Question

9. When testing gas pumps for​ accuracy, fuel-quality enforcement specialists tested pumps and found that 1310 of them were not pumping accurately​ (within 3.3 oz when 5 gal is​ pumped), and 5671 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. H 0​: p ≠ 0.2

     H 1​: p = 0.2

B. H 0​: p 0< 0.2

    H 1​: p = 0.2

C. H 0​: p = 0.2

H 1​: p < 0.2

D. H 0​: p > 0.2

H 1​: p = 0.2

E. H 0​: p = 0.2

     H 1​: p > 0.2

F. H 0​: p = 0.2

H 1​: p ≠ 0.2

The test statistic is z=____.

​( Round to two decimal places as​ needed.)

The​ P-value is____

​(Round to four decimal places as​ needed.)

Because the​ P-value is (greater than/less than) the significance​ level, (reject/fail to reject) the null hypothesis. There is (sufficient/insufficient) evidence support the claim that less than​ 20% of the pumps are inaccurate.

9. When testing gas pumps for​ accuracy, fuel-quality enforcement specialists tested pumps and found that 1310 of them were not pumping accurately​ (within 3.3 oz when 5 gal is​ pumped), and 5671 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. H 0​: p ≠ 0.2

     H 1​: p = 0.2

B. H 0​: p 0< 0.2

    H 1​: p = 0.2

C. H 0​: p = 0.2

H 1​: p < 0.2

D. H 0​: p > 0.2

H 1​: p = 0.2

E. H 0​: p = 0.2

     H 1​: p > 0.2

F. H 0​: p = 0.2

H 1​: p ≠ 0.2

The test statistic is z=____.

​( Round to two decimal places as​ needed.)

The​ P-value is____

​(Round to four decimal places as​ needed.)

Because the​ P-value is (greater than/less than) the significance​ level, (reject/fail to reject) the null hypothesis. There is (sufficient/insufficient) evidence support the claim that less than​ 20% of the pumps are inaccurate.

Answer 1

for hypothesis: option C is correct

C. H 0​: p = 0.2

H 1​: p < 0.2

test statistic is z =-2.57 ( please try -2.58 or -2.51 if this comes wrong and revert)

p value =0.0051 ( please try 0.0049 or 0.0060 if this comes wrong and revert)

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.