Koala mass: confidence intervals and hypothesis testing
A forest ranger wishes to investigate the mass of adult male koalas in a Victorian forest. A random sample of 20 such koalas has a sample mean of 11.39 kg.
It is known that the mass of adult male koalas in the forest is normally distributed with a standard deviation of 1 kg.
Find a 95% confidence interval for the population mean (the mean mass of all adult male koalas in the forest). Give your values correct to two decimal places.
Hints, answer checking and worked solutions come with a Season Pass.
Sixty such random samples are taken and their confidence intervals are calculated.
In how many of these confidence intervals would the actual mean mass of all adult male koalas in the forest be expected to lie?
Hints, answer checking and worked solutions come with a Season Pass.
The ranger wants to decrease the width of the 95% confidence interval by 60% to get a better estimate of the population mean.
How many adult male koalas should be sampled to achieve this?
Hints, answer checking and worked solutions come with a Season Pass.
It is thought that the mean mass of adult male koalas in the forest is 12 kg. The ranger thinks that the true mean mass is less than this and decides to apply a one-tailed statistical test. A random sample of 40 adult male koalas is taken and the sample mean is found to be 11.6 kg.
Write down the null hypothesis, , and the alternative hypothesis, , for the test.
Hints, answer checking and worked solutions come with a Season Pass.
The ranger decides to apply the one-tailed test at the 1% level of significance and assumes the mass of adult male koalas in the forest is normally distributed with a mean of 12 kg and a standard deviation of 1 kg.
Find the value for the test correct to four decimal places.
Hints, answer checking and worked solutions come with a Season Pass.
