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Chapter 6: Q84E (page 367)
Suppose you want to estimate a population mean,,and,,,and.Find an approximate 95% confidence interval for.
The approximate confidence interval for is .
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The following is a 90% confidence interval for p:(0.26, 0.54). How large was the sample used to construct thisinterval?
Jitter in a water power system. Jitter is a term used to describe the variation in conduction time of a water power system. Low throughput jitter is critical to successful waterline technology. An investigation of throughput jitter in the opening switch of a prototype system (Journal of Applied Physics) yielded the following descriptive statistics on conduction time for n = 18 trials: nanoseconds, s = 6.3 nanoseconds. (Conduction time is defined as the length of time required for the downstream current to equal 10% of the upstream current.)
a. Construct a 95% confidence interval for the true standard deviation of conduction times of the prototype system.
b. Practically interpret the confidence interval, part a.
c. A system is considered to have low throughput jitter if the true conduction time standard deviation is less than 7 nanoseconds. Does the prototype system satisfy this requirement? Explain.
Suppose you wish to estimate the mean of a normal population
using a 95% confidence interval, and you know from prior information that
a. To see the effect of the sample size on the width of the confidence interval, calculate the width of the confidence interval for n= 16, 25, 49, 100, and 400.
b. Plot the width as a function of sample size non graph paper. Connect the points by a smooth curve and note how the width decreases as nincreases.
Calculate the percentage of the population sampled and
the finite population correction factor for each of the following
situations.
a. n= 1,000, N= 2,500
b. n= 1,000, N= 5,000
c. n= 1,000, N= 10,000
d. n= 1,000, N= 100,000
Suppose N= 10,000, n= 2,000, and s= 50.
a. Compute the standard error of xusing the finite populationcorrection factor.
b. Repeat part a assuming n= 4,000.
c. Repeat part a assuming n= 10,000.
d. Compare parts a, b, and c and describe what happens to the standard error of xas nincreases.
e. The answer to part c is 0. This indicates that there is no sampling error in this case. Explain.
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