Q5. (5 points) Researchers were interested in determining whether soccer players

Question

Q5. (5 points) Researchers were interested in determining whether soccer players performed better or worse in front of an audience. Players were identified as either highly skilled or low skilled. They were then randomly assigned to either play in front of a crowd or alone. The percentage of goals made was recorded and compared a. State the null and alternate hypotheses. Include both interaction and main effect hypotheses (should be 3 null and 3 alternate hypotheses) b. What is the total sample size? c. Identify the independent and dependent variables d. List the test statistic and p value for the all your hypotheses? (Hint, there should be 3) e. What is your conclusion (assume a 05) f. What is the effect size? Descriptive Statistics Audience Mean Std. Deviation 249 249 498 Unskilled Alone 50.32 30.12 40.22 70.535.805498 5.953 6.0922 Audience Total 11.762 Skilled Audience Total Alone Audience Total 9.666.260 80.09 60.42 59.89 60.16 11.318 11.813 30386996 23.043 Total 498 498 Tests of Between-Subjects Effects Dependent Variable: percent.goals Type IlIl Sum of Partial Eta Squared Squares df Mean Square Sig ntercept 3604464.748 69.447 395883.985 96288.001 69.447 96288.001 3604464.748 51902.541 003 1.000 69.447 395883.985 96288.001 804 Error Audience 69.447 001 983 001 96288.001 96288.001 96288.00136.360 Skill Audience Hypothesis 2648.207 .000 727 Error 36068.819 992

Explanation / Answer

Answer:

Part a)

The null and alternative hypotheses for the given scenario are given as below:

Hypothesis 1

Null hypothesis: H0: There is no any statistically significant difference in the percentage of goals by the skilled and unskilled soccer players.

Alternative hypothesis: Ha: There is a statistically significant difference in the percentage of goals by the skilled and unskilled soccer players.

Hypothesis 2

Null hypothesis: H0: There is no any statistically significant difference in the percentage of goals by players playing alone and playing in front of audience.

Alternative hypothesis: Ha: There is a statistically significant difference in the percentage of goals by players playing alone and playing in front of audience.

Hypothesis 3

Null hypothesis: H0: There is no any statistically significant interaction between type of skilled player and presence of audience.

Alternative hypothesis: Ha: There is a statistically significant interaction between type of skilled player and presence of audience.

Part b)

Total sample size is given as 249 + 249 = 498.

Part c)

The dependent variable for this test is given as percent goals. The independent variables for this test are given as skill and audience.

Part d

The hypothesis, value for test statistic, and p-values are given as below:

Hypothesis 1

Null hypothesis: H0: There is no any statistically significant difference in the percentage of goals by the skilled and unskilled soccer players.

Alternative hypothesis: Ha: There is a statistically significant difference in the percentage of goals by the skilled and unskilled soccer players.

Test statistic = F = 4.111

P-value = 0.292

Hypothesis 2

Null hypothesis: H0: There is no any statistically significant difference in the percentage of goals by players playing alone and playing in front of audience.

Alternative hypothesis: Ha: There is a statistically significant difference in the percentage of goals by players playing alone and playing in front of audience.

Test statistic = F = 0.001

P-value = 0.983

Hypothesis 3

Null hypothesis: H0: There is no any statistically significant interaction between type of skilled player and presence of audience.

Alternative hypothesis: Ha: There is a statistically significant interaction between type of skilled player and presence of audience.

Test statistic = F = 2648.207

P-value = 0.00

Part e

Conclusions:

Hypothesis 1

Null hypothesis: H0: There is no any statistically significant difference in the percentage of goals by the skilled and unskilled soccer players.

Alternative hypothesis: Ha: There is a statistically significant difference in the percentage of goals by the skilled and unskilled soccer players.

Test statistic = F = 4.111

P-value = 0.292

= 0.05

P-value > = 0.05

So, we do not reject the null hypothesis.

There is insufficient evidence to conclude that there is a statistically significant difference in the percentage of goals by the skilled and unskilled soccer players.

Hypothesis 2

Null hypothesis: H0: There is no any statistically significant difference in the percentage of goals by players playing alone and playing in front of audience.

Alternative hypothesis: Ha: There is a statistically significant difference in the percentage of goals by players playing alone and playing in front of audience.

Test statistic = F = 0.001

P-value = 0.983

= 0.05

P-value > = 0.05

So, we do not reject the null hypothesis.

There is insufficient evidence to conclude that there is a statistically significant difference in the percentage of goals by players playing alone and playing in front of audience.

Hypothesis 3

Null hypothesis: H0: There is no any statistically significant interaction between type of skilled player and presence of audience.

Alternative hypothesis: Ha: There is a statistically significant interaction between type of skilled player and presence of audience.

Test statistic = F = 2648.207

P-value = 0.00

= 0.05

P-value < = 0.05

So, we reject the null hypothesis.

There is sufficient evidence to conclude that there is a statistically significant interaction between type of skilled player and presence of audience.

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