Question

The data below show sport preference and age of participant from a random sample of members of a sports club. Test if sport preference is independent of age at the 0.05 significant level.

H₀: Sport preference is independent of age
Ha: Sport preference is dependent on age

	18-25	26-30	31-40	41 and over
Tennis	44	59	59	47
Swimming	57	77	46	66
Basketball	70	58	66	53

a. Complete the table: Give all answers as decimals rounded to 4 places.

Observed Frequency	Expected Frequency	(O−E)2E(O-E)2E
44
59
59
47
57
77
46
66
70
58
66
53
	Total

(b) What is the chi-square test-statistic for this data?
      Test Statistic: χ2=χ2=  

(d) The p-value is...

• less than (or equal to) αα
• greater than αα

(e) The p-value leads to a decision to...

• reject the null
• fail to reject the null

(f) What is the final conclusion?

• There is sufficient evidence to conclude sport preference is dependent on age.
• There is not sufficient evidence to conclude sport preference is dependent on age.

Answer 1

a) see value of expected in the corresponding column

Observed Frequencies(O)
	18-25	26-30	31-40	41 and over	Total
Tennis	44	59	59	47	209
Swimming	57	77	46	66	246
Basketball	70	58	66	53	247
Total	171	194	171	166	702
Expected Frequencies(E)
	18-25	26-30	31-40	41 and over	Total
Tennis	171 * 209 / 702 = 50.9103	194 * 209 / 702 = 57.7578	171 * 209 / 702 = 50.9103	166 * 209 / 702 = 49.4217	209
Swimming	171 * 246 / 702 = 59.9231	194 * 246 / 702 = 67.9829	171 * 246 / 702 = 59.9231	166 * 246 / 702 = 58.1709	246
Basketball	171 * 247 / 702 = 60.1667	194 * 247 / 702 = 68.2593	171 * 247 / 702 = 60.1667	166 * 247 / 702 = 58.4074	247
Total	171	194	171	166	702
	(O-E)²/E
Tennis	(44 - 50.9103)²/50.9103 = 0.938	(59 - 57.7578)²/57.7578 = 0.0267	(59 - 50.9103)²/50.9103 = 1.2855	(47 - 49.4217)²/49.4217 = 0.1187
Swimming	(57 - 59.9231)²/59.9231 = 0.1426	(77 - 67.9829)²/67.9829 = 1.196	(46 - 59.9231)²/59.9231 = 3.235	(66 - 58.1709)²/58.1709 = 1.0537
Basketball	(70 - 60.1667)²/60.1667 = 1.6071	(58 - 68.2593)²/68.2593 = 1.542	(66 - 60.1667)²/60.1667 = 0.5656	(53 - 58.4074)²/58.4074 = 0.5006

b) Test statistic:

χ² = ∑ ((O-E)²/E) = 12.2114

df = (r-1)(c-1) = 6

d) p-value:

p-value = CHISQ.DIST.RT(12.2114, 6) = 0.0574

p-value > α

e) Decision:

fail to reject the null

f) Conclusion:

There is not sufficient evidence to conclude sport preference is dependent on age.