Question

In: Statistics and Probability

A survey of 1000 students found that 274 chose professional baseball team A as their favorite team.

A survey of 1000 students found that 274 chose professional baseball team A as their favorite team. In a similar survey involving 760 students, 240 of them chose team A as their favorite. Compute a 95% confidence interval for the difference between the proportions of students favoring team A in the two surveys. Is there a significant difference?

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Expert Solution

Solution

p1=0.274

p2 = 0.316

n1=1000 n2 = 760

H0: p1 = p2

Ha: p1 not equals p2

Two tailed test for testing of proportions

--------------------------------------------------------------------------------------

Variance of sample I = pq/n1 =

0.000216

Variance of sample II =

0.000261742

Pooled std deviation = 0.0219

Z statistic can be used as sample size is large

Z = \frac{p1-p2}{se} = \frac{-0.042}{0.0219} = -1.92

As |Z| = 1.92 <=1.96 at 95% level, H0 is accepted.

That is there is no significant difference between the two popul ations.

SUN BUNRA answered 2 years ago
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