|University||Singapore University of Social Science (SUSS)|
|Subject||ANL321: Statistical Methods|
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.
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The local NHS health board is assessing new methods of deep cleaning intensive care beds. They compare the time taken to clean ten beds with previously recorded times. The table below, give the average amount of time in minutes for each of the ten beds. Before and after the introduction of the new method.
Using a significance level of 0.05 test the hypothesis that the new procedure significantly decreases the time take to clean each bed.
The trustees of a company’s pension plan have solicited the opinions of random samples of 200 of the company’s employees regarding a proposed revision of the pension plan. A breakdown of the responses is as below:
|Responses||Manual Staff||Office Staff||Managers|
Is there any statistical evidence to infer that the responses (for or against) differ across the three groups of employees? Use 0.05 significance level.
Medical researchers want to know whether the time taken to reach full recovery after the first hip replacement surgery can be reduced by a new post-operative physiotherapy regime. A sample of 40 patients scheduled for a hip replacement was chosen. Of these 40 patients, 16 were assigned to receive the new post-operative physiotherapy regime with the remaining 24 assigned to the existing old regime. Of the 16 patients, the average length of time taken to recover fully from the surgery was 96.3 days with a standard deviation of 29.5 days. The remaining 24 patients, there
average recovery time was 128.3 days and with the standard deviation of 38.5 days.
a. Is there evidence to show that the average time taken to recover fully from the hip
replacement operation is significantly reduced by the new post-operative physiotherapy regime? Use a significance level of 0.05
b. Test the null hypothesis that the population variance of the recovery time for these 2 categories of patients are the same. use a significance level of 0.05.
A. A car manufacturer purchases components from a subcontractor who undertakes to ensure that not more than 5% of supplies will be defective. In order to provide a check on the quality of supplies, a random sample of 200 components is selected, of which 17 are found to be defective.
Does the sample evidence indicate that the subcontractor is not maintaining the quality of supplies at the agreed level? Use a significance level of =0.05.
b. In a public opinion poll of 500 randomly chosen respondents held in 2010, 350 respondents favoured reform of the House of Lords. In a follow-up poll held a year later with different respondents, 300 out of 500 respondents favoured reform. Is there evidence of a significant change of opinion? Use a significance level of =0.01.
A researcher wishes to investigate the association between two variables, denoted xi and yi. The following results have been obtained from the analysis of a sample of 30 observations:
The following Stata output refers to a regression for the determinants of the selling prices of houses in a particular location. The variable definitions are as follows:
price = selling price in £’000s
area = floorspace in square feet
age = age of house in years
a. Interpret the following results from the Stata output:
(i) Coefficients on area and age, and their t-statistics and p-values.
(ii) R-squared and Adjusted R-squared.
(iii) Root MSE (= standard error of the regression).
(iv) The F-statistic.
(b) What is the expected selling price for a 30-year old house with a floor space of 1800 square feet?
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