Find Z value When testing gas pumps for accuracy, fuel-quality enforcement speci

Question

Find Z value

When testing gas pumps for accuracy, fuel-quality enforcement specialists tested pumps and found that 1323 of them were not pumping accurately (within 3.3 oz when 5 gal is pumped), and 5653 pum ps 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 D. H:p 0.2 H1 ps0.2 F Ho p02 H1 P 0.2 OC. Ho : p > 0.2 H1 p 0.2 O E. Ho : p #02 H1 p-0.2 The test statistic isz-

Explanation / Answer

Given :-

n = 5653 , x = 1323

p^ = x/n = 1323 / 5653

p^ = 0.234

and p=0.2

Test statistic -

z = (p^ - p) / ? [(p*(1-p))/n]

z = (0.234 - 0.2) / ? [ (0.2*(1-0.2))/5653 ]

z = 6.39

p-value = 1

p-value is greater than alpha=0.01 then concluded that the fail to reject null hypothesis.

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