Answer all 25 questions. Make sure your answers are as complete as possible.
Show all of your work and reasoning. In particular, when there are
calculations involved, you must show how you come up with your answers wit
...
Answer all 25 questions. Make sure your answers are as complete as possible.
Show all of your work and reasoning. In particular, when there are
calculations involved, you must show how you come up with your answers with
critical work and/or necessary tables. Answers that come straight from
programs or software packages will not be accepted. If you need to use
software (for example, Excel) and /or online or hand-held calculators to aid in
your calculation, please cite the sources and explain how you get the results.
1. True or False. Justify for full credit.
(a) If the variance of a data set is zero, then all the observations in this data set are zero.
No, all the observations will be same but it is not necessary that all the observations will be
zero, because if all the observations are same even then the variance will be zero.
(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9.
No, because if A and B are disjoint then P(A AND B) = 0.
(c) Assume X follows a continuous distribution which is symmetric about 0. If
, then .
Yes, P(X<-3) will be less than 0.3 because the value will be towards negative side.
(d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter.
Yes, a 95% confidence interval is wider than a 90% confidence interval of the same
parameter because increasing the confidence limit we increases the acceptance region and
reduces the rejection region.
(e) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic
follows a Student’s t-distribution with P(T < 1.5) = 0.96, then we fail to reject the null
hypothesis at 0.05 level of significance .
No, we will not be able to reject the null hypothesis as we reject the null hypothesis is test
statistic is greater than the tabulated value of t.
Refer to the following frequency distribution for Questions 2, 3, 4, and 5. Show all work. Just the
answer, without supporting work, will receive no credit.
The frequency distribution below shows the distribution for checkout time (in minutes) in
UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.
Checkout Time (in
minutes)
Frequency Relative
Frequency
1.0 - 1.9 3
2.0 - 2.9 12
3.0 - 3.9 0.20
4.0 - 4.9 3
5.0 -5.9
Total 25
2. Complete the frequency table with frequency and relative frequency. Express the relative
frequency to two decimal places.
Checkout Time (in minutes) Frequency Relative Frequency
1.0 - 1.9 3 0.12
2.0 - 2.9 12 0.48
3.0 - 3.9 5 0.20
4.0 - 4.9 3 0.12
5.0 -5.9 2 0.08
Total 25 1
3. What percentage of the checkout times was at least 3 minutes?
Percentage of the checkout times was at least 3 minutes
= (5 + 3 +2)/25*100
= 40%
4. In what class interval must the median lie? Explain your answer.
We will make the intervals continuous by subtracting 0.05 from lower limit and adding 0.05 in
upper limit therefore the corresponding intervals will be 0.95-1.95, 1.95 - 2.95, 2.95 - 3.95, 3.95 -
4.95, 4.95 -5.95. N=25 therefore, N/2=12.5,
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