A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard.
A) The z-statistic is -2.25
B) The z-statistic is 2.25
C) The z-statistic is -1.00
D) The z-statistic is 1.00

Question

Quizplus · Accepted Answer

To determine the z-statistic, we can use the formula:
z = (x - μ) / (σ / sqrt(n))
where x is the sample proportion (10/500 = 0.02), μ is the population proportion (0.01), σ is the standard deviation (sqrt(0.01 * 0.99) = 0.0995), and n is the sample size (500).

Plugging in the values, we get:
z = (0.02 - 0.01) / (0.0995 / sqrt(500)) = 2.24

Rounding to two decimal places, we get a z-statistic of 2.25, which corresponds to answer choice B. This result indicates that the sample proportion of products that did not meet the standard is more than 2 standard deviations away from the population proportion, suggesting that the manufacturer's claim is unlikely to be true.

A Manufacturer Claims That Less Than 1% of All His