Question

Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 5% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased; what is the critical value? (please round your answer to 2 decimal places)

Answer 1

Given                          
p = 0.48   (48%)           Population proportion              
n = 115              Sample Size              
46 out of 115 traded in their old car                          
p̂ = 46/115 = 0.4           Sample proportion              
α = 0.05             Level of significance              
                          
The null and alternative hypothesis are                          
                          
Ho : p = 0.48                          
H1 : p < 0.48                          
                          
This is a left tailed test                          
                          
We find z, the test statistic as                           
where                           
   
z = -1.72                          
                          
We find p-value using Standard Normal tables or Excel function NORM.S.DIST                          
p-value = NORM.S.DIST(-1.7172, TRUE)                   (for left tailed we keep the second parameter TRUE)      
p-value = 0.04                          
                          
0.04 < 0.05                          
That is p-value < α                          
Hence, we Reject Ho          

Conclusion :                          
There is sufficient evidence to conclude that                          
the proportion of new-car buyers that trade in their old car has statistically significantly decreased