Often, cruise ships conduct all on-board transactions, with the exception of gam

Question

Often, cruise ships conduct all on-board transactions, with the exception of gambling, on a cashless basis. At the end of the cruise, guests pay one bill that covers all on-board transactions. Suppose that 56single travelers and 68 couples were surveyed as to their on-board bills for a seven-day cruise from Los Angeles to the Mexican Riviera. Below is a summary of the bills for each group.

Part (a)

Fill in the relative frequency for each group. (Round your answers to four decimal places.)

Part (b)

Construct a histogram for the singles group. Scale the x-axis by $50 widths. Use relative frequency on the y-axis.

Part (c)

Construct a histogram for the couples group. Scale the x-axis by $50 widths. Use relative frequency on the y-axis.

Part (d)

Compare the two graphs:(i) List two similarities between the graphs. (Select all that apply.)

The bars of each graph represent an interval of $50.Both graphs show a wide spread of the data.Both graphs represent a relative frequency distribution.Both graphs represent a bimodal distribution.

(ii) List two differences between the graphs. (Select all that apply.)

One graph is skewed to the right and the other graph is not.One graph is symmetrical and the other graph is not symmetrical.The center of each distribution is different.One graph is bimodal and the other graph is not bimodal.

Part (e)

Construct a new graph for the couples by hand. Since each couple is paying for two individuals, instead of scaling the x-axis by $50, scale it by $100. Use relative frequency on the y-axis.

Part (f)

Compare the graph for the singles with the new graph for the couples. List two similarities between the graphs. (Select all that apply.)

Both graphs show lowest relative frequencies near the tails.Both graphs show a wide spread of data values.Both graphs represent a relative frequency distribution.The center value of each graph is the same.

Part (g)

By scaling the couples graph differently, how did it change the way you compared it to the singles?

It changed the center of the Couples graph.It changed the number of intervals being compared.     It changed the skewness of the Couples graph.It changed the spread of the Couples graph.

Part (h)

Based on the graphs, do you think that individuals spend the same amount, more or less, as singles as they do person by person as a couple?

Yes, individuals spend about the same whether they are traveling as a single or as a couple.No, individuals appear to spend more when traveling as a single rather than a couple.     

Singles Amount ($) Frequency Relative Frequency 51-100 4 101-150 10 151-200 14 201-250 14 251-300 10 301-350 4 Relative Frequency 0.30E 0.25 0.20 0.15 0.10 0.05 Amount ($) 50 100 150 200 250 300 350

Explanation / Answer

Relative Frequency

Formula : Relative Frequency=class frequency / Total frequency

singles

Amount

Frequency

Relative Frequency

51-100

4

0.0714

101-500

10

0.1786

151-200

14

0.25

201-250

14

0.25

251-300

10

0.1786

301-350

4

0.0714

56

couples

Amount

Frequency

Relative Frequency

100-150

4

0.0588

151-200

4

0.0588

201-250

4

0.0588

251-300

4

0.0588

301-350

11

0.1618

351-400

11

0.1618

401-450

11

0.1618

451-500

11

0.1618

501-550

4

0.0588

551-600

4

0.0588

68

singles

Amount

Frequency

Relative Frequency

51-100

4

0.0714

101-500

10

0.1786

151-200

14

0.25

201-250

14

0.25

251-300

10

0.1786

301-350

4

0.0714

56

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