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18.06.2020 •
Mathematics
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
Solved
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Ответ:
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
Step-by-step 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
Null hypothesis:-H₀ : p =0.8
Alternative Hypothesis :H₁: p < 0.8
Step(ii):-
Test statistic
population proportion p =0.8
q = 1-p = 1-0.8 =0.2
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.
Ответ: