Question

Journalists periodically muse about whether taller candidates win presidential elections. I will provide you with a random sample of 20 president's heights along with the heights of their main opponent in the election. I will send out these samples by Canvas email on Wed. June 3. Please conduct a hypothesis test to investigate the claim that the taller candidate wins the election. In your write-up, you should include: 1) the parameter you are testing in English) 2) the null and alternative hypotheses about that parameter 3) a check of the conditions (including sketches of any graphs you use) 4) the name of the test you are using and why 5) the test statistic (including what you entered in your calculator to find this) 6) the P-value (including a sketch of the distribution with the middle and the test statistic labeled, and the P-value shaded) 7) your decision about the hypotheses and 8) a conclusion in context
Carry out the test even if you find the conditions are not met, but make a note of that. Use a significance level of 2%. Give your answers to 4 decimal places.

(president)   (opponent)
188 173
185 177
178 180
180 168
180 178
173 178
189 170
163 191
193 173
191 165
178 174
188 173
178 175
178 196
182 180
177 168
183 187
182 180
182 180
175 163

Answer 1

The parameter is the president's heights along with the heights of their main opponent.

The normality plot is:

The normality condition is met.

The hypothesis being tested is:

H0: µd = 0

Ha: µd ≠ 0

The Paired t-test will be used here.

The test statistic is 1.653.

The p-value is 0.1148.

Since the p-value (0.1148) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that taller candidates win presidential elections.

(president)	(opponent)	d
188	173	15
185	177	8
178	180	-2
180	168	12
180	178	2
173	178	-5
189	170	19
163	191	-28
193	173	20
191	165	26
178	174	4
188	173	15
178	175	3
178	196	-18
182	180	2
177	168	9
183	187	-4
182	180	2
182	180	2
175	163	12
	181.150	mean (president)
	176.450	mean (opponent)
	4.700	mean difference ((president) - (opponent))
	12.716	std. dev.
	2.843	std. error
	20	n
	19	df
	1.653	t
	.1148	p-value (two-tailed)

The distribution is:

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