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 DATA Hongkong Meals 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 DATA file 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? The mean cost of comparable meals in Hong Kong is Select than in Tokyo.

Answer 1

Solution,

a)

The calculation of sample mean is as follows.

$\bar{x}=\frac{1}{n}\sum x=\frac{1}{42}(22.78+33.89+....+39.93)$   $=\frac{1}{42}(1371.72)=32.66$

The calculated value of the mean is 32.66

This value indicates the average mean price for two in Hong-Kong mid-range restaurent.

The calculation of sample standard deviation is as follows.

$S=\sqrt{\frac{1}{n-1}\sum (x_{i}-\bar{x})^{2}}$

1 V 42 - 1 {(22.78 – 32.66)2 + ...... + (37.93 – 32.66)2}
$=\sqrt{\frac{1}{41}(1910.981)}$

$=6.83$

The calculated value of the sample standard deviation is 6.83

This value indicates the variation price for two in Hong-Kong mid-range restaurent.

The degree of freedom is,

df = n - 1 =42 - 1 = 41

The critical value of t for 5% level of significance and 41 degrees of freedom is 2.020

Since use ( = TINV (0.05 , 41) )

now, the calucation of the margin of error is,

$ME = t_{\frac{\alpha }{2}}\left ( \frac{s}{\sqrt{n}} \right )=>(2.020)\left ( \frac{6.83}{\sqrt{42}} \right )=2.13$The margin of error value is

ME = 2.13

The margin error value is 2.13

b)

The calculation of the 95% confidence interval is as follows.

$CI=\bar{x}\pm t_{\frac{\alpha }{2}}\left ( \frac{s}{\sqrt{n}} \right )$

  $=32.66\pm 2.13=>(30.53,34.79)$

The calculated values of 95% confidence interval is (30.53 , 34.79) From 95% confidence interval , we are 95% confidence that the true average mean price in Hong-Kong mid-range restaurent is lies between 30.53 , 34.79.

c)

From the mean meal price in the Tokyo and 95% confidence interval for Hong-Kong restaurent , observe that the price in Hong-Kong restaurents is significantly lower than Tokyo restaurents.

The price in Hong-Kong restaurent is significantly lower than Tokyo restaurents.

Since the entire 95% confidence interval for Hong-Kong restaurent is below the mean price for Tokyo restaurent.