A travel agency surveyed 38 customers holidaying in Australia who took their spouses on either a skiing or a golfing vacation.  The data comprises amounts (in hundreds of dollars).  The skiing holiday is at Mount Buller in Victoria whereas the golfing holiday is on the Gold Coast in Queensland.

You will now make your data unique by taking the last 4 digits of your student identification number and putting the first two digits at the end of the 'Skiing Holiday' data and the last two digits at the end of the 'Golfing Holiday data.  For example:  If the last 4 digits of your student number are  1234  then put 12 under the value '26' in the 'Skiing Holiday' column and 34 under the value '22' in the 'Golfing Holiday' column.  There will now be a total of 40 values for 40 couples. 

Question 1:

a) Show a table that displays all the summary statistics for 'Golfing Holidays' and highlight the values for the mean and standard deviation.

b) Use formula to find the mean and standard deviation for 'Skiing Holidays'.  Write down the formulas shown on the toolbar (to verify that you used the correct formulas).

Question 2:

a) Display a histogram for 'Golfing Holidays' using class widths of 5.  Describe the shape of the distribution in terms of skewness and kurtosis.   What are the values for the skew and for the kurtosis?

b) Display an ogive* for 'Golfing Holidays' and estimate the proportion of holiday makers who spend more than $3,000 on their golfing holiday.

Question 3:

We wish to randomly select eight of the twenty couples from the 'Skiing Holiday' data.  Explain what you must do before you can select the eight couples.  Which Excel technique will you use?  Randomly sample the eight couples and sort the sample data using 'Data-Sort'.  Why is it recommended that the data be sorted?

Question 4:

Of the twenty couples who chose a golfing holiday, 8 couples originated from Japan, 4 from Israel, 5 from India, 1 from Ireland and 1 from Canada.  The twentieth couple is represented by you and your spouse (or friend if you are not married) so you will need to put yourself in one of the categories or create a new category (showing your country of origin). Show two different ways of displaying this information to best advantage (one of these displays must not be a frequency distribution).

Question 5:

  a)  It has been determined from past golfing data that the number of hours a couple spend playing golf per day is normally distributed with a mean of 5 and a standard deviation of 2. Use an appropriate Excel function (ƒx) to determine the probability that a couple spend more than 6 hours playing golf per day.  Write down the formula shown in the shortcut tool bar.

 b)  Snowfalls occur randomly and independently over the course of winter on Mount Buller.  The average is one snowfall every three days.  Find the probability of a snowfall the day you and your friend plan to ski.  Use an appropriate Excel function (ƒx) and write down the formula shown in the shortcut tool bar.

Question 6:

Can we infer that skiers and golfers differ in their vacation expenses? Test at the 1% level of significance. Highlight the relevant critical value or p-value and the test statistic.