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If the variance of a data set is zero, then all the observations in this data set are zero.
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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, the immediate less observation lies in 2.0-2.9 i.e. 1.95-2.95.

 

5.Does this distribution have positive skew or negative skew? Why? 

 

The distribution is positively skewed as the frequency in the second interval is 12 and all the proceeding frequencies are very less. This can also be seen in the following graph

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