Question

A housing loan corporation states that it sanctions 80% of all housing loans within 7 working days once the verification process is completed. A customer group believes that all housing loans applied to this corporation that are settled within 7 working days is less than 80% of all housing loans. In a sample of 120 housing loan applications, the group found that 92 were settled within 7 working days.

State the null and the alternative hypotheses.
H_0: p = 0.8 vs. H_a: p notequalto 0.8
H_0: p = 0.8 vs. H_a: p > 0.8
H_0: p = 0.8 vs. H_a: p lessthanorequalto 0.8
H_0: p = 0.8 vs. H_a: p greaterthanorequalto 0.8
H_0: p = 0.8 vs. H_a: p < 0.8
Find the point estimate of the population proportion.
0.80
0.23
0.77
0.50
0.20
Calculate the value of the test statistic.
-0.933
0.913
0.933
-0.913
-0.863

Answer 1

a)

Answer : d)

Null hypothesis:-H₀ : p =0.8

Alternative Hypothesis :H₁: p < 0.8

b)

Answer : c)0.77

point estimate of the population proportion= 0.77

c)

Answer : e) -0.863

Explanation:

step(i):-

Given Population proportion 'p' =80% = 0.80

Given a sample of 120 housing loan applications, the group found that 92 were settled within 7 working days.

Sample proportion or point estimation

`p^(-) = (x)/(n) = (92)/(120) =0.766`

Null hypothesis:-H₀ : p =0.8

Alternative Hypothesis :H₁: p < 0.8

Step(ii):-

Test statistic

`Z = \frac{p^(-) -p}{\sqrt{(p q)/(n) } }`

population proportion p =0.8

q = 1-p = 1-0.8 =0.2

`Z = \frac{0.77 -0.80}{\sqrt{(0.80 x 0.20)/(120) } }`

Z = -0.863

|Z| = | -0.863| = 0.863 < 1.96 at 0.05 level of significance

Null hypothesis is accepted

. A customer group believes that all housing loans applied to this corporation that are settled within 7 working days is equal to the 80% of all housing loans.