Sampling distribution and confidence intervals.

1.A look at all Ontario households using natural gas heating in 2012 shows that the mean monthly consumption of natural gas is 107.73 ft³, with a standard deviation of 13.94 ft³. For a sample of 64 households, the sample mean found was 105.64 ft³. Use this information to find the margin of error E and to construct a 93% confidence interval for the mean monthly consumption for the population of all Ontario households. Is this sample a good estimation of the population mean monthly consumption of natural gas for all Ontario households?

2.Suppose that we have only 10 temperatures of people undergoing surgery, as below.

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a)Calculate the sample mean x and standard deviation s.

b)Find the margin of error E and construct the 99% confidence interval for the mean of all body temperatures (a prior study has shown that body temperatures are normally distributed).