MATH 221 Week 6 Quiz 1

MATH 221 Week 6 Quiz 1 | Devry University

Week 6: Quiz

Question 1

 (CO 5) A company claims that its heaters last at most 5 years. Write the null and alternative hypotheses and note which is the claim.  

·         Ho: μ = 5 (claim), Ha: μ ≥ 5  

·         Ho: μ = 5 (claim), Ha: μ > 5  

·         Ho: μ = 5, Ha: μ > 5 (claim)  

·         Ho: μ > 5 (claim), Ha: μ ≤ 5

 

Question 2

 (CO 5) An executive claims that her employees spend no more than 2.5 hours each week in meetings. Write the null and alternative hypotheses and note which is the claim.  

·         Ho: μ = 2.5 (claim), Ha: μ ≥ 2.5  

·         Ho: μ = 2.5 (claim), Ha: μ > 2.5  

·         Ho: μ = 2.5, Ha: μ < 2.5 (claim)  

·         Ho: μ > 2.5, Ha: μ = 2.5 (claim)

 

Question 3

 (CO 5) In hypothesis testing, a key element in the structure of the hypotheses is that the math tests the support for the ________________________.  

·         claim  

·         alternative hypothesis  

·         the truth    

·         null hypothesis

 

 Question 4

 (CO 5) A landscaping company claims that at least 90% of workers arrive on time. If a hypothesis test is performed that fails to reject the null hypothesis, how would this decision be interpreted?  

·         There is not sufficient evidence to support the claim that at least 90% of workers arrive on time  

·         There is not sufficient evidence to support the claim that more than 90% of workers arrive on time  

·         There is sufficient evidence to support the claim that more than 90% of workers arrive on time  

·         There is sufficient evidence to support the claim that a least 90% of workers arrive on time

 

Question 5

 (CO 5) A textbook company claims that their book is so engaging that less than 55% of students read it. If a hypothesis test is performed that rejects the null hypothesis, how would this decision be interpreted?  

·         There is sufficient evidence to support the claim that less than 55% of students read this text  

·         There is sufficient evidence to support the claim that no more than 55% of students read this text  

·         There is not sufficient evidence to support the claim that less than 55% of students read this text  

·         There is not sufficient evidence to support the claim that no more than 55% of students read this text

 

 Question 6

 (CO 5) An advocacy group claims that the mean braking distance of a certain type of tire is 75 feet when the car is going 40 miles per hour. In a test of 45 of these tires, the braking distance has a mean of 76 and a standard deviation of 5.9 feet. Find the standardized test statistic and the corresponding p-value.  

·         z-test statistic = 1.14, p-value = 0.1278  

·         z-test statistic = -1.14, p-value = 0.1278 

·         z-test statistic = 1.14, p-value = 0.2555  

·         z-test statistic = -1.14, p-value = 0.2555

 

 Question 7

 (CO 5) The heights of 82 roller coasters have a mean of 280.7 feet and a standard deviation of 59.3 feet. Find the standardized test statistics and the corresponding p-value when the claim is that roller coasters are less than 290 feet tall.  

·         z-test statistic = -1.42, p-value = 0.1556  

·         z-test statistic = 1.42, p-value = 0.0797  

·         z-test statistic = 1.42, p-value = 0.1556   

·         z-test statistic = -1.42, p-value = 0.0797

 

 Question 8

 (CO 5) A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 720 hours. A random sample of 51 light bulbs as a mean of 705.4 hours with a population standard deviation of 62 hours. At an α=0.05, can you support the company’s claim?  

·         Claim is the null, fail to reject the null and support claim as p-value (0.092) is greater than alpha (0.05)    

·         Claim is the null, reject the null and cannot support claim as p-value (0.046) is less than alpha (0.05)  

·         Claim is the alternative, fail to reject the null and cannot support claim as the p-value (0.046) is less than alpha (0.10)  

·         Claim is the alternative, reject the null and support claim as p-value (0.046) is greater than alpha (0.05)

 

Question 9

 (CO 5) A restaurant claims the customers receive their food in less than 16 minutes. A random sample of 39 customers finds a mean wait time for food to be 15.8 minutes with a population standard deviation of 1.4 minutes. At α = 0.04, can you support the organizations’ claim?  

·         Claim is the alternative, fail to reject the null so cannot support the claim as the p-value (0.186) is greater than alpha (0.04)  

·         Claim is the null, reject the null so cannot support the claim as the p-value (0.186) is less than alpha (0.04)  

·         Claim is the alternative, reject the null so support the claim as the p-value (0.186) is less than alpha (0.04)  

·         Claim is the null, fail to reject the null so support the claim as the p-value (0.186) is greater than alpha (0.04)

 

 Question 10

 (CO 5) A manufacturer claims that their calculators are 6.800 inches long. A random sample of 55 of their calculators finds they have a mean of 6.812 inches with a standard deviation of 0.05 inches. At α=0.08, can you support the manufacturer’s claim using the p value?  

·         Claim is the null, fail to reject the null and support claim as p-value (0.038) is greater than alpha (0.08)  

·         Claim is the alternative, reject the null and cannot support claim as p-value (0.038) is greater than alpha (0.08)  

·         Claim is the alternative, fail to reject the null and support claim as p-value (0.075) is less than alpha (0.08)  

·         Claim is the null, reject the null and cannot support claim as p-value (0.075) is less than alpha (0.08)

 

Question 11

 (CO 5) A travel analyst claims that the mean room rates at a three-star hotel in Chicago is greater than $152. In a random sample of 36 three-star hotel rooms in Chicago, the mean room rate is $165 with a population standard deviation of $41. At α=0.10, can you support the analyst’s claim using the p-value?  

·         Claim is the alternative, fail to reject the null as p-value (0.029) is less than alpha (0.10), and can support the claim    

·         Claim is the alternative, reject the null as p-value (0.029) is less than alpha (0.10), and can support the claim  

·         Claim is the null, fail to reject the null as p-value (0.029) is less than alpha (0.10), and cannot support the claim  

·         Claim is the null, reject the null as p-value (0.029) is less than alpha (0.10), and cannot support the claim

 

 Question 12

 (CO 5) A car company claims that the mean gas mileage for its luxury sedan is at least 24 miles per gallon. A random sample of 7 cars has a mean gas mileage of 23 miles per gallon and a standard deviation of 1.1 miles per gallon. At α=0.05, can you support the company’s claim assuming the population is normally distributed?  

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

·         Yes, since the p-value is less than alpha, the null is rejected. The claim is the alternative, 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

 

 Question 13

 (CO 5) A state Department of Transportation claims that the mean wait time for various services at its different location is more than 6 minutes. A random sample of 16 services at different locations has a mean wait time of 9.5 minutes and a standard deviation of 7.3 minutes. At α=0.05, can the department’s claim be supported assuming the population is normally distributed?  

·         No, since p of 0.037 is less than 0.05, fail to reject the null. Claim is alternative, so is not supported  

·         Yes, since p of 0.037 is less than 0.05, fail to reject the null. Claim is null, so is supported  

·         Yes, since p of 0.037 is less than 0.05, reject the null. Claim is alternative, so is supported 

·         No, since p of 0.037 is less than 0.05, reject the null. Claim is null, so is not supported

 Question 14

 (CO 5) A used car dealer says that the mean price of a three-year-old sport utility vehicle in good condition is $18,000. A random sample of 20 such vehicles has a mean price of $18,450 and a standard deviation of $1930. At α=0.08, can the dealer’s claim be supported assuming the population is normally distributed?  

·         Yes, since the p-value of 0.310 is less than alpha of 0.08, the null is rejected. The claim is the alternative, so is supported  

·         No, since the p-value of 0.310 is close to the alpha of 0.08, the null is not rejected. The claim is the null, so is supported  

·         No, since the p-value of 0.310 is less than alpha of 0.08, the null is rejected. The claim is the null, so is not supported    

·         Yes, since the p-value of 0.310 is greater than alpha of 0.08, the null is not rejected. The claim is the null, so is supported

 

 Question 15

 (CO 5) A researcher wants to determine if daily walks together strengthen a marriage. One group of wives and one group of husbands are selected and have daily walks. 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?  

·         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  

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

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

 

Question 16

 (CO 5) Assuming the population is normally distributed, test the claim that the mean is more than 24 using an α of 0.05.  The sample statistics are a mean of 24.9, standard deviation of 2.11, and an n of 19.  

·         The data do not support the claim, as the null was not rejected and the claim is the alternative.  

·         The data support the claim, as the null was not rejected and the claim is the null.  

·         The data do not support the claim, as the null was rejected and the claim is the alternative.   

·         The data support the claim, as the null was rejected and the claim is the alternative.

 

 Question 17

 (CO 5)  A company claims that the hold times for customer service averages at most 10 minutes.  A random sample of 24 hold times has a mean of 11.2 minutes with a standard deviation of 7.2 minutes.  Is there enough evidence to support the claim at α = 0.05?  Assume the population is normally distributed.  

·         No, since p-value of 0.211 is greater than 0.05, reject the null. Claim is null, so is not supported  

·         Yes, since p-value of 0.211 is less than 0.05, reject the null. Claim is null, so is supported  

·         No, since p-value of 0.211 is greater than 0.05, fail to reject the null. Claim is alternative, so is not supported   

·         Yes, since p-value of 0.211 is greater than 0.05, fail to reject the null. Claim is null, so is supported

 

 Question 18

 (CO 5) A coach claims that all players can run more than 1.5 miles.  A random sample of 17 players finds that they can run an average of 1.7 miles with a standard deviation of 0.3 miles.  Is there enough evidence to support the claim at α of 0.01? Assume the population is normally distributed.  

·         Yes, since p of 0.007 is greater than 0.01, reject the null. Claim is alternative, so is supported  

·         No, since p of 0.007 is greater than 0.01, fail to reject the null. Claim is null, so is not supported   

·         Yes, since p of 0.007 is less than 0.01, reject the null. Claim is alternative, so is supported  

·         No, since p of 0.007 is less than 0.01, reject the null. Claim is null, so is not