The mean cost of a meal for two in a mid-range restaurant in tokyo is $40 (numbeo. com website, december 14, 2014). how do prices for comparable meals in hong kong compare? the datafile hongkongmeals contains the costs for a sample of 42 recent meals for two in hong kong mid-range restaurants. data: meal price ($)22.7833.8922.7718.0423.2935.2842 .3836.8838.5541.6825.7334.1931.7525 .2426.3219.5736.5732.9736.8330.1737 .2925.3724.7128.7932.8343.0035.2334 .7633.0627.7331.8938.4739.4240.7243 .9236.5145.2533.5129.1730.5426.7437 .93a. 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?

a)

b) So on this case the 95% confidence interval would be given by (30.53;34.79)    

c) On this case the confidence interval not contains the price $40, so we can conclude that the prices for Hong Kong mid-range restaurants are significant less than the prices for mid range restaurants in Tokyo at 5 % of significance.

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

represent the sample mean for the sample  

population mean (variable of interest)

s represent the sample standard deviation

n represent the sample size  

2) Part a

The margin of error is given by:

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,41)".And we see that

3) Part b

The confidence interval for the mean is given by the following formula:

  (1)

In order to calculate the mean and the sample deviation we can use the following formulas:  

(2)  

(3)  

The mean calculated for this case is

The sample deviation calculated

Now we have everything in order to replace into formula (1):

So on this case the 95% confidence interval would be given by (30.532;34.788)    

4) Part d

On this case the confidence interval not contains the price $40, so we can conclude that the prices for Hong Kong mid-range restaurants are significant less than the prices in mid range restaurants in Tokyo at 5 % of significance.