Question

Rachel measured the lengths of a random sample of 100 screws. The mean length was 2.9 inches, and the population standard deviation is 0.1 inch. To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?

Answer 1

Answer:

z = 10

Step-by-step explanation:

The value of the z-statistic is given by:

$z = \frac{X - \mu}{s}$

In which:

X is the measured value.

$\mu$ is the expected value.

$s = \frac{\sigma}{\sqrt{n}}$ is the standard deviation of the sample. $\sigma$ is the standard deviation of the population.

In this question:

The mean length was 2.9 inches, and the population standard deviation is 0.1 inch.

This means that $\mu = 2.9, \sigma = 0.1$

Random sample of 100 screws.

This means that n = 100.

To see if the batch of screws has a significantly different mean length from 3 inches, what would the value of the z-test statistic be?

3 inches, so $X = 3$

$s = \frac{0.1}{\sqrt{100}} = 0.01$

$z = \frac{X - \mu}{s}$

$z = \frac{3 - 2.9}{0.01}$

$z = 10$