Question

I keep getting the z score wrong on this question? Please advise

According to a recent​ census,17​% of the people in the United States are of Hispanic origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey​ data, which was a random sample of 493 county​ residents, and found that 50 of those surveyed are of Hispanic origin.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.17

H_a : p 0.17

n = 493

x = 50

= x / n = 50 / 493 = 0.1014

P₀ = 0.17

1 - P₀ = 1 - 0.17 = 0.83

z = - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1014 - 0.17 / [(0.17 * 0.83) / 493]

= -4.05

Test statistic =

P(z < -4.05) = 0

P-value = 2 * 0 = 0

= 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to that the county supervisor believes her county has a different proportion of

Hispanic people than the nation as a whole .