Question

The mean cost of a meal for two in a mid-range restaurant in Tokyo is $40 (Numbeo.com website, December 14, 2014). How do prices for comparable meals in Hong Kong compare? The DATAfile HongKongMeals contains the costs for a sample of 42 recent meals for two in Hong Kong mid-range restaurants.

Data:

Meal Price ($)
22.78
33.89
22.77
18.04
23.29
35.28
42.38
36.88
38.55
41.68
25.73
34.19
31.75
25.24
26.32
19.57
36.57
32.97
36.83
30.17
37.29
25.37
24.71
28.79
32.83
43.00
35.23
34.76
33.06
27.73
31.89
38.47
39.42
40.72
43.92
36.51
45.25
33.51
29.17
30.54
26.74
37.93

a. With 95% confidence, what is the margin of error (to 2 decimals)?

b. What is the 95% confidence interval estimate of the population mean (to 2 decimals)?

c. How do prices for meals for two in mid-range restaurants in Hong Kong compare to prices for comparable meals in Tokyo restaurants?

Answer 1

a) The margin of error (E) = 2.06

b) Confidence interval (CI) = 32.66±2.06475

==> CI = [30.59 < μ < 34.72]

c) The mean cost of a meal for two in a mid-range restaurant in Tokyo is $40 and the mean cost of a meal for two in a mid-range restaurant in Hong Kong is $32.66. The mean cost in Hong Kong is lesser than the mean cost in Tokyo.

Explanation:

a) By margin of error = ±Z*SE

If we compute the SE - Standard error, we have 1.05344 and Z statistics from statistical table is 1.96.

That gave us, 2.06 (2 decimal place)

b) By confidence interval (CI) = μ± margin of error

If we compute mean from the data give, we have 32.66. Thus, the interval is what we have in (b).

c) The mean cost in Honk Kong (whether up or lower value ) is strictly less than the mean value in Tokyo.