the final Exam of the Statistics for Business I
8
HARDMAN
DSC 210
Review for Final Exam
- Know the definitions of the following terms:
- Margin of Error
- Mean
- Range
- Parameter
- Continuous
- Outliers
- Scatterplot
- Mutually Exclusive
- Statistic
- IQR
- Median
- Correlation
- Sample Space
- Standard Deviation
- Independent
- Quartiles
- Boxplot
- Event
- Discrete
- DRAW THE APPROPRIATE PICTURES, and calculate each of the following probabilities.
a.
b.
- Suppose that X~Bin(12, 0.4):
- Calculate the probability that X = 8
- Calculate
- Assume that you will take a sample of size 36 from a population of GPAs with a mean value of 2.1 and a population standard deviation of 0.4.
- Specify the sampling distribution of , your sample mean value.
- Calculate .
- Suppose that you do know the value of the population standard deviation and that you want to calculate an 80% CI for , the population mean value. Determine the value of the critical number that you would use to calculate this CI.
- Given the following probability distribution table for the random variable X:
X: -3 2 7
f(x): 0.3 0.5 0.2
- Calculate the Expected Value of X.
- Calculate the Variance of X.
- Given the following heights measured in inches: 68, 72, 65, 69, 72:
- Calculate the mean height for this sample.
- Calculate the standard deviation for this sample of heights.
- Suppose that you will pick two cards from a standard deck of 52 cards, without replacement, and you are only interested in whether each of the cards that you select is a diamond, or not.
- Draw the complete tree diagram, with all of the twig probabilities in place.
- What is the probability that exactly 1 of the two cards that you select is a diamond?
- Use the data set in question 7 to find the 95% CI for .
- Name the two desirable properties for any CI.
- Students were given a quiz, and the amount of time (measured in minutes) it took each student to finish the quiz was recorded. The results follow:
10, 11, 11.25, 12.5, 12.5, 14, 15, 18, 18, 20, 22
- Complete the 5-Number summary of this data set:
Min: _____
Q1: _____
Q2: _____
Q3: _____
Max: _____
- Calculate the IQR for this data set.
- Calculate the Upper Fence for this data set.
- What is the reason that you would calculate the Fences in an analysis?
- Consider the following scatterplots:
#1 #2 #3
- Which scatterplot has the smallest r-value?
- Which scatterplot shows the weakest linear correlation?
- Which scatterplot has an r-value closest to 1?
Answers. Note that for the most part I am only giving answers, without ANY of my work shown. You MUST REMEMBER to SHOW ALL OF YOUR WORK that leads to the answer you give. Any answer without the appropriate supporting work will NOT receive full credit…even if your answer is correct. I consider the work that you do to get your answer PART OF YOUR ANSWER.
- Know the definitions of the following terms: You can look these up yourself.
- Margin of Error
- Mean
- Range
- Parameter
- Continuous
- Outliers
- Scatterplot
- Mutually Exclusive
- Statistic
- IQR
- Median
- Correlation
- Sample Space
- Standard Deviation
- Independent
- Quartiles
- Boxplot
- Event
- Discrete
- DRAW THE APPROPRIATE PICTURES, and calculate each of the following probabilities.
a.
Using our T-Table: .10 – 0.01 = 0.09 (it shoulda been 1.333, not just 1.33)
b.
Using our Z-Table: 0.9913 – 0.7291 = 0.2622
- Suppose that X~Bin(12, 0.4):
- Calculate the probability that X = 8
0.0420426547
- Calculate
0.3195241759
- Assume that you will take a sample of size 36 from a population of GPAs with a mean value of 2.1 and a population standard deviation of 0.4.
- Specify the sampling distribution of , your sample mean value.
- Calculate .
0.0669043732
- Suppose that you do know the value of the population standard deviation and that you want to calculate an 80% CI for , the population mean value. Determine the value of the critical number that you would use to calculate this CI.
Z-crit = (approximately) 1.28
- Given the following probability distribution table for the random variable X:
X: -3 2 7
f(x): 0.3 0.5 0.2
- Calculate the Expected Value of X.
1.5
- Calculate the Variance of X.
12.25
- Given the following heights measured in inches: 68, 72, 65, 69, 72:
- Calculate the mean height for this sample.
69.2
- Calculate the standard deviation for this sample of heights.
2.949576241
- Suppose that you will pick two cards from a standard deck of 52 cards, without replacement, and you are only interested in whether each of the cards that you select is a diamond, or not.
- Draw the complete tree diagram, with all of the twig probabilities in place.
D = B1
12/51
13/52 D N = B2
39/51
o
13/51
39/52 N D = B3
38/51
N = B4
- What is the probability that exactly 1 of the two cards that you select is a diamond?
1014/2652
- Use the data set in question 7 to find the 95% CI for .
From TI-83 Calculator: (65.538, 72.862)
- Name the two desirable properties for any CI.
- Narrow, short, small… LHEP and RHEP as close to each other as possible.
- High Confidence Coefficient.
- Students were given a quiz, and the amount of time (measured in minutes) it took each student to finish the quiz was recorded. The results follow:
10, 11, 11.25, 12.5, 12.5, 14, 15, 18, 18, 20, 22
- Complete the 5-Number summary of this data set:
Min: __10___
Q1: _11.25__
Q2: __14___
Q3: __18___
Max: __22___
- Calculate the IQR for this data set.
6.75
- Calculate the Upper Fence for this data set.
28.125
- What is the reason that you would calculate the Fences in an analysis?
Fences are calculated in an analysis in order to identify observations that are outliers. Any observation in the data set that is less than the Lower Fence is an outlier and any observation in the data set that is greater than the Upper fence is an outlier.
- Consider the following scatterplots:
#1 #2 #3
- Which scatterplot has the smallest r-value?
#3
- Which scatterplot shows the weakest linear correlation?
#2
- Which scatterplot has an r-value closest to 1?
#1
1.0 1.5 1.8 2.0 2.3 2.5 2.7 3.0 3.1 3.4 3.5 3.6 4.0 4.1 4.2 0.8 1.25 4.0 1.3 3.4 2.6 3.8 2.5 1.3 1.1 3.6 1.2 2.5 0.6 3.7 2.05 0.1 0.7 2.09
1.0 1.3 1.5 0.9 2.1 2.5 2.6 2.9 3.1 3.4 3.4 3.7 4.0 4.3 5.0 4.7 4.4 5.1 4.1 3.6 3.2 3.4 3.0 2.7 2.6 2.4 2.1 1.9
1.0 1.1 1.4 1.7 1.9 2.0 2.1 2.5 2.7 3.0 3.2 3.5 3.7 4.0 0.8 0.4 1.5 1.1 2.1 2.0 2.5 2.3 3.0 3.7 2.9 3.7 4.2 3.9
1.0 1.5 1.8 2.0 2.3 2.5 2.7 3.0 3.1 3.4 3.5 3.6 4.0 4.1 4.2 0.8 1.25 4.0 1.3 3.4 2.6 3.8 2.5 1.3 1.1 3.6 1.2 2.5 0.6 3.7 2.05 0.1 0.7 2.09
1.0 1.3 1.5 0.9 2.1 2.5 2.6 2.9 3.1 3.4 3.4 3.7 4.0 4.3 5.0 4.7 4.4 5.1 4.1 3.6 3.2 3.4 3.0 2.7 2.6 2.4 2.1 1.9
1.0 1.1 1.4 1.7 1.9 2.0 2.1 2.5 2.7 3.0 3.2 3.5 3.7 4.0 0.8 0.4 1.5 1.1 2.1 2.0 2.5 2.3 3.0 3.7 2.9 3.7 4.2 3.9
