Question

In a sample of 47 adults selected randomly from church hill, it is found that 9 of them have been exposed to the flu this year test the claim that the proportion of all adults in church hill that have been exposed to the flu this year is more than 10% use A=0.1

A)claim, null hypo, alternative hypo

B) test to be used, what is the p-value

C) Classical approach test statistic, and the critical value?

E) What is the conclusion

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.10

H_a : p > 0.10

= x / n = 9 / 47 = 0.1915

P₀ = 0.10

1 - P₀ = 0.90

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.1915 - 0.10 / [(0.10 * 0.90) / 47]

= 2.09

P(z > 2.09) = 1 - P(z < 2.09) = 0.0183

P-value = 0.0183

= 0.1

Z _0.1 = 1.28

z > 1.28

Critical value = 1.28

Test statistic > critical value

Reject the null hypothesis .