Question

	1970’s	1980’s	1990’s
	97	105	78
	105	108	87
	109	106	90
	87	114	87
	96	111	113
	102	111	90
	102	115	99
	114	114	97
	118	102	108
	113	123	92

This table uses the data file that contains the scores of the winning teams from the final NBA Championship game. I would like to know if the average winning score is the same for each decade listed in the table. Test the claim that the samples all come from populations with the same mean. Use a significance level of 0.05.

  

• Mean of 1970’s data:

• Mean of 1980’s data:

• Mean of 1990’s data:

• Write each statement:

• (null hypothesis):
• (alternative hypothesis):
• Write the “test statistic” here:
• Write the P-value here:

REJECT    YES or NO

• What is your conclusion? Do all of the samples come from populations with the same mean or is at least one group different?

Answer 1

• Mean of 1970’s data:

• Mean of 1980’s data:

• Mean of 1990’s data:

In this example, the hypotheses are:

Null hypothesis There is no significant difference in the average winning score in each decade.
Alternative hypothesis At least one the average winning score is different among the three decade.

Null hypothesis H₀: μ₁ = μ₂ = μ₃ = μ₄

Alternative hypothesis H₁: The means are not all equal.

Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Decade 3 1970’s, 1980’s, 1990’s

The test statistic for testing H₀: μ₁ = μ₂ = ... = μ4 is:

The test statistic for testing H₀: μ₁ = μ₂ = ... = μ4 is:

where

• = individual observation,

• = sample mean of the j^th treatment (or group),
• = overall sample mean,
• k = the number of treatments or independent comparison groups, and
• N = total number of observations or total sample size.

In order to determine the critical value of F we need degrees of freedom, df₁=k-1 and df₂=N-k. In this example, df₁=k-1=3-1=2 and df₂=N-k=30-3=27.

The critical value is

and the decision rule is as follows: Reject H₀ if F > 3.3541.

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Factor	2	1433	716.4	9.12	0.0009
Error	27	2122	78.59
Total	29	3555

P-value=0.0009

Conclusion:

We reject H₀ because F-value=9.12 > F-critical value= 3.3541 and also P-value=0.0009< level of significance=0.05.

We have statistically significant evidence at α=0.05

Hence, At least one the average winning score is different among the three decade.