In a random sample of 400 items where 82 were found to be defective, the null hypothesis that 20% of the items in the population are defective produced ZSTAT=+0.25. Suppose someone is testing the null hypothesis H0: π=0.20 against the two-tail alternative hypothesis H1: π≠0.20 and they choose the level of significance α=0.01. What is their statistical decision? What is the statistical decision? Determine the p-value. The p-value for the given ZSTAT is p-value=nothing. (Type an integer or a decimal. Round to three decimal places as needed.)

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belgrad belgrad · Answer 1 · 2020-12-24T03:28:25+01:00

Answer:

Z - statistic = 0.25

P-value

P(Z=0.25) = 0.802587

The result is not significant at p<0.01

Step-by-step explanation:

Step(i):-

Given the random sample size 'n'' = 400

A random sample of 400 items where 82 were found to be defective

Sample proportion

[tex]p = \frac{x}{n} = \frac{82}{400} = 0.205[/tex]

Given Population proportion

P = 0.20

Null Hypothesis : P = 0.20

Alternative Hypothesis : P≠ 0.20

Step(ii):-

Test statistic

[tex]Z = \frac{p-P}{\sqrt{\frac{PQ}{n} } }[/tex]

[tex]Z = \frac{0.205-0.20}{\sqrt{\frac{0.20X0.80}{400} } }= \frac{0.005}{0.02} =0.25[/tex]

Z - statistic = 0.25

Level of significance =0.01

P-value

P(Z=0.25) = 0.802587

Conclusion:-

The result is not significant at p<0.01