Question

When testing gas pumps for​ accuracy, fuel-quality enforcement specialists tested pumps and found that 1271 of them were not pumping accurately​ (within 3.3 oz when 5 gal is​ pumped), and 5715 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 two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.20

H_a : p < 0.20

= x / n = 1271 / 5715 = 0.2224

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.2224 - 0.20 / [(0.20 * 0.80) / 5715]

= 4.233

P-value = 1

= 0.01

P-value >

Fail to reject the null hypothesis .

There is sufficient evidence to suggest that  the claim of an industry representative

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