Question

1. (3 pts) Use data given. You are trying to evaluate which golf ball goes the furthest distance. a. Set up your null and alternative hypotheses.

Use PHStat –> Multi-Sample Tests -> One Way ANOVA select the Tukey-Kramer Proceedure checkbox. Get the P-value from the ANOVA sheet generated. Use the p-value to find your confidence and write up a short conclusion.

Your report should include:

• Hypotheses

• Output from Descriptive Statistics that check assumptions. If there are assumption issues then explain how they might affect your results.

• Output from excel that give you the P-value.

• A write-up that details how confident you are that the means differ and if they do, how they differ. If there were assumption issues account for these in your conclusions (for example, if the normality of the data was in question but the p-value was very high your conclusion may still be valid).

Design1	Design2	Design3	Design4
199.78	217.27	224.11	207.28
200.38	211.46	236.22	199.22
201.37	217.31	226.33	201.96
201.55	223.31	228.52	202.25
202.9	211.99	221.44	194.97
201.47	230.05	230.36	198.75
198.98	214.81	231.48	201.9
201.67	220.93	220.15	206.19
200.99	217.71	223.31	196.15
201.7	221.5	232.12	201.15

Answer 1

The hypothesis being tested is:

H₀: µ₁ = µ₂ = µ₃ = µ₄

H_a: At least one means is not equal

	Mean	n	Std. Dev
	201.079	10	1.1106	Design1
	218.634	10	5.5815	Design2
	227.404	10	5.2016	Design3
	200.982	10	3.9130	Design4
	212.025	40	12.2917	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	5,219.5529	3	1,739.85096	93.10	5.02E-17
Error	672.7913	36	18.68865
Total	5,892.3442	39

The p-value is 0.000.

Since the p-value (0.000) is less than the significance level (0.05), we can reject the null hypothesis.

Therefore, we can conclude that at least one means is not equal.

Using the Tukey Method and 90% Confidence

Factor	N	Mean	Grouping
Design3	10	227.40	A
Design2	10	218.63		B
Design1	10	201.079			C
Design4	10	200.98			C

Means that do not share a letter are significantly different.

The plot is:

All the assumptions are met.