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Sunny_sXe [5.5K]
3 years ago
8

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
Mathematics
1 answer:
ki77a [65]3 years ago
6 0

Answer:

a)

<em>Answer : d)</em>

Null hypothesis:-H₀ : p =0.8

Alternative Hypothesis :H₁: p < 0.8

<em>b)</em>

<em> Answer : c)0.77</em>

point estimate of the population proportion= 0.77

<em>c)</em>

<em> Answer : e)</em> -0.863

Step-by-step explanation:

<u><em>step(i)</em></u>:-

<em>Given Population proportion 'p' =80% = 0.80</em>

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

<em>Sample proportion or point estimation</em>

                      p^{-} = \frac{x}{n} = \frac{92}{120} =0.766

<em>Null hypothesis:-H₀ : p =0.8</em>

<em>Alternative Hypothesis :H₁: p < 0.8</em>

<em>Step(ii):-</em>

<em>Test statistic </em>

<em>  </em>Z = \frac{p^{-} -p}{\sqrt{\frac{p q}{n} } }<em></em>

<em>population proportion p =0.8</em>

<em>                                  q = 1-p = 1-0.8 =0.2</em>

<em></em>

<em>       </em>Z = \frac{0.77 -0.80}{\sqrt{\frac{0.80 x 0.20}{120} } }<em></em>

<em>      Z = -0.863</em>

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

<em>Null hypothesis is accepted </em>

<em>. 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.</em>

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