Question

The next day, Valentines Day, February 14th, the owner tries to improve her sales technique pushing for orders of higher amounts. Again she attempts to write down a number of random sale amounts as the day goes on. As she is so busy she manages to record only n=14 sale prices among all flower sales that day. She calculated the average sale price of the 14 sales as 97.71 euro and calculated that they varied with a standard deviation of 15.73 euro.

Estimate the value of the population mean, µ, the true mean sale amount of all sales on February 14, by calculating a 95% confidence interval. Fill in the blanks in the following:

An estimate of the population mean is:____________

The standard error is .:__________

The distribution is (examples: normal / t12 / chisquare4 / F5,6). _________________

For a 95% confidence interval the distributional cut-off is (3 dec places). ________________

It is quite likely that the true mean sale amount of all sales on February 14 is between ______________and __________ , with 95% confidence.

Answer 1

Let's consider X be the sale price of the flowers.

Given n=14

As she calculated the standard deviation from this sample.

The sample standard deviation is

s=15.73 euro

We want to find the 95% confidence interval for the true population mu the true meaning sale amount of all sales on February 14,

An estimate of population mean is

The standard error is

Since the population standard deviation is not know the distribution is the with 13 degrees of freedom.

For 95% confidence interval the distribution cutoff, ie t critical value at 13 degrees of freedom with 5% level of significance is

The 95% confidence interval for the true population mean is given by

It is quite likely that the true mean sale amount of all sales on February 14, is between 88.62 euro and 106.80 euro with 95% confidence.