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?

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.