Question

John polled the Russian public about Vladimir Putin's popularity for a very long time before the 2000 election. The proportions in this problem come from their findings; the sample sizes are made up but are consistent with their polling techniques.

1. (a) In May 2000, 478 of 783 Russians surveyed had a “highly favorable” or “somewhat favorable” opinion of Vladimir Putin. Test the hypothesis that less than 64% of Americans had an opinion this high of Vladimir Putin's at a significance level of α = .1.

2. (b) In August 1996, 41% of 635 Russians surveyed had a “highly favorable” opinion of Vladimir Put-on; in August 1997, 33% of 696 did. Test the hypothesis that this opinion was held by at least 5% more of the American public in August 1966 than it was in August 1967 at a significance level of α = .05.

Answer 1

(a) The hypothesis being tested is:

H0: p = 0.64

Ha: p < 0.64

Observed	Hypothesized
0.6105	0.64	p (as decimal)
478/783	501/783	p (as fraction)
478.	501.12	X
783	783	n
	0.0172	std. error
	-1.72	z
	.0426	p-value (one-tailed, lower)

The p-value is 0.0426.

Since the p-value (0.0426) is less than the significance level (0.10), we can reject the null hypothesis.

Therefore, we can conclude that p < 0.64.

(b) The hypothesis being tested is:

H0: p1 - p2 0.05

Ha: p1 - p2 < 0.05

p1	p2
0.41	0.33	p (as decimal)
260/635	230/696	p (as fraction)
260.35	229.68	X
635	696	n
	0.08	difference
	0.05	hypothesized difference
	0.0264	std. error
	1.14	z
	.8718	p-value (one-tailed, lower)

The p-value is 0.8718.

Since the p-value (0.8718) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we cannot conclude that p1 - p2 0.05.

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