Question

A study conducted by ABC International showed that Paris is the most expensive place to live of the 12 European Community cities. Paris ranks second in housing expense, with a rental unit of six to nine rooms costing an average of $4292 a month. Suppose a company’s CEO believes this figure is too high and decides to conduct her own survey. Her assistant contacts the owners of 55 randomly selected rental units of six to nine rooms and finds that the sample average cost is $4008, with a standard deviation of $386. Using the sample results and a 1% significance level, test to determine whether the figure published by ABC International is too high. (Use P-Value Approach.)

Answer 1

Ho :   µ =   4292
Ha :   µ <   4292
      
Level of Significance ,    α =    0.010
sample std dev ,    s =    386.0000
Sample Size ,   n =    55
Sample Mean,    x̅ =   4008.0000
      
degree of freedom=   DF=n-1=   54
      
Standard Error , SE = s/√n =   386/√55=   52.0482
t-test statistic= (x̅ - µ )/SE =    (4008-4292)/52.0482=   -5.456
      
critical t value, t* =        -2.397
      
p-Value   =   0.0000
Decision:   p-value<α, Reject null hypothesis   
Conclusion: There is enough evidence to conclude that figure published by ABC International is too high