Question

in 2014 the pew research centers American trend panel sought to better understand what americans know about science. it was observed that among a random selection of 3278 adults, 2065 adults could correctly interpret a scatterplot. is this good evidence that more than 60% of Americans are able to correctly interpret scatterplots?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.60

H_a : p > 0.60

= x / n = 2065 / 3278 = 0.63

P₀ = 0.60

1 - P₀ = 0.40

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.63 - 0.60 / [(0.60 * 0.40) / 3278]

= 3.50

P(z > 3.50) = 1 - P(z < 3.50) = 0.0002

P-value = 0.0002

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to suggest that good evidence that more than 60% of Americans are

able to correctly interpret scatter plots .