Question

A building company claims that 70% of all new houses they build are finished within 3 weeks. A study show that, over 45 new houses, only 20 have been done in 3 weeks. Does the company claim valid at a level of significance of 0.05 and 0.01

Answer 1

Calculated z= 3.515

The Z∝/2 = ±1.96 for ∝= 0.05

The Z∝/2 = ± 2.58 for ∝= 0.01

Yes the company claims valid at a level of significance of 0.05 and 0.01

Explanation:

Here p1= 70% = 0.7

p2= 20/45= 0.444 q= 1-p= 1-.444= 0.56

The level of significance is 0.05 and 0.01

The null and alternative hypotheses are

H0; p1= p2 Ha: p1≠p2

The test statistic used here is

Z= p1-p2/ √pq/n

Z= 0.7-0.44/ √ 0.44*0.56/45

z= 0.26/ √0.2464/45

z= 3.515

The Z∝/2 = ±1.96 for ∝= 0.05

The Z∝/2 = ± 2.58 for ∝= 0.01

For the significance level 0.05 reject null hypothesis

For the significance level 0.01 reject null hypothesis

Yes the company claims valid at a level of significance of 0.05 and 0.01