Answer:
See below
Step-by-step explanation:
a)
<u>Hypothesis:
</u>
: The employees’ daily zinc intake is 14 mg.
: The employees’ daily zinc intake is less than mg.
So, this is a left-tailed test
<u>Assumptions:
</u>
Population standard deviation of intakes
= 0.9 mg.
Mean of the sample:
= 13.8
Mean of the population
= 14
Sample size
70
<u>Test statistic:
</u>
p-value:
This is the area under the Normal curve N(0,1) to the left of the test statistic -1.8592. Hence
p-value = 0.0315
<u><em>Conclusion:
</em></u>
Since p-value<level of significance we reject
(b) Suppose the population mean really was 14. Before sampling, what was the probability the test would reject H0 : µ = 14 even though it is true? Which type of error is this?
The probability the test would reject is precisely the level of significance =0.05. So if we reject the null given that it is true, we would be making a Type 1 error.