Question

**Note: Express all values accurate to 4 decimals (0.1234)
or as percentages accurate to 2 decimals (12.34%) unless otherwise
stated.**

**You may work with others on this
assignment.**

**(a: 1; b: 5; c: 2; d: 2; total: 10 marks)**

In a manufacturing plant, dowel widths are normally distributed with an average of 5 mm and standard deviation of 0.02 mm. Each hour, a random sample of 25 dowels is taken to ensure that the average width is not significantly different from 5 mm. In one sample, the average was 5.0054 mm.

- Why is the Z test the appropriate test for this situation?
- Test the hypothesis at a 5% level of significance.
- If the level of significance were 7.68%, what conclusion would be reached and why?
- If a level of significance had not been specified, what conclusion would be reached and why?

Answer #1

(a) The Z test is the appropriate test for this situation because we know the population standard deviation.

(b) The hypothesis being tested is:

H0: µ = 5

Ha: µ ≠ 5

The test statistic, z = (x - µ)/σ/√n = (5.0054 - 5)/0.02/√25 = 1.35

The p-value is 0.1770.

Since the p-value (0.1770) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we can conclude that the average width is not significantly different from 5 mm.

(c) Since the p-value (0.1770) is greater than the significance level (0.0768), we cannot reject the null hypothesis.

Therefore, we can conclude that the average width is not significantly different from 5 mm.

(d) Since the p-value (0.1770) is greater than the significance level (0.10), we cannot reject the null hypothesis.

Therefore, we can conclude that the average width is not significantly different from 5 mm.

In a manufacturing plant, dowel widths are normally distributed
with an average of 5 mm and standard deviation of 0.02 mm. Each
hour, a random sample of 25 dowels is taken to ensure that the
average width is not significantly different from 5 mm. In one
sample, the average was 5.0054 mm.
Why is the Z test the appropriate test for this situation?
Test the hypothesis at a 5% level of significance.
If the level of significance were 7.68%, what...

PLEASE SHOW WORK. It is necessary to round a probability to 2
decimal places. I must understand so clear writing is much
appreciated.
All test of hypotheses are to be done at the 5% level of
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PLEASE SHOW WORK. It is necessary to round a probability to 2
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appreciated.
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