I wish to estimate µ, the mean of a population. After I collect
and an-
alyze the data, I obtain an estimate for µ of 15.2 with a 95%
confidence
interval of (14.1, 16.3).
The meaning of the confidence interval is:
{ a) The intervals were computed in such a way that if we
repeatedly drew sample from the population, for about 95%
of these sample, the sample mean would lie in the interval
(14.1, 16.3).
{ b) The interval was computed in such a way that if we re-
peatedly drew samples from the population and computed a
new condence interval based on each sample, about 95% of
these itervals would contain the true value of µ.
{ c) There is a 95% chance lies in the interval (14.1, 16.3).
Ans :
{ b) The interval was computed in such a way that if we
re-
peatedly drew samples from the population and computed a
new condence interval based on each sample, about 95% of
these itervals would contain the true value of µ.
I wish to estimate µ, the mean of a population. After I collect and an- alyze...
Suppose you take a random sample of 30 individuals from a large population. For this sample, the sample mean is 4.2 and sample variance is 49. You wish to estimate the unknown population mean µ. (a) Calculate a 90% confidence interval for µ. (b) Calculate a 95% confidence interval for µ. (c) Based on (a) and (b), comment on what happens to the width of a confidence interval (increase/decrease) when you increase your confidence level. (d) Suppose your sample size...
Consider a population having a standard deviation equal to 9.96. We wish to estimate the mean of this population. (a) How large a random sample is needed to construct a 95% confidence interval for the mean of this population with a margin of error equal to 1? (Round your answer to the next whole number.) The random sample is units. (b) Suppose that we now take a random sample of the size we have determined in part a. If we...
Let's say we have constructed a 95% confidence interval estimate for a population mean. Which of the following statements would be correct? A. We expect that 95% of the intervals so constructed would contain the true population mean. B. We are 95% sure that the true population mean lies either within the constructed interval or outside the constructed interval. C. Taking 100 samples of the same size, and constructing a new confidence interval from each sample, would yield five intervals...
Suppose that the monthly return of stock A is approximately normally distributed with mean µ and standard deviation σ, where µ and σ are two unknown parameters. We want to learn more about the population mean µ, so we collect the monthly returns of stock A in nine randomly selected months. The returns are given (in percentage) as follows: 0.3, 1.3, 1.5, −0.6, −0.2, 0.8, 0.8, 0.9, −1.2 Answer the following questions about the confidence intervals for µ. (a) Construct...
a) Suppose you collect a SRS of size n from a population and from the data collected you computed a 95% confidence interval for the mean of the population. Which of the following would produce a new confidence interval with larger width (larger margin of error) based on these same data? A. Use a larger confidence level. B. Use a smaller confidence level. C. Nothing can guarantee absolutely that you will get a larger interval. One can only say the...
AM You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals. A random sample of 35 home theater systems has a mean price of $144.00. Assume the population standard deviation is $15.60. Construct a 90% confidence interval for the population mean. The 90% confidence...
You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence ntervals for the population mean. Interpret the results and compare the widths of the confidence intervals. If convenient, use technology to construct the confidence intervals A random sample of 45 home theater systems has a mean price of $138.00. Assume the population standard deviation is 516.40. Construct a 90% confidence interval for the population mean. The 90% confidence interval...
If you wish to estimate a population mean with a sampling distribution error SE = 0.34 using a 95% confidence interval and you know from prior sampling that σ² is approximately equal to 5.9, how many observations would have to be included in your sample?
Suppose you wish to estimate the mean of a normal population using a 95% confidence interval, and you know from prior information that σ2 ≈ 1. 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 n on graph paper. Connect the points by a smooth curve and...
If you wish to estimate a population mean with a margin of error MEequals=0.33 using a 95% confidence interval and you know from prior sampling that σ2 is approximately equal to 4.6 how many observations would have to be included in your sample? The number of observations that would have to be included in your sample is (______) (Round up to the nearest observation.)