Statistics Assignment | Get Paper Help

Econ 3060                                                                         Last Name______________________

Final Exam                                                                       First Name______________________

Spring 2020                                                                              CIN #______________________

 

IMPORTANT NOTE: You are required to show all of your work and upload your completed take-home final to Canvas. Email submission will not be accepted.

 

1. (25 points) For a random sample of 25 Econ 3060 students, the table shows the amount of time spent last week studying for this test.

 

Hours                                           No. of students                                                       c.r.f.

0 – 4                                             10

4 – 8                                               4

8 – 12                                             6

12 – 16                                            3

16 – 20                                            2

 

 

• (5 points) Find the cumulative relative frequency for this sample (that is, complete the final column in the table).

 

• (5 points) Calculate the sample mean time spent studying for the test. Use the correct symbol to label your answer.

 

 

 

 

 

• (10 points) Calculate the sample variance and the sample standard deviation of time spent studying. Use the correct symbols to label your answer.

 

 

 

 

 

 

 

 

 

 

 

 

• (5 points) In which class is the sample median?

 

2. (25 points) A corporation produces packages of candy. The numbers of pieces of candy per package vary, as indicated in the accompanying table.

 

Number of Pieces                    18         19          20          21          22

Probability                              .14        .24         .32         .21         .09

 

• (5 points) Find the probability that the numbers of pieces of candy per package will be at least 20.

 

 

 

• (20 points) The cost (in cents) of producing a package of candy is 30 + 4X, where X is the number of pieces of candy in the package. The revenue from selling the packages, however many pieces it contains, is $2.  If profit is defined as the difference between revenue and cost, find the mean and the variance of profit per package.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

3. (10 points) It is known that amounts of money spent on textbooks in a year by students follow a normal distribution with mean $380 and standard deviation $50.  Find the shortest range of dollar spending on textbooks in a year that includes 60% of all students.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

1. (10 points)  A new television series is to be shown. A broadcasting executive feels that his uncertainty about the rating which the show will receive in its first month can be represented by a normal distribution with mean 18.2 and standard deviation 1.6.  According to this executive, the probability is .2 that the rating will be less than what number?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5. (20 points) Given a normal population with standard deviation equal to 4, a random sample of 25 observations is taken.

 

(a)  (10 points)  What is the probability that the sample mean exceeds the population mean by more than 2?

 

 

 

 

 

 

 

 

 

 

 

(b)  (10 points)  What is the probability that the sample mean differs from the population mean by less than 1?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

6. (10 points) It has been found that candidates for an MBA program have undergraduate grade point averages that are normally distributed with standard deviation .45.  A random sample of 25 applicants is taken, yielding a sample mean GPA of 2.90.  Find a 95% confidence interval for the population mean GPA.

 

 

 

 

 

 

 

 

7. (10 points) The population standard deviation of daily output on an assembly line is 30 units.  We would like to obtain a 95% confidence interval for the mean daily output of the assembly line extending 5 units on each side of the sample mean.  Find the required sample size to achieve such an interval?

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8. (10 points) A random sample of six bottles of shampoo yielded the sample mean weight 21 ounces. Test at the 5% level against a two-sided alternative the null hypothesis that the true mean is 22 ounces given that the population standard deviation is 2 ounces. Show all steps.