Question

Write the claim mathematically and identify Upper H 0 and Upper H Subscript a. ​(b) Find the critical​ value(s) and identify the rejection​ region(s). (c) Find the standardized test statistic.​ (d) Decide whether to reject or fail to reject the null hypothesis. An environmental agency recently claimed more than 27​% of consumers have stopped buying a certain product because of environmental concerns. In a random sample of 1040 ​consumers, you find 30​% have stopped buying the product. At alphaequals0.04​, do you have enough evidence to support the​ claim?

Answer 1

See explanation

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.