Confidence interval for a single mean, using Z
Suppose that the following data appeared on a computer printout:
Assume that the samples were drawn randomly from the identifiable populations.
Calculate 95% confidence intervals for
of the population means and state in words what
such an interval tells you.
A psychologist is interested in the long-term effects of divorce on children.
is obtained of 10 children whose parents were divorced at least 5 years before.
Each child is
given a personality questionnaire that measures depression.
Their scores were:
= 12, estimate the population mean:
using a point estimate
using an interval estimate that provides 90% confidence.
Hypothesis test for single mean, using Z
A local factory has a machine which is designed to fill lemonade bottles with 600mls
of liquid, with a standard deviation of 10mls.
To check whether the machine is calibrated
correctly, a quality control officer took a random sample of 36 bottles and found the mean
amount of liquid was actually 595 ml.
Assuming a normal distribution,
What are the appropriate H
= .05, test the hypotheses in part (a).
What conclusion can be made?
Refer to the data for schools in Q. 8.
For each sample, decide whether or not it came
from a population that had a mean of 100.
at .05 and use a two-tailed test. Compare
each decision with the relevant confidence interval that you calculated previously.