Section C: Confidence interval for two samples

7. The following data table gives the daily amount of milk produced by each cow in two herds

(in L). Suppose it is assumed that the standard deviation of milk produced by a cow is equal

across the two herds, and that the daily amount of milk produced by a cow is normally

distributed. Give a 99% confidence interval for the difference between the mean amount of

milk produced per cow in herd 1 and the mean amount of milk produced per cow in herd

2.

Herd 1 12.4 12.7 11.8 11.6 10.3 9.4 11.7 12.1

Herd 2 11.3 10.5 9.6 10.2 10.0 11.1 11.4

8. In a study of the rate at which the pesticide hexaconazole is absorbed through skin, skin

specimens were exposed to 24 g of hexaconazole. Four specimens were exposed for 30

minutes and four others were exposed for 60 minutes. The amounts (in g) that were

absorbed were:

30 minutes: 3.1 3.3 3.4 3.0

60 minutes: 3.7 3.6 3.7 3.4

It is assumed that the data are normally distributed. It is also assumed that the absorption

over 30 minute exposure has a standard deviation of 0.1 while exposure over 60 minutes

has a standard deviation of 0.12. Give a 95% confidence interval for the mean amount

absorbed in the time interval between 30 and 60 minutes after exposure.

9. A researcher is studying the relationship between sugar consumption and adult onset of

diabetes. She takes a random sample of 40 adults with high sugar consumption and 44

adults with low sugar consumption. In the first sample, 17 people have diabetes while in the second sample, 11 people have diabetes.

a) Give a 90% confidence interval for the difference between the proportions of people

with high sugar consumption who have diabetes and the proportion of people with low

sugar consumption who have diabetes.

b) What conclusions could this researcher draw about the relationship between sugar

consumption and adult onset of diabetes? Explain.

10. In a random sample of 340 cars driven at low altitudes, 46 of them produced more than 10

g of particulate pollution per L of fuel consumed. In a random sample of 85 cars driven at

high altitudes, 21 of them produced more than 10 g of particulate pollution per L of fuel

consumed. Find a 98% confidence interval for the difference between the proportions for high-altitude and low-altitude vehicles.