One-Sample Test of Means. A Different Perspective In this example, I\'d like you
ID: 3065061 • Letter: O
Question
One-Sample Test of Means. A Different Perspective In this example, I'd like you to substitute different numbers into the Z-score equation, as instructed, to observe the effect of different variables on the outcome of the test. Here is the scenario: 4. The owners of a power plant claim that the levels of particulate matter in the surrounding air are significantly lower than the national average of 120 micrograms per cubic meter. You collect 40 samples and find that the mean level is 116 Hgm-3 with a standard deviation of 17 uHgm-3. a) What is the z-observed, and assuming that this is a one-tailed test, what is the z-critical value associated with a 95% confidence level ( -0.05)? Do the numbers above yield a statistically significant result? b) What is the z-critical value associated with a 90% confidence level for a one-tailed test? Is the result from above significant at the 90% confidence level? If the mean and the standard deviation remained the same, what is the minimum sample size that would be necessary to achieve a significantly significant result (at the original significance level, a-0.05)? c) d) If the sample size and the standard deviation remained the same as above (40 and 17, respectively), what is the maximum mean value for the sample (rounded to the nearest integer) that would yield a statistically significant result at -0.05? If the sample size and the original sample mean remained the same as above (40 and 116), what is the maximum standard deviation for the sample (rounded to the nearest integer) that would yield a statistically significant result (at =0.05)? e) f) Assuming all else remains equal, complete the following statements for the absolute value of the z- observed: g) a) As sample size increases, the absolute value of z-observed b) As the difference between means increases, the absolute value of z-obs. c) As the standard deviation increases, the absolute value of z-obsExplanation / Answer
a)
z =(Xbar - mu)/(sd/sqrt(n)
=(116 -120)/(17/sqrt(40))
= -1.4881
z-critical = -1.645
no , it is not significant
b)
z-critical = -1.282
yes , it is significant at 90 %
c)
(116 -120)/(17/sqrt(n)) < -1.645
n > 48.877
n = 49
d)
(Xbar - 120)/(17/sqrt(40)) < -1.645
Xbar < 115.578
e)
(116 -120)/(s/sqrt(40)) < -1.645
s < 15.3789
f) |z| = 1.4881
g) increase
increase
decrease
Please rate
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.