Question

Air quality is of concern to everyone. One measure is the number of micrograms of particulate present per cubic meter of air. In a small city in South Dakota, data was obtained for five randomly selected 24-hour periods during June. These readings are:

45,          50,          62,          57,          70

1. Construct a normal probability plot. Is it plausible that the given sample observations were selected from a normal distribution?
2. Calculate the sample mean and sample standard deviation and use the correct symbol to identify each sample statistic :
3. Calculate a 95% confidence interval for the true average micrograms of particulate present per cubic meter of air. Interpret this confidence interval.
4. Predict the micrograms of particulate present per cubic meter of air resulting from a single future reading by calculating a 95% prediction interval. Compare the width of this interval to the width of the confidence interval in part (C).
5. Calculate an interval for which you have a high degree of confidence that at least 95% of all 24-hour periods will have readings between the limits of the interval.

Answer 1

Given Data: 45,          50,          62,          57,          70

a)

b) sample mean and sample standard deviation

sample mean = ( 45+50+62+57+70)/5

= 56.8

sample standard deviation :

c) The Confidence Interval formula is   

For 95% Confidence Interval Z = 1.960

d) The range of 95% confidence interval is from 48.181 to 65.419

There are 95% chances of getting the air quality between 48.181 to 65.419

width of the confidence interval

= 65.419 - 48.181

= 17.238