Question 1

Gwynedd county council is eager to improve the rates of waste food recycling. They have conducted a survey of 100 households in Bangor city and 80 households scattered about in rural Snowdonia. The survey found the average amount of food waste recycled per week was:

3.5 Kilograms (standard deviation 1.2 kilograms) for city houses

2.2 Kilograms (standard deviation 1.3 kilograms) for the rural houses.

Furthermore, for the two samples 25 of the houses in Bangor, and 32 of the Snowdonia houses failed to recycle any food waste.

a. Does the sample indicate that the average amount of food waste recycled per week by the city and rural households differs? Use a significance level of 0.05.

b. Does the survey evidence indicate that proportionally more city households than households in Snowdonia recycle food waste? Use a significance level of 0.05.

A random sample of eight incoming calls dealt with by the out of hours GP service, gave the following results for call duration (minutes):

14.3 13.6 6.2 14.5 5.0 13.6 8.5 16.4

a. Test the null hypothesis that the average duration of calls is 10 minutes against an the alternative hypothesis that the average duration is more than 10 minutes, using a a significance level of 0.05.

b. Test the null hypothesis that the population variance is 15 minutes against a two-sided alternative hypothesis, using a significance level of 0.05.