Question

In 2018, the American Automobile Association (AAA) reported that the average roundtrip ticket price for a flight taken during the Memorial Day holiday weekend was $168. Suppose you believe the average ticket price was actually higher than $168. You are able to survey a random sample of 100 adults who traveled during this time, and you find they spent an average of $176 on their roundtrip tickets, with a sample standard deviation of $45.   Use the information above to answer Questions 1 through 5. Be sure to review the Chapter 22 and Chapter 23 lecture videos for more details about the steps necessary to conduct a hypothesis test, and think very carefully about whether you are working with proportions or means since this will have an impact on the computation of the test statistic. Assume the alpha level is .05.

1.   What are the appropriate hypotheses?

Ho: Ha:

2.   What is the test statistic? Please show all of your work as you calculate this value.

3.   What p-value do you get?

4.   Based on your p-value, what should your final decision be, and why?

5.   Look again at your answer to Question 4. If the alpha level had been 0.01 rather than 0.05, would you make the same decision? Please explain why or why not.

Answer 1

Ho :   µ =   168  
Ha :   µ >   168   (Right tail test)
          
Level of Significance ,    α =    0.050  
sample std dev ,    s =    45.0000  
Sample Size ,   n =    100  
Sample Mean,    x̅ =   176.0000  
          
degree of freedom=   DF=n-1=   99  
          
Standard Error , SE = s/√n =   45/√100=   4.5000  
t-test statistic= (x̅ - µ )/SE =    (176-168)/4.5=   1.778  
          
          
p-Value   =   0.0393   [Excel formula =t.dist(t-stat,df) ]
Decision:   p-value≤α, Reject null hypothesis       

...........

Level of Significance ,    α =    0.010

p-Value   =   0.0393
Decision:   p-value>α, Do not reject null hypothesis

.............

Please let me know in case of any doubt.

Thanks in advance!

Please upvote!