Respuesta :
Answer:
A. We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.
B. Null hypothesis:[tex]p=0.1[/tex]
Alternative hypothesis:[tex]p \neq 0.1[/tex]
C. [tex]z=\frac{0.0912 -0.1}{\sqrt{\frac{0.1(1-0.1)}{362}}}=-0.558[/tex]
D. [tex]z_{\alpha/2}=-1.96[/tex] [tex]z_{1-\alpha/2}=1.96[/tex]
E. Fail to the reject the null hypothesis
F. So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of inaccurate orders is not significantly different from 0.1.
Step-by-step explanation:
Data given and notation
n=362 represent the random sample taken
X=33 represent the number of orders not accurate
[tex]\hat p=\frac{33}{363}=0.0912[/tex] estimated proportion of orders not accurate
[tex]p_o=0.10[/tex] is the value that we want to test
[tex]\alpha=0.05[/tex] represent the significance level
Confidence=95% or 0.95
z would represent the statistic (variable of interest)
[tex]p_v[/tex] represent the p value (variable of interest)
A: Write the claim as a mathematical statement involving the population proportion p
We need to conduct a hypothesis in order to test the claim that the true proportion of inaccurate orders p is 0.1.
B: State the null (H0) and alternative (H1) hypotheses
Null hypothesis:[tex]p=0.1[/tex]
Alternative hypothesis:[tex]p \neq 0.1[/tex]
When we conduct a proportion test we need to use the z statistic, and the is given by:
[tex]z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}[/tex] (1)
The One-Sample Proportion Test is used to assess whether a population proportion [tex]\hat p[/tex] is significantly different from a hypothesized value [tex]p_o[/tex].
C: Find the test statistic
Since we have all the info required we can replace in formula (1) like this:
[tex]z=\frac{0.0912 -0.1}{\sqrt{\frac{0.1(1-0.1)}{362}}}=-0.558[/tex]
D: Find the critical value(s)
Since is a bilateral test we have two critical values. We need to look on the normal standard distribution a quantile that accumulates 0.025 of the area on each tail. And for this case we have:
[tex]z_{\alpha/2}=-1.96[/tex] [tex]z_{1-\alpha/2}=1.96[/tex]
P value
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 [tex]\alpha=0.05[/tex]. The next step would be calculate the p value for this test.
Since is a bilateral test the p value would be:
[tex]p_v =2*P(z<-0.558)=0.577[/tex]
E: Would you Reject or Fail to Reject the null (H0) hypothesis.
Fail to the reject the null hypothesis
F: Write the conclusion of the test.
So the p value obtained was a very high value and using the significance level given [tex]\alpha=0.05[/tex] we have [tex]p_v>\alpha[/tex] so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the true proportion of inaccurate orders is not significantly different from 0.1.
