Question

A new soft drink is being market tested. A sample of 400 individuals participated in the taste test and 140 indicated that they like the taste. If less than 40% of the population likes the taste of the new soft drink, the company will not begin a national marketing campaign for the product. Set up the appropriate hypotheses and test, using the critical value and p-value approaches, at the .05 level of significance (alpha) whether less than 40% of the population likes the soft drink. State your conclusion about the hypotheses. Should the manufacturer begin marketing the product based on your conclusions? Why or why not?

Answer 1

Given                      
n = 400       Sample Size          
140 out of 400 individuals like the taste                      
p̂ = 140/400 = 0.35           Sample proportion of individuals who like the taste          
p = 0.4   (40%)             Population (Standardised) proportion          
α = 0.05           Level of significance          
                      
The null and alternative hypothesis are                      
                      
Ho : p = 0.4                      
H1 : p < 0.4                      
                      
This is a left tailed test                      

Test statistic         
We find z, the test statistic as                       
where                       

z = -2.0412                      

p-value             
We find p-value using Standard Normal tables or Excel function NORM.S.DIST                      
p-value = NORM.S.DIST(-2.0412, TRUE)                      
p-value = 0.0206                    
                      
Critical Value of Z                      
We find z-critical using Standard Normal tables or Excel function NORM.S.INV                      
α = 0.05                      
z-critical = NORM.S.INV(0.05)                      
z-critical = -1.645

Rejection Criteria
Reject Ho if calculated test statistic z < -1.645                      
or Reject Ho if p-value < 0.05                      
                      
                      
0.0206 < 0.05                      
That is p-value < α                      
Hence, we Reject Ho                      
Also,                      
-2.0412 < -1.645                      
that is calculated test statistic z < z-critical                      
Hence, we Reject Ho                     
                      
Conclusion :                      
Reject Ho. There is sufficient evidence at α = 0.05, to conclude that less than 40% of the population likes the soft drink  

Since the hypothesis test proves that less than 40% of the population likes the soft drink                   
the manufacturer should not begin marketing the product.                      
                      

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