Question

For many florists, the days leading up to Valentine's Day are among the busiest of the year. An owner of a florist wanted to estimate the average sale amount for all sales made on the day before Valentine's Day, February 13th. When she had time she wrote down the sale price of a transaction of fresh flowers on a sheet of paper. By 3pm she had collected n=41 sale prices of all flower sales that were made day. The variable of interest is the total euro amount of each purchase. During her quick tea-break she calculated the average sale price of the 41 sales as 76.45 euro and found that they varied with a standard deviation of 22.41 euro.

Estimate the value of the population mean, µ, the true mean sale amount of all sales on February 13, 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________ .

It is quite likely that the true mean sale amount of all sales on February 13 is between______  and________ , with 95% confidence.

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.

The owner had a goal of acheiving a per sale amount of 110 euro for all sales made on February 14. Based on the inference carried out so far, do you think she may be disappointed?

a. Yes, because the sample mean estimated from this sample was less than 110 euro.

b. No, because the value 110 euro is contained in the confidence interval and therefore could be a possible value for the mean sale amount.

c. Yes, because the value 110 euro is not contained in the confidence interval and is therefore not a likely value for the mean sale amount.

Answer 1