Question

In the survey on the quality of coffee A carried out among 90 randomly selected customers of the company dealing with its distribution, the following ratings were obtained:

Rating	1	2	3	4	5	6	7	8	9
Number of people	2	4	4	10	17	18	21	8	6

a) Based on the above data, the hypothesis was verified that 40% of all customers put coffee higher than '6' with the alternative that less than 40% giving such a rating. So the p-value of the relevant test is:

b) The p-value calculated in the previous section will be LOWER / SAME / HIGHER than the p-value calculated for the alternative assuming that the percentage is different from 40%

Answer 1

a)

Ho :   p ≥ 0.4  
H1 :   p <   0.4   (Left tail test)
          
Level of Significance,   α =    0.05  
Number of Items of Interest,   x = 21+8+6 = 35  
Sample Size,   n =    90  
          
Sample Proportion ,    p̂ = x/n =    0.3889  
          
Standard Error ,    SE = √( p(1-p)/n ) =    0.05164  
Z Test Statistic = ( p̂-p)/SE =    (0.3889-0.4)/0.0516=   -0.2152  
          

p-Value   =   0.4148   [excel function =NORMSDIST(z)]

2)

The p-value calculated in the previous section will be LOWER than the p-value calculated for the alternative assuming that the percentage is different from 40%