Answer:
a. Z = 2.6667
b.
c. Upper limit = 3.39
Step-by-step explanation:
Part a
We are given
Population mean = 3
Population standard deviation = 0.3
Sample mean = 3.2
Sample size = n = 16
Level of significance = 0.05
Null hypothesis: H0: µ = 3
Alternative hypothesis: Ha: µ > 3
The test statistic formula is given as below:
Z = (sample mean – population mean) / [SD / sqrt(n)]
Z = (3.2 – 3)/[0.3/sqrt(16)]
Z = 2.6667
Part b
Type I error is the probability of rejecting the null hypothesis that the population mean is 3 ppm when actually it is 3 ppm. Type II error is the probability of do not rejecting the null hypothesis that the population mean is 3 ppm when actually it is exceeding 3 ppm. Type II error is the serious in this scenario.
Part c
We are given
Population mean = 3
Population standard deviation = 0.3
Sample mean = 3.2
Sample size = n = 16
Confidence level = 90%
Critical z value = 2.3263
Formula is given as below:
Lower limit =sample mean – z*SD/sqrt(n)
Upper limit = sample mean + z*SD/sqrt(n)
Lower limit = 3.2 – 2.5758*0.3/sqrt(16)
Lower limit = 3.01
Upper limit = 3.2 + 2.5758*0.3/sqrt(16)
Upper limit = 3.39
