Answer:
a)<em> Null hypothesis : H₀</em>: the proportion of defective item of computer has been lowered. That is P < 0.15
<u><em>Alternative hypothesis: H₁:</em></u> The proportion of defective item of computer
has been higher. That is P> 0.15 (Right tailed test)
b) Test statistic
c) Calculate the value of the test statistic = 0.991
d) The critical value at 0.01 level of significance = Z₀.₀₁ = 2.57
e) Null hypothesis accepted at 0.01 level of significance
f) we accepted null hypothesis.
Hence t<em>he proportion of defective item of computer has been lowered. </em>
Step-by-step explanation:
<u>Step(i)</u>:-
<em>Given the sample size 'n' = 42</em>
Given random sample of 42 computers were tested revealing a total of 4 defective computers.
The defective computers 'x' = 4
<em>The sample proportion of defective computers </em>
<em>Given The Population proportion 'P' = 0.15</em>
<em>The level of significance ∝=0.01</em>
<u>Step(ii)</u>:-
a)<em> Null hypothesis : H₀</em>: the proportion of defective item of computer has been lowered. That is P < 0.15
<u><em>Alternative hypothesis: H₁:</em></u> The proportion of defective item of computer
has been higher. That is P> 0.15 (Right tailed test)
b)
Test statistic
c)
Calculate the value of the test statistic Z = - 0.9991
|Z| = |- 0.9991| = 0.991
<u>Step(iii)</u>:-
d)
The critical value at 0.01 level of significance = Z₀.₀₁ = 2.57
e) Calculate the value of the test statistic Z = 0.991 < 2.57 at 0.01 level of significance.
<u><em>Conclusion</em></u>:-
Hence the null hypothesis is accepted at 0.01 level of significance.
f)
<em> The proportion of defective item of computer has been lowered.</em>