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.
Solution :
This is the two tailed test .
The null and alternative hypothesis is
H0 : p = 0.17
Ha : 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 / [P0 * (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 .
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