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torresq6647
16.11.2020 •
Mathematics
In manufacturing processes, it is of interest to know with confidence the proportion of defective parts. Suppose that we want to be reasonably certain that less than 4% of a company’s widgets are defective. To test this, we obtain a random sample of 250 widgets from a large batch. Each of the 250 widgets is tested for defects, and 6 are determined to be defective, based upon the manufacturer’s standards. Using α = 0.01, is this evidence that less than 4% of the company’s widgets are defective? State the hypotheses, list and check the conditions, calculate the test statistic, find the p-value, and make a conclusion in a complete sentence related to the scenario.
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Ответ:
The calculated value Z = 1.3114 < 2.576 at 0.01 level of significance
null hypothesis is accepted
The evidence that less than 4% of the company’s widgets are defective
Step-by-step explanation:
Step(i):-
Given Population proportion
P = 4% = 0.04
Given sample proportion
Null hypothesis :- P < 0.04
Alternative Hypothesis : P ≠ 0.04
Step(ii):-
Test statistic
Z = - 1.3114
|Z| = | - 1.3114|
The tabulated value Z = 2.576
The calculated value Z = 1.3114 < 2.576 at 0.01 level of significance
null hypothesis is accepted
The evidence that less than 4% of the company’s widgets are defective
Ответ:
Yes it is true left side is the most simplified on the right 2x-x is x-3
x-3=x-3