Answer:
See explanation
Step-by-step explanation:
Solution:-
- The claim made was made on the customer ( population ) that more than 27% of the consumers have stopped buying the product due to environmental concern.
- We will denote ( p ) as the population proportion for which the claim was made. The hypothesis would be:
Null Hypothesis : p ≥ 0.27 .. ( 27 ) %
- Then the only possibility to rejects or disband the claim made would be if the proportion ( p ) of consumers who stopped buying a certain product due to environmental issues is less than the value claimed.
Alternate Hypothesis : p < 0.27 ... ( 27 ) %
- A random sample of n = 1040 customers were taken. The sample proportion ( p^ ) = 0.3 .. ( 30 )%. The population standard deviation ( σ ) as follows:
σ = √p*( 1 - p ) / n
σ = √0.27*( 1 - 0.27 ) / 1040
σ = √0.00018 = 0.01376
- Then we will evaluate the Z-statistics value:
Z-test = ( p^ - p ) / σ
Z-test = ( 0.3 - 0.27 ) / 0.01376
Z-test = 2.180
- The p-value is the probability of standard normal less than Z-test value:
P ( Z < Z-test ) = P ( Z < 2.18 )
P ( Z < 2.18 ) = 0.985
- To reject the Null hypothesis the p-value must be less than significance level α = 0.04.
p-value > α
0.985 > 0.04
Conclusion:- There isn't sufficient evidence to reject the claim made by the researcher. Hence, the claim made is statistically correct as per sample obtained.
