Question

When testing gas pumps for​ accuracy, fuel-quality enforcement specialists tested pumps and found that 1264 of them were not pumping accurately​ (within 3.3 oz when 5 gal is​ pumped), and 5703 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

Solution :

This is the less tailed test .

The null and alternative hypothesis is

H₀ : p = 0.20

H_a : p < 0.20

= x / n = 1264 / 5703 = 0.2216

P₀ = 0.20

1 - P₀ = 0.80

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2216 - 0.20 / [(0.20 * 0.80) / 5703]

= 4.085

P(z < 4.085) = 1

P-value = 1

= 0.05

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to the 0.01 significance level to test the claim of an industry representative

that less than​ 20% of the pumps are inaccurate .