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# The following table contains the data of a sample of 10 boxes of cereals. Product 1 2 3 4 5 6 7 8 9 10 Cereal Name 100% Bran AlI-Bran All-Bran...

#1. The following table contains the data of a sample of 10 boxes of cereals.

Product Cereal Name Manufacturer Calories Sodium Fiber Carbs Sugars
1 100% Bran Nabisco 70 130 10 5 6
2 AlI-Bran Kellogg 70 260 9 7 5
3 All-Bran w/Extra Fiber Kellogg 50 140 14 8 0
4 Almond Delight Ralston Purina 110 200 1 14 8
5 Apple Cinn Cheerios General Mills 110 180 1.50 10.50 10
6 Apple Jacks Kellogg 110 125 1 11 14
7 Basic 4 General Mills 130 210 2 18 8
8 Bran Chex Ralston Purina 90 200 4 15 6
9 Bran Flakes Post 90 210 5 13 5
10 Cap'n'Crunch Quaker 120 220 0 12 12

a) Compute measures of dispersion for the variable “Fiber”.

b) Suppose that you are a sales person at Nabisco, create a graph that shows how Nabisco cereals compare to non-Nabisco cereals in terms of calories (assume calories is a discrete variable).

#2. The table below displays information collected from a survey of students at a MBA program with a population size of 1000 students.

MBA Student Survey
Gender
Average of Female Male Grand Total
Nights out/week 1.85 1.88 1.87
Study hours/week 18.50 17.80 18.03
Number of International Students International Student
Gender No Yes Grand Total
Female 5 5 10
Male 15 5 20
Grand Total 20 10 30

Number of Students Gender
Undergraduate concentration Female Male Grand Total
Engineering 3 6 9
Liberal Arts 1 5 6
Other 1 3 4
Sciences 3 1 4
Grand Total 10 20 30

#3. In problem #2 above,

a) Can you detect any problems with the sample that was surveyed? If yes, what are those problems? If no, why not?

b) Would you want to use this sample to make inferences about the population? Why or why not?
#4. The graph below shows the histogram of the ages of students at an MBA program. Also, the table below gives summary statistics for the variable age.

Answer this question: Does this data appear to be normally distributed? Why or why not?

Five-Number Summary
Mean 21.0600
Median 20.5000
Mode 20.0000
1st Quartile 19.0000
3rd Quartile 22.0000

#5. The table below provides descriptive statistics from a sample of 100 employees in a firm on employees’ current salary (in dollars), beginning salary (in dollars), previous experience (in months) when hired, and education (in years).

Answer this question: What conclusions about each variable can you draw from these statistics?

Current Salary Beginning Salary Previous Experience (months) Education (years)
Mean 33632.60 16938.60 95.61 13.22
Median 27825.00 14250.00 60.50 12.00
Mode 19650.00 11250.00 0.00 12.00
Standard Deviation 17289.55 8347.83 105.48 2.72
Kurtosis 5.99 8.80 2.36 -0.20
Skewness 2.31 2.71 1.60 -0.12
Minimum 16350.00 9750.00 0.00 8.00
Maximum 103750.00 60000.00 460.00 19.00

#6. The table below provides the correlation matrix for the data in Problem #5.

Answer this question: Given the correlation matrix, what conclusions can you draw?

Current Salary Beginning Salary Previous Experience (months) Education (years)
Current Salary 1.00
Beginning Salary 0.89 1.00
Previous Experience (months) 0.02 0.12 1.00
Education (years) 0.56 0.53 -0.16 1.00

#7. From a marketing survey of 100 consumers who drink energy drinks, we find that only three brands are consumed. Using the survey results, we create a cross-tabulation of frequencies as shown below.

Answer this question: What is the probability that among women Brand 3 is consumed?

Energy Drinks

Cross-tabulation Brand 1 Brand 2 Brand 3 Total
Male 25 17 21 63
Female 9 6 22 37
Total 34 23 43 100

#8. In determining automobile mileage ratings in the United States, it was found that miles-per-gallon (mpg) in American cities is normally distributed with a mean of 24 mpg and a standard deviation of 1.0 mpg. Find the following:

a) P(mpg < 25)

b) P(23 < mpg < 25)

c) P(mpg > 26)

#10. The table below provides statistics and all relevant information for calculating confidence intervals in a sample of 100 employees in a firm on employees’ current salary (in dollars), beginning salary (in dollars), previous experience (in months) when hired, and education (in years).

a) Calculate the margin of error for each variable.

b) Assume the population standard deviation for current salary is \$15,000. What is the confidence level we applied to compute the confidence interval for current salary as shown above? Give the value of the percentage of that confidence level.

Previous
Current Beginning Experience Education
Salary Salary (months) (years)
Sample Standard Deviation \$17,290 \$8,348 105 2.72
Sample Mean \$33,633 \$16,939 96 13
Sample Size 100

Confidence Interval
Interval Lower Limit \$30,202 \$15,282 75 12.68
Interval Upper Limit \$37,063 \$18,595 117 13.76

#1. The following table contains the data of a sample of 10 boxes of cereals. Product Cereal Name Manufacturer Calories Sodium Fiber Carbs Sugars 1 100% Bran Nabisco 70 130 10 5 6 2 AlI-Bran Kellogg 70 260 9 7 5 3 All-Bran w/Extra Fiber Kellogg 50 140 14 8 0 4 Almond Delight Ralston Purina 110 200 1 14 8 5 Apple Cinn Cheerios General Mills 110 180 1.50 10.50 10 6 Apple Jacks Kellogg 110 125 1 11 14 7 Basic 4 General Mills 130 210 2 18 8 8 Bran Chex Ralston Purina 90 200 4 15 6 9 Bran Flakes Post 90 210 5 13 5 10 Cap'n'Crunch Quaker 120 220 0 12 12 a) Compute measures of dispersion for the variable “Fiber”. b) Suppose that you are a sales person at Nabisco, create a graph that shows how Nabisco cereals compare to non-Nabisco cereals in terms of calories (assume calories is a discrete variable). #2. The table below displays information collected from a survey of students at a MBA program with a population size of 1000 students. MBA Student Survey Gender Average of Female Male Grand Total Nights out/week 1.85 1.88 1.87 Study hours/week 18.50 17.8 0 18.03 Number of International Students International Student Gender No Yes Grand Total Female 5 5 10 Male 15 5 20 Grand Total 20 10 30 Number of Students Gender Undergraduate concentration Female Male Grand Total Business 2 5 7 Engineering 3 6 9 Liberal Arts 1 5 6 Other 1 3 4 Sciences 3 1 4 Grand Total 10 20 30 1
#3. In problem #2 above, a) Can you detect any problems with the sample that was surveyed? If yes, what are those problems? If no, why not? b) Would you want to use this sample to make inferences about the population? Why or why not? #4. The graph below shows the histogram of the ages of students at an MBA program. Also, the table below gives summary statistics for the variable age. Answer this question: Does this data appear to be normally distributed? Why or why not? Five-Number Summary Mean 21.0600 Median 20.5000 Mode 20.0000 1st Quartile 19.0000 3rd Quartile 22.0000 2
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