The current advertising campaign for a major soft drink bran

The current advertising campaign for a major soft drink brand would be changed if less than 30 percent of the consumers like it. A random sample of 300 consumers was surveyed, and 84 respondents indicated that they liked the campaign. Should the campaign be changed based on the statisical test?

(For all statistical tests, the default signgicance level is 5%)

Solution

Set Up Hypothesis
Null,30% percent of the consumers like it H0:P=0.3
Alternate,less than 30 percent of the consumers like it H1: P<0.3
Test Statistic
No. Of Success chances Observed (x)=84
Number of objects in a sample provided(n)=300
No. Of Success Rate ( P )= x/n = 0.28
Success Probability ( Po )=0.3
Failure Probability ( Qo) = 0.7
we use Test Statistic (Z) for Single Proportion = P-Po/Sqrt(PoQo/n)
Zo=0.28-0.3/(Sqrt(0.21)/300)
Zo =-0.7559
| Zo | =0.7559
Critical Value
The Value of |Z | at LOS 0.05% is 1.64
We got |Zo| =0.756 & | Z | =1.64
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Left Tail -Ha : ( P < -0.75593 ) = 0.22485
Hence Value of P0.05 < 0.22485,Here We Do not Reject Ho

No, the campaign n\'t to be changed based on the statisical test