6VD. Hypothesis test example, sample standard deviation (Links to an external site.) (5:12)

6DE. When to use z and when to use t distribution (Links to an external site.) (DOCX)  

·         No, since p-value of 0.09 is greater than 0.10, fail to reject the null. Claim is alternative, so is not supported    

·         Yes, since p-value of 0.09 is less than 0.10, reject the null. Claim is alternative, so is supported  

·         Yes, since p-value of 0.09 is greater than 0.10, fail to reject the null. Claim is null, so is supported  

·         No, since p-value of 0.09 is less than 0.10, reject the null. Claim is null, so is not supported

 

 Question 15

A researcher wants to determine if daily walks together strengthen a marriage. One group of wives and one group of husbands are selected and take walks each day. After 2 weeks, all are asked if they felt their marriage was stronger based on the walks 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?

6DF. Paired sample experiment structure requirements and assumptions (Links to an external site.) (DOCX)

·         That the husbands and wives selected were married to each other  

·         That the wives group was positive on marriage before the walks

·         That all husbands and wives in the test had been married about the same amount of time 

·         That the both groups were positive on marriage before the walks