Mathematics, 17.12.2019 23:31, mikayleighb2019

In a random sample of 400 items where 84 were found to be defective, the null hypothesis that 20% of the items in the population are defective produced upper z subscript statequalsplus 0.50. suppose someone is testing the null hypothesis upper h 0: piequals0.20 against the two-tail alternative hypothesis upper h 1: pinot equals0.20 and they choose the level of significance alphaequals0.10. what is their statistical decision?

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answered: austinparness02

$z=\frac{0.21 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=0.5$

p_v =2*P(Z0.5)=0.617

So the p value obtained was a very high value and using the significance level given $\alpha=0.1$ we have $p_v\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 10% of significance the true proportion of defectives it's not significant different from 0.2.

Step-by-step explanation:

1) Data given and notation

n=400 represent the random sample taken

X=84 represent the number of items defective

$\hat p=\frac{84}{400}=0.21$ estimated proportion of defectives

p_o=0.2 is the value that we want to test

$\alpha=0.1$ represent the significance level

Confidence=90% or 0.90

z would represent the statistic (variable of interest)

p_v represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.2 or 20%:

Null hypothesis: p=0.2

Alternative hypothesis: $p \neq 0.2$

When we conduct a proportion test we need to use the z statisitc, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value p_o .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.21 -0.2}{\sqrt{\frac{0.2(1-0.2)}{400}}}=0.5$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.1$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

p_v =2*P(Z0.5)=0.617

answered: Guest

the answer is 15% decrease

answered: Guest

It’s hard to understand what you put.. can you show a picture ?

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In a random sample of 400 items where 84 were found to be defective, the null hypothesis that 20% of...