Question

Problem 1
Calculate the 95 percent confidence interval please show work

n = 20, mean = 9.10, standard deviation = 2.404, se mean = .538

Problem 2
True or false for each of the following question:

a. If a large number of random samples are selected and we form the 95% confidence interval for each sample mean, the population mean will lie in about 95% of these confidence intervals.

b. The 95% confidence interval around a given sample mean is wider than the 90% confidence interval around that mean.

c. If sample size is larger than 30, there is a 95% chance that the population mean will be in the confidence interval.

d. If a very large number of random samples are selected, there is a 95% chance that one of the sample means is equal to the population mean.

Solution Preview

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Since n < 30 we will use a t distribution with (n-1) degrees of freedom. The critical value for a 95% confidence interval with 19 degrees of freedom is 2.093.

Lower limit: 9.1 – 2.093 x 0.538 = 7.974
Upper limit: 9.1 + 2.093 x 0.538 = 10.226

The confidence interval is...

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