Question

The mean cost of a meal for two in a mid-range restaurant in Tokyo is $40 (Numbeo 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. Click on the datafile logo to reference the data.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

Answer:

a. 2.13. b. (30.53, 34.79). c. The mean prices for two in mid-range restaurants in Hong Kong are relatively less than those in Tokyo restaurants.

Explanation:

The size of the sample is 42 and the mean of the sample is ∑$x_{i}n$ = 32.66 and the standard deviation of the sample (σ) is √[∑($x_{i}$-μ)^2 - 1] = √46.6092 = 6.8271

a. α = 1 - (95/100) = 0.05; α/2 = 0.025; the degree of freedom = n-1 = 42-1 = 41; tα/2 = t0.025 = 2.02. Thus, the error margin = (tα/2)*(σ/√n) = 2.02*(6.83/√42) = 2.1279

b. Lower level limit = 32.66 - 2.1279 = 30.5321; Upper level limit = 32.66+2.1279 = 34.7879. The interval estimate = (mean± margin of error) = (30.53, 34.79).

c. The mean prices for two in mid-range restaurants in Hong Kong are relatively less than those in Tokyo restaurants.