Question

According to the most recent census, 16.3% of US residents are of Hispanic origin. One county supervisor believes her county has a smaller percentage than what was reported in the census. A survey of 220 individuals in the county was conducted, and each person was asked to report their origin. It was found that 10.02% of those surveyed identified as being of Hispanic origin. Test the appropriate hypotheses using a significance level of 0.05.

• H0:H0: Select an answer p̂ p  ? = > ≠ <     Ha:Ha: Select an answer p̂ p  ? > ≠ <  
• αα =    decision rule: reject H0H0 if probability ? > ≠ <   αα
• Test Statistic: z =   (Note: round the z-score to two decimal places - carry at least four decimal places throughout all of your calculations)
• probability =   (Note: round the probability to four decimal places)
• Decision: Select an answer Reject H₀ Fail to reject H₀
• Conclusion: At the 0.05 level, there Select an answer is not is  significant evidence to conclude the percentage of residents in this county who are of Hispanic origin is Select an answer less than greater than different than  16.3%.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.163

H_a : p 0.163

n =220

= 0.1002

P₀ = 0.163

1 - P₀ = 1 - 0.163

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1002 - 0.163 / [0.163 * 0.837 / 220 ]

= −2.53

Test statistic = z = −2.53

P-value = 0.0114

= 0.05

P-value <

0.0114 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that