Question

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 488 county​ residents, and found that 42 of those surveyed are of Hispanic origin.

Calculate the test statistic (z score) and the P-value  

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H0 : p = 0.17

Ha : p 0.17

= x / n = 42 /488 = 0.086

P0 = 0.17

1 - P0 = 1 -0.17 = 0.83

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

= 0.086 - 0.17/ [0.17 * (0.83) /488 ]

= -4.936

P(z < -4.936) = 0

P-value = 0.0000