Mathematics, 12.12.2019 22:31 anniekwilbourne

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.

Answers: 2

Show answers

Answers

Answer from: suzyleonardsl0

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

$z=\frac{0.185 -0.2}{\sqrt{\frac{0.2(1-0.2)}{6999}}}=-3.137$

p_v =P(z

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

$\hat p=\frac{1294}{6999}=0.185$ estimated proportion of pumps that were not pumping accurately

p_o=0.2 is the value that we want to test

$\alpha=0.01$ represent the significance level

Confidence=99% or 0.99

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 that less than 20% of the pumps are inaccurate:

Null hypothesis: $p\geq 0.2$

Alternative hypothesis: p < 0.2

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:

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

$z=\frac{0.185 -0.2}{\sqrt{\frac{0.2(1-0.2)}{6999}}}=-3.137$

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 $\alpha=0.01$ . The next step would be calculate the p value for this test.

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

p_v =P(z

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.

Answer from: Quest

answer: the answer is 127 degrees