Problem 3
a. A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine the 95% confidence interval estimate of the population mean.
b. Repeat part (a) with a sample size of 100.
c. Repeat part (a) with a sample size of 400.
d. Describe what happens to the confidence interval estimate when the sample size increases.

Problem 4
a. A statistics practitioner randomly sampled 100 observations from a population with a standard deviation of 5 and found that is 10. Estimate the population mean with 90% confidence.
b. Repeat part (a) with a sample size of 25.
c. Repeat part (a) with a sample size of 10.
d. Describe what happens to the confidence interval estimate when the sample size decreases.

Solution Preview

3. a) The critical value for 95% confidence interval is 1.96.
a.margin of error=1.96*5/sqrt(25)=1.96
upper limit: 80+1.96=81.96
lower limit: 80-1.96=78.04
Therefore, 95% confidence interval is [78.04, 81.96].

b) margin of error=1.96*5/sqrt(100)=0.98
upper limit: 80+0.98=80.98
lower limit: ...

Solution Summary

The solution assists with answering the probability problem set.

... b) Make a frequency distribution for the data set using 5 ...Problem 2. The table shows the results of a survey ... Total 622 644 1266 (a) Find the probability that a ...

Statistical Problems. ... c. The probability of making exactly two sales. ... 5.) In establishing warranties on HDTV sets, the manufacturer wants to set the limits so ...

... For this problem, the critical value of the ... the Poisson distribution to find the indicated probabilities. ... randomly selected day, find the probability that the ...

... 34% rate is correct, estimate the probability that in ... Detailed solutions to all the four questions are provided ... P(x > 74) in a normally distributed set of data ...

Statistical Analysis and Probability Sample Questions. ... Compare the variation of the data sets. Decide if one data set is more variable than the other. ...

... This is a probability question. However, my real problem is with the integration of the problem. For every one-dimensional set C for which the integral exists ...

... Suppose Consolidated Power has been experiencing technical problems with the ... Other things being equal, should Consolidated Power set the probability of a ...

... Where should the warranty limits be set so so that only 10 percent of the ... The solution gives the details of computing probability based on normal distribution ...