We wish to investigate whether female university students are, on average, taller than their mothers. A random sample of thirty female students is selected. Each student's height and the height of her mother is recorded. The data is shown below.

a)

Give a confidence interval for the proportion of daughters who are taller than their mothers.

b)

Are more than half of the daughters taller than their mothers? Do the appropriate test. State null and alternative hypothesis, value of the test statistic and p-value. What is your conclusion at ? at ?

There is concern that a percentage of elementary school children with hearing problems is on the increase. Suppose that in the past of children had hearing problems. A sample of 400 children is screened and 35 of the children are found to have hearing problems. Test whether the proportion of children with hearing problems is greater now than in the past. What do you conclude? Base your conclusion on the p-value for your test.

A police department conducts a test on the brakes of 40 randomly selected trucks. 14 of the trucks are found to have falty brakes.

a)

Calculate a confidence interval for the proportion of trucks with faulty brakes.

b)

Suppose the examiners decide that the confidence interval was too wide. They wish to construct a confidence interval with a margin of error of . How many randomly selected trucks do they need to examine for brakes faults to achieve this goal?

A biologist wishes to estimate the proportion of crayfish from a certain lake which contains more than 9 parts per billion of mercury.

a)

If she wishes to construct a confidence interval with a margin of error of 0.04, how many crafish does she need to analyze?

b)

If she knows that more than of the crayfish contain over 9 ppb of mercury, how will this affect the sample size needed to attain a confidence interval with margin of error of 0.04?