﻿ Ken Szulczyk's Exam 1 for Statistical Methods HcWjnyVHiTd8hN_8STvJ2rWaXvhPz4wXYCNGvD4qDkU

# Data Analysis and Economic Forecasting Examination 1

These questions are from the test bank. Some questions have multiple parts.

## Theoretical Questions

1. If you have mean, mode, and median, which ones are sensitive to outliers in the data?

If you have a range and standard deviation, which ones are sensitive to outliers?

Should you drop the outliers?

2. What are continuous, discrete, and categorical variables?

Does the data matter how we analyze our data?

3. What is the difference between standard error and standard deviation?

4. Why do statisticians use the t-statistic, rather than the z-values from a normal distribution, when making inferences about the population parameters?

5. What is stratified random sampling?

Is there any potential biases if a researcher uses this method?

6. What are some methods you can use to determine if you have a skewed distribution?

7. What are Box-Whisker Plots?

What are the benefits of these plots?

8. A random sample requires three conditions for it to be truly random. What are the three conditions?

9. What are Type I and Type II errors?

Why are significance levels usually set at 10%, 5%, or 1%?

What is the power of a test?

How can researchers increase a statistical test's power?

## Empirical Questions

10. You are given the following sample data, please calculate the mean, mode, and median.

9 1 9 6 5 2 10 9 8 9

Now calculate the range, variance, and standard deviation.

Now calculate the standard error.

What does the standard error mean?

11.Explain how you can obtain 100 random numbers in Excel that are normally distributed with a mean of 100 and standard deviation of 15.

12.Using the data below, please construct a leaf plot.

5.3 3.0 1.6 8.4 1.7 7.4 5.5 7.2 6.0

6.9 7.0 8.5 0.6 2.5 2.6 0.5 8.1 2.7

What is a benefit of using a leaf plot?

13.Using the information below, please construct a histogram?

 Macroeconomics I Grade Percent Grade Frequency 90-100 A 30 80-89.9 B 28 70-79.9 C 12 60-69.9 D 1 Below 60 F 6 Total 77

What are the widths of the bins?

Can bins be of unequal widths? Is this okay?

14.Unfortunately, Excel does not make it easy to construct a histogram. What are the steps in constructing one?

Must contain three parts.
(i) Selecting the bin width
(ii) Using the countif statement in Excel
(iii) When tabulating the bins, how do you prevent double counting?

15.You sampled one hundred students from the university, 35 students plan to pursue a Master's degree.

(i) Please calculate the mean, variance and standard error for this data.
(ii) Please calculate the 95% confidence interval for the true population mean.
(iii) Check the hypothesis that 50% of students plan to pursue a Master's degree.

16.In 2008, the United States had 300 billionaires. In 2009, the billionaire club shrinks to 100. Check the hypothesis that his drop is do to random sampling error.

(i) Which distribution are you using?
(ii) Please calculate the mean, variance, and pooled standard error for this data.
(iii) Calculate the z-statistic and check if the population means are the same for both years.

17.You have 10,000 surveys from people who live in the City of Almaty and 5,000 surveys from people who live in Astana. You calculate the average income and standard deviation. The average income for Almaty is \$600 per month and the standard deviation is \$100, while the average income for Astana is \$800 per month and a standard deviation of \$200.

(i) Test the hypothesis that incomes are the same for both cities, assuming the calculated standard deviation is equal to the true population standard deviation.

Designed by Kenneth R. Szulczyk ©2011
Last updated May 1, 2012