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# Testing of hypothesis problems

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I need help with these nine stat. questions.

They come in two labs. Lab 6 and 7 and you need to use the data in the excel.

I need to use the top half of the lab to answer the questions for the bottom half of the lab.

Thank You
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The goal of this lab is to learn about hypothesis testing (This lab is out of 13 points).

Use V3, the salaries of your 40 hitters, as the variable x you're interested in learning about on this lab.

MAKE SURE TO HAND IN THE ANSWER SHEET ONLY WHEN YOU HAND IN LAB 6!

(2 points) 1. Use Excel to compute the mean and standard deviation of your data. If you don't remember how to do this, refer back to the instructions on page 2 of Lab 2.

Also, sort your data and write down the 16th value (call that L) and the 25th value (call that H). You will use your values for the sample mean, the sample standard deviation, L and H in the rest of this problem. Assume that the sample standard deviation is the true standard deviation.

(1 points) 2. What is the standard deviation of the mean? Remember that your sample size is 40.

(4 points) 3. You will now test the hypothesis that the true mean is equal to L (the number you wrote
down in Question 1) against the alternative that the true mean is less than L.

i) Write down the null and alternative hypotheses.
ii) Is this a one-tailed test or a two-tailed test?
iii) What is the critical value for this test if ? Please make sure to state your
value.
iv) Do we accept or reject the null hypothesis that the true mean is equal to L at the
5% significance level?

(4 points) 4. Now you will test the hypothesis that the true mean is equal to H (the number you wrote
down in Question 1) against the alternative that the true mean is not equal to H.

i) Write down the null and alternative hypotheses.
ii) Is this a one-tailed test or a two-tailed test?
iii) What are the critical values for this test if ? Please make sure to state
a z-value.
iv) Do we accept or reject the null hypothesis that the true mean is equal to H at the
10% significance level?

(2 points) 5. If you accepted the null hypothesis in problem 4, what is the smallest significance level
at which you would be able to reject the null hypothesis? If you rejected the null
hypothesis in problem 4, what is the biggest significance level for which you could
accept the null hypothesis?

You should hand in only the answer sheets (in your folder with the previous labs, of course) when you hand in Lab 6. Make sure to include all your work on these problems.

1.
Sample mean = = ______________
Standard deviation = = _____________
L = _________________
H = __________________

2.

3.
i) Null hypothesis H0: ___________________________

Alternative hypothesis H1: _________________________

ii) Circle one: One-tailed test Two-tailed test

iii)

iv) Circle one: Accept H0 Reject H0

4.
i) Null hypothesis H0: ___________________________

Alternative hypothesis H1: _________________________

ii) Circle one: One-tailed test Two-tailed test

iii)

Answer: Lower critical value = _______________; Higher critical value = ________________

iv) Circle one: Accept H0 Reject H0

5.

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The goal of this lab is to learn about chi-squared testing (This lab is out of 12 points).

For this lab you will use chi-square testing to see if there is a significant relationship between slugging percentage (your V2) and salary (your V3) for your 40 players.

MAKE SURE TO HAND IN THE ANSWER SHEET ONLY WHEN YOU HAND IN LAB 7!

(2 points) 1. Use Excel to find the mean of your players' slugging percentages and the mean of your players' salaries. Classify each of your 40 observations as falling into one of the following four categories.

1. Value of slugging percentage is less than or equal to the mean and value of salary is less than or equal to the mean.
(slugging percentage low, salary low)

2. Value of slugging percentage is less than or equal to the mean, but value of salary is greater than the mean.
(slugging percentage low, salary high)

3. Value of slugging percentage is greater than the mean, but value of salary is less than or equal to the mean.
(slugging percentage high, salary low)

4. Value of slugging percentage is greater than the mean and value of salary is greater than the mean.
(slugging percentage high, salary high)

Enter into the table the frequencies of each of these categories in your data. The four
numbers that you enter in the table should add up to 40.

On the next page, there is an example of how you need to classify your observations for
this problem.

(2 points) 2. If slugging percentage and salary are independent, then we would expect that salary is equally likely to be high, regardless of whether slugging percentage is high or low. Given the sums of the two rows and two columns that you found in problem 1, what would you expect the table to look like if slugging percentage and salary are independent? Round your answers to the nearest tenth.

(Hint: If slugging percentage and salary are independent, then the probability of salary being low (or high) does not depend on whether slugging percentage is low or high. So the fraction of the observations in column 1 that are in row 1 should be the same as the fraction of observations in column 2 that are in row 1.)

(6 points) 3. Using the tables from problems 1. and 2., test at the 5% significance level the hypothesis that slugging percentage and salary are independent. Your null hypothesis is that they are independent and the alternative hypothesis is that they are dependent.

i) The test statistic follows a chi-square distribution with how many
degrees of freedom?
ii) What is the value of the test statistic?
iii) What is the critical value for this test?
iv) Do you reject the hypothesis that slugging percentage and salary are independent at the 5% significance level?

(2 points) 4. In two sentences, describe at least two things you've learned by analyzing

Example for problem 1:

Suppose that my mean slugging percentage was 0.425 and my mean salary was \$1,500,000. Then suppose the table below describes slugging percentage and salary for three players:

Cirillo, Jeff IF 0.293 6975000
Davis, Ben C 0.4 1400000

Each of these players goes into the following categories.

Slugging percentage
low Slugging percentage
high Total
Salary low Ben Davis Johnny Estrada
Salary high Jeff Cirillo
Total

For example, Jeff Cirillo goes into the lower-left box because his slugging percentage (0.293) is below the mean and his salary (\$6,975,000) is above the mean.

You need to classify each of your forty players by comparing their slugging percentages and salaries to the means for each variable. Be careful to make sure to you use your mean for slugging percentage and your mean for salary, and not the numbers used in this example.

You should hand in only this sheet (in your folder with the previous labs, of course) when you hand in Lab 7. You should include all your work on these problems.

1.
Slugging percentage
low Slugging percentage
high Total
Salary low
Salary high
Total

2. Start by writing the column and row totals from the table above in the below table. Then fill in the four cells that have "Answer:" written in them.

Slugging percentage
low Slugging percentage
high Total
Total

3.

i) Degrees of freedom = ________

ii)
Test statistic = _____________

iii)

Critical value = _____________________

iv) Circle one: Accept H0 Reject H0

4.