Question

In a recent poll, 1,000 Americans were asked how well the term patriotic described them. Some results from the poll are contained in the following summary table.

	Age Group
	All	18–34	60+
Very well	0.53	0.34	0.75
Somewhat well	0.31	0.44	0.17
Not Very well	0.10	0.14	0.03
Not well at all	0.06	0.08	0.05

(a)

If the 18–34 and 60+ age groups consisted of 340 and 150 individuals, respectively, find a 98% confidence interval for the difference in proportions of those in these age groups who agreed that patriotic described them very well. (Use the (60+ age group) − (the 18–34 age group). Round your answers to two decimal places.)

,

(b)

Based on the interval that you obtained in part (a), do you think that the difference in proportions of those who view themselves as patriotic is as large as 0.6? Explain.

The upper endpoint of the interval is greater than 0.6, so there is evidence that the true difference in proportions is as large as 0.6. The upper endpoint of the interval is greater than 0.6, so there is not compelling evidence that the true difference in proportions is as large as 0.6.     The upper endpoint of the interval is less than 0.6, so there is evidence that the true difference in proportions is as large as 0.6. The upper endpoint of the interval is less than 0.6, so there is not compelling evidence that the true difference in proportions is as large as 0.6.

Answer 1

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a) 98% confidence Interval is ( 0.29608 , 0.52392 )

b)

The upper endpoint of the interval is less than 0.6, so there is not compelling evidence that the true difference in proportions is as large as 0.6.