Complete Ec315 Midterm Exam with Answers

EC/315 Midterm Examination

Directions:

This test is open-book and open notes and covers the content from weeks 1 through week 4 of EC/315. The test will be typed and submitted in the Dropbox marked Midterm Exam. The midterm is due the last day of Week 4.

PROBLEM 1 (Weight 20 points).

NBC TV news, in a segment on the price of gasoline, reported last evening that the mean price nationwide is $1.50 per gallon for self-serve regular unleaded. A random sample of 35 stations in the Milwaukee, WI, area revealed that the mean price was $1.52 per gallon and that the standard deviation was $0.05 per gallon. At the .05 significance level, can we conclude that the price of gasoline is higher in the Milwaukee area? Calculate the p-value and interpret.

Null hypothesis Ho: μ = $1.50

Alternative hypothesis Ha: μ > $1.50

Test statistic:













Therefore,



Determination of the P-value: The test is based on (n -1) = (35-1) = 34 degrees of freedom

Table shows area under the 34 df curve to the right of t = 2.36 is 0.012

Conclusion: with significance level = 0.05, above shows P-value <= significance level, [0.012 <= 0.05].

Null hypothesis Ho: μ = $1.50 should be rejected. Therefore, the "true mean" of price of gasoline in Milwaukee, Wisconsin area is higher than $1.50 to a significance level of 0.05.

PROBLEM 2: (Weight 20 points).

Suppose Babsie generated the following probability distribution: X p(x)

5 .25

7 .30

10 .25

12 .05

15 .15

a. Is this probability distribution discrete or continuous? Explain your reasoning.

b. Calculate the expected value of X. Show your work!!

c. Calculate the variance of X. Show your work!!!

d. Calculate the standard deviation. Show your work!!

a) Since in this case, the random variable is a discrete variable, and hence its probability distribution is a discrete probability distribution.

b) The expected value of the variable is given as Σx*p(x) = 8.7

c)