Question

Quantitative Variable we are interested in comparing: # of HR’s (Home Run’s)

American League:                                                                National League:

Sample Size:                                      28                                Sample Size:                                      22

Sample Mean:                                   20.14286                        Sample Mean:                                   18.77

Sample Standard Deviation:           10.44107                        Sample Standard Deviation:            8.257

You are now going to do a two-sample hypothesis test on this data

Hypothesis: I would expect an American League player to hit more HR’s (Home Run’s) on average, than a National League Player?

1. Introduction: State the topic of your study and the hypothesis you’re interested in testing. Your hypothesis should note a statistically significant result that you expected to find and the rationale for why you expected this result.

2. Define Populations: Define clearly the populations that you intend for your study to represent. (Examples: all NFL football players on two different teams, all cars manufactured this year for Ford and Chevy, all biology and chemistry majors at your school, etc.)
3. Define Variables: Define clearly the variables that you are using (Examples: Comparing ages, salaries, prices, miles per gallon, scores on test, etc.).
4. Results: Descriptive Statistics: Give descriptive statistics for each data set.
   1. Table: Give sample size, mean, and standard deviation for each data set.
5. Study Design: Identify the statistical test you conducted to analyze your data. Was it left-tailed, right-tailed, or two-tailed? State the null and alternative hypotheses, both in words and in appropriate symbols.

Identifying the statistical test we conducted to analyze our data:

Left-tailed, right-tailed, or two-tailed?

6. Results: Statistical Analysis: Report the results of your test. Include the test statistic, degrees of freedom, and the p-value of the significance test. Please use Excel to complete.

Test Statistic:

Degrees of freedom:

P-Value:

7. Findings: Interpret the results in the context of your original research question. Do your analyses support your expected findings? Explain. Interpret the p-value and compare it to an alpha level of .05 (draw a conclusion on the test).
8. Discussion: What conclusions, if any, do you believe you can draw as a result of your study? If the results were not what you expected, what factors might explain your results? What did you learn from the project about the populations you studied? What did you learn about the research variable? What did you learn about the specific statistical test you conducted?

Answer 1

Let µ₁ be American League.

Let µ₂ be National League.

The hypothesis being tested is:

H₀: µ₁ = µ₂

H₁: µ₁ > µ₂

The calculations are:

American League	National League
20.14286	18.77	mean
10.44107	8.257	std. dev.
28	22	n
	48	df
	1.3728600	difference (American League - National League)
	91.1493642	pooled variance
	9.5472176	pooled std. dev.
	2.7200161	standard error of difference
	0	hypothesized difference
	0.505	t
	.3080	p-value (one-tailed, upper)

Test Statistic: 0.505

Degrees of freedom: 48

P-Value: 0.3080

Since the p-value (0.3080) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that American League players hit more HR’s (Home Run’s) on average than a National League Player.