A manufacturer must test that his bolts are 2.00 cm long when they come off the assembly line. He must recalibrate his machines if the bolts are too
long or too short. After sampling 169 randomly selected bolts off the assembly line, he calculates the sample mean to be 2.05 cm . He knows that the
population standard deviation is 0.29 cm . Assuming a level of significance of 0.01 , is there sufficient evidence to show that the manufacturer needs
to recalibrate the machines?
Step 2 of 3 : Compute the value of the test statistic. Round your answer to two decimal places.
Answer 2 Points

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UpStudy AI · Accepted Answer

To compute the test statistic $$ z $$, use the formula:

$$
z = \frac{\bar{x} - \mu_0}{\sigma / \sqrt{n}}
$$

Where:
- $$\bar{x} = 2.05$$ cm (sample mean)
- $$\mu_0 = 2.00$$ cm (hypothesized population mean)
- $$\sigma = 0.29$$ cm (population standard deviation)
- $$n = 169$$ (sample size)

Plugging in the values:

$$
z = \frac{2.05 - 2.00}{0.29 / \sqrt{169}} = \frac{0.05}{0.29 / 13} = \frac{0.05}{0.0223077} \approx 2.24
$$

**Test Statistic:** $$ z = 2.24 $$
The test statistic is 2.24.

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