Question

1)

You are asked the conduct the following hypothesis test concerning a population proportion:

H₀: prop = 0.27

H_A: prop < 0.27

You draw a sample of size 248 from the population. There are 51 individuals in the sample who satisfy the criteria in which we are interested. Calculate the p-value for this test.

Round your answer to 4 decimal places.

2)

You are asked the conduct the following hypothesis test concerning a population proportion:

H₀: prop = 0.43

H_A: prop > 0.43

You draw a sample of size 429 from the population. There are 198 individuals in the sample who satisfy the criteria in which we are interested. Calculate the p-value for this test.

Round your answer to 4 decimal places.

Answer 1

Solution ;

1 ) Given that,

This is the left tailed test .

The null and alternative hypothesis is

H₀ : p = 0.27

H_a : p < 0.27

n = 248

x = 51

= x / n = 51 / 248 =0.206

P₀ = 0.27

1 - P₀ = 1 - 0.27 = 0.73

z = - P₀ / [P_{0 *} (1 - P₀ )/ n]

= 0.206 - 0.27 / [0.27 *(1 - 0.27) / 248]

= - 2.28

z = - 2.28

P value = 0.0113

2 ) Given that,

This is the right tailed test .

The null and alternative hypothesis is

H₀ : p = 0.43

H_a : p > 0.43

n = 429

x = 198

= x / n = 198 / 429 = 0.461

P₀ = 0.43

1 - P₀ = 1 - 0.43 = 0.57

z = - P₀ / [P_{0 *} (1 - P₀ )/ n]

= 0.461 - 0.43 / [0.43 *(1 - 0.43) / 429]

= 1.32

z = 1.32

This is the right tailed test .

P(z > 1.32 ) = 1 - P(z < 1.32 ) = 1 - 0.9066

P-value = 0.0934