When testing gas pumps for accuracy, fuel-quality enforcement specialists tested

Question

When testing gas pumps for accuracy, fuel-quality enforcement specialists tested pumps and found that 1325 of were not pumping accurately (within 3.3 oz when 5 gal is pumped), and 5673 pumps were accurate. Use a 0.01 significance level to test the claim of an industry representative that less than 20% 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 notequalto 0.2 H_1: p = 0.2 B. H_0: p = 0.2 H_1: p 0.2

Explanation / Answer

Here Total number= 5673+1325 = 6998

sample proportion p = 1325 / 6998 = 0.1893

a)HO: p   is = to 0.2

H1: p is < 0.2

(b) The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(0.1893-0.2)/sqrt(0.2*0.8/6998)

=-2.229

(c) It is a left-tailed test.

So the p-value = P(Z<-3.32) =0.0129 (from standard normal table)

(d)Conclusion: There is sufficient evidence to support the claim.

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