Distance Education Statistics Lab F Eric Parslow and Russell T. Hurlburt University of Nevada, Las Vegas

This lab will consist of 3 parts:
1. Practice using "ttest2" in ESTAT.
2. Cumulative review.
3. The Quiz.





Part 1 - ttest2

1. Open ESTAT and enter the exercise called "ttest2"

2. Macintosh users: Much like we did in "ttest1", simply answer the yes/no questions: Do you reject the null hypothesis? Windows users: Take the eyeball-calibration Path 1.

3. Essentially, you are comparing by eyeball the two samples shown in the histograms and deciding whether they come from different populations or the same population.
- If the sample means are 'relatively far apart,' reject the null hypothesis and conclude the two samples come from different populations
- If the sample means are 'relatively close together,' do not reject the null hypothesis and conclude the two samples come from the same population

4. Use the "New Data Set" button six or eight times to gain a sense of what 'relatively far apart' and 'relatively close together' entails. You should be able to determine the vast majority without error.

5. For extra practice and comprehension, you may wish to follow the tutorial and learn to eyeball-estimate, step by step, the observed value of t. This is optional but useful.


Part 2 - Cumulative review

1. Recognize that thus far in the course we have identified 5 basic types of statistics/tests:

a. Area under the normal curve.
b. Confidence interval.
c. 1 sample z hypothesis test.
d. 1 sample t hypothesis test.
e. 2 sample t hypothesis test.

2. You should be able to determine which statistic or test to use given any problem.

3. This can be done by looking for various clues or characteristics within the questions, as follows:

Step I.
Determine whether the problem asks a question that has a Yes/No answer. (Examples: Does fertilizer increase yield [Yes or No]? Does marijuana slow reaction time [Yes or No]?) If the problem asks a question that has a Yes/No answer, go to step II. If it does not, go to Step IV.

Step II.
Because the problem asks a question that has a Yes/No answer, it is likely to be a hypothesis test. Therefore we must determine whether there are two groups. Does the problem supply the data (or a summary of the data) from two samples? Note that a phrase such as 'Previous research has shown that the mean IQ is 100' is NOT a statement about a sample (it is an inference about a population). If there are two samples, the problem is about a two-sample hypothesis test [(e) in the above list] and you are finished. If not, then go to Step III.

Step III.
The problem must refer to a one-sample test. Therefore you must determine whether the population standard deviation sigma is known. The problem will say something like 'sigma is known to be 15,' or 'previous research has shown that the standard deviation is 15.' If sigma is known, the problem is about a one-sample z hypothesis test [(c) in the above list] and you are finished. If not, then go to Step III. If sigma is not known, the problem is about a one-sample t hypothesis test [(d) in the above list] and you are finished.

Step IV.
The problem is NOT a hypothesis test. Now determine whether the problem asks you to specify a range of values where the population mean is likely to be. (Example: 'What can be said with 95% confidence about the true mean IQ of UNLV students?') If the problem asks you to specify a range of values where the population mean is likely to be, then it is likely to be a confidence interval [(b) in the above list] and you are finished.

Step V.
Now determine whether the answer to the problem will be a percentage or proportion. (Examples: 'what percentage of individuals have IQs between 70 and 85?' 'What percentage of automobiles are traveling faster than 70 mph?') If the answer to the problem will be a percentage or proportion, then the problem is likely to be about the areas under a normal distribution [(a) in the above list]. There is one exception -- see Step VI.

Step VI.
The exception to Step V: Does the problem ask about the results of an opinion poll? (Example: 'What can we say about the percentage of all voters who favor Smith?') The answer to this question is a range of values, such as 52% plus or minus 3%. Therefore, this is a confidence interval for a proportion [(b) in the above list] and you are finished.



4. Test your skill on the following six problems. Answer each problem on a piece of scratch paper before pressing the Continue button.


#1. The following set of data represents the average number of blocks a sample of UNLV students walk to and from school each day. In order to be 95% certain of our statement, what would we say about the average distance students in general walk to and from school?

X: 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 6.
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.





















































Answer #1. The following set of data represents the average number of blocks a sample of UNLV students walk to and from school each day. In order to be 95% certain of our statement, what would we say about the average distance students in general walk to and from school?

X: 2, 2, 2, 2, 2, 3, 3, 3, 3, 5, 5, 6.
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.

Explanation: This asks for a range of values of mu, the average distance students in general walk to school. Therefore this is (b) a confidence interval.



#2. Suppose a researcher wants to determine if people eat "Bob's Ice Cream" faster than other ice creams. From his extensive research in the area, he knows that people eat a pint of ice cream with a mean of 24 hours, with a standard deviation of 10 hours. In his sample, the 36 people ate pints of Bob's with a mean 22 hours and a standard deviation of 8 hours. Do people actually eat Bob's Ice Cream faster than others' ice cream?
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.



















































Answer #2. Suppose a researcher wants to determine if people eat "Bob's Ice Cream" faster than other ice creams. From his extensive research in the area, he knows that people eat a pint of ice cream with a mean of 24 hours, with a standard deviation of 10 hours. In his sample, the 36 people ate pints of Bob's with a mean 22 hours and a standard deviation of 8 hours. Do people actually eat Bob's Ice Cream faster than others' ice cream?
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.

Explanation: It asks a Yes/No question ('Do people actually eat Bob's Ice Cream faster than others' ice cream?'), so it is a hypothesis test. There is only one sample (36 people at Bob's). The comparison of Bob's is to a population with mean mu of 24 hours, not to another sample. The standard deviation is known ('with a standard deviation of 10 hours'), so this is (c) a z test.



#3. The following set of data represents the average percentage scores of students on exams at UNLV. What percentage of students score above 90%?

X: 45, 60, 80, 82, 83, 85, 88, 89, 90, 93, 97, 99
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.



















































Answer #3. The following set of data represents the average percentage scores of students on exams at UNLV. What percentage of students score above 90%?

X: 45, 60, 80, 82, 83, 85, 88, 89, 90, 93, 97, 99
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.

Explanation: This involves finding a percentage, so the answer is (a) the area under the curve.



#4. Suppose a researcher wants to know if Pac-10 teams perform differently in the NCAA tournament than SEC teams. Studying past years, he finds that the last 10 Pac-10 teams won an average of 3.2 games with a variance of 1.2 games². However, he finds that the last 10 SEC teams have won an average of 3.7 games with variance of 1.9 games². Do SEC teams and Pac-10 teams perform differently?
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.



















































Answer #4. Suppose a researcher wants to know if Pac-10 teams perform differently in the NCAA tournament than SEC teams. Studying past years, he finds that the last 10 Pac-10 teams won an average of 3.2 games with a variance of 1.2 games². However, he finds that the last 10 SEC teams have won an average of 3.7 games with variance of 1.9 games². Do SEC teams and Pac-10 teams perform differently?
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.

Explanation: The problem asks a Yes/No question ('Do SEC teams and Pac-10 teams perform differently?'), so it is a hypothesis test. There are two groups, the 10 SEC teams and the 10 PAC teams. Therefore the answer is (e) a 2-sample t test.



#5. In a poll of 80 UNLV students, 60% were not satisfied with the amount of financial aid they were getting. What can we say about the proportion of students at UNLV that are satisfied with their financial aid?
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.



















































Answer #5. In a poll of 80 UNLV students, 60% were not satisfied with the amount of financial aid they were getting. What can we say about the proportion of students at UNLV that are satisfied with their financial aid?
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.

Explanation: This problem asks about an opinion poll, so the answer is (b) a confidence interval for a proportion




#6. Suppose a researcher wants to determine if people complete their projects at a company at a different rate after they get a raise. Because the researcher has studied the company many times before, she knows that on average, people complete their projects in 7 days. In her sample of 36 people who recently got raises, it was found that they were completing their projects in 8 days with a standard deviation of 1 day. Is their rate of project completion different?
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.



















































Answer #6. Suppose a researcher wants to determine if people complete their projects at a company at a different rate after they get a raise. Because the researcher has studied the company many times before, she knows that on average, people complete their projects in 7 days. In her sample of 36 people who recently got raises, it was found that they were completing their projects in 8 days with a standard deviation of 1 day. Is their rate of project completion different?
a. % area under the curve.
b. confidence interval.
c. 1 sample z test.
d. 1 sample t test.
e. 2 sample t test.

Explanation: This problem asks a Yes/No question ('Is their rate of project completion different?'), so it is a hypothesis test. There is only one group, the 36 people who got raises. The comparison is not to another group but to the population mean of long-term study results. The standard deviation that is reported is the standard deviation s of the sample, not the standard deviation sigma of the population. Therefore, this is (d) a one-sample t test


PART 3: THE QUIZ

Once you are comfortable with the distribution of variables, distributions of means, and their relationship, you are prepared to take the quiz.


You will need the quiz password, which is
7654321