Question

When testing gas pumps for​ accuracy, fuel-quality enforcement specialists tested pumps and found that 1334 of them were not pumping accurately​ (within 3.3 oz when 5 gal is​ pumped), and 5663 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.

Answer 1

We accept H0, Therefore we conclude that there is no evidence to support the claim that less than 20% of the pumps are inaccurate.

Explanation:

We have,

x = 1334

n = 1334 + 5663 = 6997

we have to:

p = x / n = 1334/6997 = 0.1907

The hypothesis is:

H0: P = 0.20

H1: P <0.20

P = 0.2 and Q = 1 - P = 0.8

the test statistic is:

Z = (p - P) / [(P * Q / n) ^ (1/2)]

replacing:

Z = (0.1907 - 0.20) / [(0.2 * 0.8 / 6997) ^ (1/2)]

Z = -1.96

now, the p-value is

P = 0.0250, from normal table, attached

Here p-value> 0.01, so we accept H0, Therefore we conclude that there is no evidence to support the claim that less than 20% of the pumps are inaccurate.