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# Question 4(a) (2 marks) modality(b) (4 marks(c) (4 marks) (d) (10 marks) Step 1 (2 marks)Step 2 Step 3

Fast Burger is a mobile food truck operating in Adelaide. Currently, the major fast food chains offer a lower-priced combination meal in an effort to attract budget-conscious customers. In order to determine the next marketing strategy, an analyst gathers the amount spent from 72

randomly selected customers at a lunch service. The resulting data is summarized below.

Describe the symmetry and  of the distribution.

) Use the 1.5xIQR rule to identify any outliers in this distribution. If yes, state the values of the outliers.

Which measures of central tendency and dispersion should be used to describe this distribution? Give (brief) reasons. Give and interpret their values.

Analysis of past sales records has revealed that a customer will spend an average of \$5.95 on lunch for food and drinks. At the 0.01 level of significance, is there evidence that the average amount spent on lunch with Fast Burger has changed? Use the information provided in the question description on the amount spent from 72 randomly selected customers at a lunch service.

H0: _________________________

H1: _________________________

a =_________________________ (0.5 mark)

z-test statistic: (2.5 marks)

Step 4 Decision rule and decision (use a diagram): (3 marks)

Step 5 Conclusion: (2 marks)

(e) (2 marks) From the data, we are 99% confident that the true population mean amount spent on lunch is between \$6.45 and \$7.28. If the marketing team is proposing a meal deal for \$6.25 inclusive of a burger, fries and drink, do you think this would be popular choice for customers? Explain briefly.

Amount Spent (\$)
Histogram of Amount Spent on Lunch
Mean
6.864583
Standard Error
0.209577
18
Median
6.575
16
Mode
6
14
Standard Deviation
1.778321
Frequency
ONAMOON
Sample Variance
3.162425
Kurtosis
33.45997
Skewness
4.748056
Range
16.3
Minimum
2.95
Maximum
19.25
5
5.5
6
6.5
7 7.5
8
8.5
9 9.5 More
Sum
494.25
Amount Spent (S)
Count
72
Quartile 1
6
Quartile 3
7.3125

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