Question

1) A marketing survey involves product recognition in New York and California. Of 558 New Yorkers surveyed, 193 knew the product while 196 out of 614 Californians knew the product. At the 0.05 significance level, test the claim that the recognition rates are the same in both states.

1. Use the traditional method to test the given hypothesis. Assume that the samples are independent and that they have been randomly selected.
2. Supported by Confidence intervals estimation?

Answer 1

To test the claim that the recognition rates are the same in both states, you can use the traditional method for testing hypotheses. Calculate the test statistic and compare it with the critical value to make a decision. If the test statistic falls in the rejection region, reject the null hypothesis and conclude that the recognition rates are different in both states.

Step-by-step explanation:

To test the claim that the recognition rates are the same in both states, we can use the traditional method for testing hypotheses.

1. Null hypothesis (H0) : The recognition rates are the same in both states (p1 = p2)
2. Alternative hypothesis (Ha) : The recognition rates are different in both states (p1 ≠ p2)
3. Calculate the test statistic: z = (p1 - p2) / sqrt(p * (1-p) * (1/n1 + 1/n2)), where p = (x1 + x2) / (n1 + n2) and p1 and p2 are the sample proportions in New York and California respectively.
4. Refer to the z-distribution table to find the critical value(s) for the desired significance level. Compare the calculated test statistic value with the critical value(s) to make a decision.
5. If the calculated test statistic falls in the rejection region, reject the null hypothesis and conclude that there is evidence to support the claim that the recognition rates are different in both states.
6. If the calculated test statistic does not fall in the rejection region, fail to reject the null hypothesis and conclude that there is not enough evidence to support the claim that the recognition rates are different in both states.

Based on the provided information, I cannot perform the calculations as the number of respondents who knew the product is not given for both states. However, this should give you an idea of how to approach the problem.