Question

Exercise 9-59 Algo In order to conduct a hypothesis test for the population proportion, you sample 400 observations that result in 212 successes. (You may find it useful to reference the appropriate table: z table or table) He: p > 0.54; HA: P < 0.54 a-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.) Test statistic a-2. Find the p-value 0.025 < p value <0.05 0.05 s p-value < 0,10 p-value 20.10 D-value < 0.01 0.01 s p-value <0.025 a-3. At the 0.01 significance level, What is the conclusion?

Answer 1

a-1)

sample success x   =		212
sample size          n    =		400
std error σp =√(p*(1-p)/n) =		0.0249
sample prop p̂ = x/n=212/400=		0.5300
z =(p̂-p)/σp=(0.53-0.54)/0.025=		-0.40

a-2)

Iv D-value 0.10

a-3)

Do not reject Hy since the p-value is greater than significance level

a-4)

We cannot conclude that the population proportion is less than 0.54

b-1)

z =(p̂-p)/σp=(0.53-0.54)/0.025=

-0.40

b-2)

p-value ? 0.10

b-3)

Do not reject Ho since the p-value is greater than significance level.

b-4)

We cannot conclude that the population proportion differs from 0.54.