Question

The mean cost of a meal for two in a midrange restaurant in City A is $48. How do prices for comparable meals in Hong Kong compare? The file HongKongMeals contains the costs for a sample of 42 recent meals for two in Hong Kong midrange restaurants.

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 for the estimated mean cost in dollars for a mid-range meal for two in Hong Kong? (Round your answer to the nearest cent.)

$

(b)

What is the 95% confidence interval estimate of the population mean cost in dollars for a mid-range meal for two in Hong Kong? (Round your answers to the nearest cent.)

$  to $

Answer 1

a)

sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =6.8271
Sample Size ,   n =    42
Sample Mean,    x̅ =   32.6600

Level of Significance ,    α =    0.05          
degree of freedom=   DF=n-1=   41          
't value='   tα/2=   2.020   [Excel formula =t.inv(α/2,df) ]      
                  
Standard Error , SE = s/√n =   6.8271   / √   42   =   1.0534
margin of error , E=t*SE =   2.0195   *   1.0534   = $ 2.13

b)

confidence interval is                   
Interval Lower Limit = x̅ - E =    32.66   -   2.127474   =   30.5325
Interval Upper Limit = x̅ + E =    32.66   -   2.127474   =   34.7875
95%   confidence interval is (   30.53   < µ <   34.79   )