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Course: BUSINESS Res 342, Spring 2009School: University of Phoenix
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342 Res Quiz 1 Ron Konnick 1. (2 points) What does a confidence interval tell you? What does it mean? A confidence interval gives two numbers that have a stated probability of includeing the value of the parameter of interest. For example a 95% confidence interval says that there is a 95% chance that the interval contains the actual parameter values. What two things can a researcher do to reduce the width of a...
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342 Res Quiz 1 Ron Konnick 1. (2 points) What does a confidence interval tell you? What does it mean? A confidence interval gives two numbers that have a stated probability of includeing the value of the parameter of interest. For example a 95% confidence interval says that there is a 95% chance that the interval contains the actual parameter values. What two things can a researcher do to reduce the width of a confidence interval? What are the effects? The sample size can be increased. Of course there will be additional cost involved. The other other option is to decrease the confidence level. This means there will be a smaller probability that the interval will contain the value of the population parameter.
2.
(4 points) Compute the 95% confidence interval on the population mean if a sample of 1000 is taken and the sample mean is found to be 15.95 and standard deviation is 4.2. Large sample, confidence interval on the mean. The formula of interest is
X
zs n
The z value for a 95% confidence interval is 1.96. Plugging in the sample values
n 1.96 * 4.2 15.95 1000 8.232 31.6228 15.95 15.95 0.26
X
zs
Or, 15.69 to 16.21
Interpret the interval. What does it mean? There is a 95% chance that the interval 15.69 to 16.21 brackets (includes) the actual population mean.
3.
(4 points) Test to see if a population mean is greater than the assumed (or historical) value of 16. When a sample of 1000 was taken the sample mean was computed to be 15.95 and the sample standard deviation was 4.2. The test is to prove that the mean is greater than 16. This is the alternate hypothesis Ho: 16 Ha: > 16 Alpha is not given. Ill use of 5%, the usual value. This is a one group, test of means, large sample. We are not given the population standard deviation so we must use the sample standard devation. The z statistic applies
z=
( X ) s n
For an alpha of 5%, one tail test, z stat, the critical value is z = 1.64 or 1.65. Ill use 1.65 the more extreme value. Computing the observed z value:
z=
(X ) s
n (15.95 16) z= 4.2 1000 0.05 0.1328 z = 0.3765 z=
The z value is less than the critical value so the null is not rejected. The mean is less than 16.
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