MATH 533 Final Exam 4 Different Sets

MATH 533  Final Exam 4 Different Sets

MATH 533 Week 8 Final Exam Set 1

MATH 533 Week 8 Final Exam Set 2

MATH 533 Week 8 Final Exam Set 3

MATH 533 Week 8 Final Exam Set 4

 

1. Given the following sample of 10 high temperatures from March: 55, 60, 57, 43, 59, 66, 72, 65, 59, 47.

 

1. Determine the mean.


2. Determine the median.


3. Determine the mode.


4. Describe the shape of the distribution.


5. Determine Q1, Q2, Q3 and IQR.

1. Your friend is applying for 4 jobs. The hourly pay rate for the 4 jobs are, $8, $12, $15, $20. The probability distribution below shows the probability of getting each of these jobs:

Job Pay Rate, X	Probability, P(X)
8	.30
12	.20
15	.40
20	.10

 

 

1. What is the probability that your friend will get a job paying at least $15/hour?


2. What is the expected pay rate for your friend

 

• You ask all 200 students at school how much money they have in their pockets. The amount ranges from $0 to $130. You determine the mean to be $56.40 with standard deviation of $8.40. You believe that the amount is normally distributed.
  
  1. If you pick a person at random, what is the probability that he/she has at least $45?
  
  
  2. What percentage of the students will have between $40 and $50 in their pockets.
  
  
  3. If you pick a person at random, what is the probability that he/she has either less than $30 or more than $70.
  
  
  4. Approximately how many people in the class do you expect to have at least $65?
  
  
  5. We want to identify the students with top 10.5% amounts as “rich”. What is the minimum dollar amount the students in this group would need in their pockets.
  
  


• A sample of 100 exams yielded an average grade of 82 and standard deviation of 14. Find a 95% confidence interval for the average exam grade.


• Preliminary studies have shown that 20% of the voters might be willing to vote for Sran for President.
  
  1. Construct a 90% confidence interval for the proportion of voters who would be willing to support Sran.
  
  
  2. Before entering the race, Sran would like to conduct a poll to check his level of support. How big should be the sample be if he wants to be 95% sure that the error is no more than 2%? 
  
  


• The average weight of men joining a gym has historically been 170 pounds with a standard deviation of 27. The owner feels that the average weight has now decreased to less than 165 pounds. To support his claim, the owner conducts a sample of 25 men and finds their average to be 153. He would like to use a significance level of .05 to test his claim.
  
  1. State the null hypothesis.
  
  
  2. State the alternate hypothesis.
  
  
  3. Will you use z or t distribution for this problem?
  
  
  4. Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.
  
  
  5. Determine the critical value.
  
  
  6. Determine the rejection region.
  
  
  7. Calculate the test statistic.
  
  
  8. Would you accept or reject the owner’s claim? Explain.
  
  


• A presidential candidate states that she currently has exactly 30% of the vote. A newspaper thinks that this number is inaccurate. So it conducts a sample 500 voters and finds 175 people support the candidate. The newspaper would like to test its claim using .05 significance level.
  
  1. State the null hypothesis.
  
  
  2. State the alternate hypothesis.
  
  
  3. Will you use z or t distribution for this problem?
  
  
  4. Is this a two-tail test or a one-tail test? Draw a normal curve representing the problem.
  
  
  5. Determine the critical value.
  
  
  6. Determine the rejection region.
  
  
  7. Calculate the test statistic.
  
  
  8. Would you accept or reject the newspaper’s claim?
  
  

 

MATH 533 Final Exam 4 Different Sets