When testing gas pumps for accuracy, fuel-quality enforcement specialists tested pumps and found that 1294 of them were not pumping accurately (within 3.3 oz when 5 gal is pumped), and 5705 pumps were accurate. Use a 0.01 significance level to test the claim of an industry representative that less than 20% of the pumps are inaccurate. Use the P-value method and use the normal distribution as an approximation to the binomial distribution. Identify the null hypothesis and alternative hypothesis.A. H0: p=0.2H1:p>0.2B. H0: p=0.2H1: ≠0.2C. H0: p≠0.2H1: p=0.2D.H0: p>0.2H1: p=0.2E.H0: p=0.2H1: p<0.2F. H0: P<0.2H1: P=0.2The Test static is z=The P-Value is=Because the P-Value is (greater than/less than) the significance level (fail to reject/reject) the null hypothesis. There is (sufficient/insufficient) evidence support the claim that less than 20% of the pumps are inaccurate.

Because the P-Value is (less than) the significance level (reject) the null hypothesis. There is (sufficient) evidence support the claim that less than 20% of the pumps are inaccurate.

Step-by-step explanation:

1) Data given and notation

n=1294+5705=6999 represent the random sample taken

X=1294 represent the number of pumps that were not pumping accurately

[tex]\hat p=\frac{1294}{6999}=0.185[/tex] estimated proportion of pumps that were not pumping accurately

[tex]p_o=0.2[/tex] is the value that we want to test

[tex]\alpha=0.01[/tex] represent the significance level

Confidence=99% or 0.99

z would represent the statistic (variable of interest)

[tex]p_v[/tex] 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 that less than 20% of the pumps are inaccurate:

Null hypothesis:[tex]p\geq 0.2[/tex]

Alternative hypothesis:[tex]p < 0.2[/tex]

E.H0: p=0.2H1: p<0.2

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].

3) Calculate the statistic

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

[tex]z=\frac{0.185 -0.2}{\sqrt{\frac{0.2(1-0.2)}{6999}}}=-3.137[/tex]

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 [tex]\alpha=0.01[/tex]. The next step would be calculate the p value for this test.

Since is a one left tailed test the p value would be:

[tex]p_v =P(z<-3.137)=0.00085[/tex]

Because the P-Value is (less than) the significance level (reject) the null hypothesis. There is (sufficient) evidence support the claim that less than 20% of the pumps are inaccurate.