Question

Question 1: At the local community college it has been reported the average age of first year college students is 20 years of age with a standard deviation of 7.2 years. As a college professor you believe it’s less. To test your claim, you take a random sample of 200 students, the average age 19.4 years. At an alpha of 0.02 what do you conclude? (1 point each for a total of 4 points)

a) Ho:                                              ; Ha:                                 

b) Critical Value for Decision Making:                                 

c) Calculated Test Statistic:                                                   

d) Conclusion:                                                                        

Question 2: As the summer director of Exploratory Camp, you provide academic enrichment for students that scored poorly on the DCAS. Capital School District thinks the summer program will influence test scores in the fall. The historical average of summer mathematics assessments is 21.3 with a standard deviation of 5. To test the claim of the school district, you assess 80 students in mathematics. The sample average on the test is 20.03. At an alpha of 0.05 what can you conclude? (1 point each for a total of 4 points)

a) Ho:                                              ; Ha:                                 

b) Critical Value for Decision Making:                                 

c) Calculated Test Statistic:                                                   

d) Conclusion:                                                                        

Question 3: Goodyear Tire and Rubber Company manufacture tires in North America. The daily production of the Eagle GT tire follows the normal distribution, with a mean of 200 and a standard deviation of 31. Recently, because of market expansion, new production methods have been introduced and new employees hired. The CEO of the company would like to investigate whether there has been a change in the weekly production of the Eagle GT and asks the Production Manager for the 180-day output report. The report stated that on average 205 tires were produced per day. At an alpha of 0.01 significance what can you conclude? (1 point each for a total of 4 points)

a) Ho:                                              ; Ha:                                 

b) Critical Value for Decision Making:                                 

c) Calculated Test Statistic:                                                   

d) Conclusion:                                                                        

For the following scenarios write the Ho & Ha, identify the critical value (CV) used for the decision rule, calculate the p-value test statistic and state a conclusion. Write your answer in the spaces provided.

Question 4: Your company reports that the historical average number of vacation days taken by full-time employees is 10.2 days per year with a standard deviation of 7.55 vacation days. You believe the average number of vacation days taken by full-time employees is lower. To test your claim, you take a random sample of 121 employees at your company. You find the sample average to be 8.9 vacation days. At an alpha of 0.05 what can you conclude? (1 point each for a total of 4 points)

a) Ho:                                              ; Ha:                                 

b) Critical Value for Decision Making:                                 

c) Calculated Test Statistic:                                                   

d) Conclusion:                                                                        

Answer 1

Question 1: At the local community college it has been reported the average age of first year college students is 20 years of age with a standard deviation of 7.2 years. As a college professor you believe it’s less. To test your claim, you take a random sample of 200 students, the average age 19.4 years. At an alpha of 0.02 what do you conclude? (1 point each for a total of 4 points)

a) Ho: u = 20

Ha : u < 20

As the population s.d is mentioned in the question we will use z table to conduct the test

B)

From z table, P(z<-2.05) = 0.02

So, critical value is -2.05

So we will reject Ho if test statistics is less than -2.05

C)

Test statistics z = (sample mean - claimed mean)/(s.d/√n)

Z = (19.4 - 20)/(7.2/√200) = -1.18

D)

As -1.18 is not less than -2.05

We fail to reject the null hypothesis

So we do not have enough evidence to conclude that mean is less than 20