0 ### Product Recognition Study Analysis#### ContextA marketing survey was conducted to evaluate product recognition in two different states: Texas and California. The sample consisted of:- **Texans:** 366 individuals surveyed, of which 78 knew the product.- **Californians:** 449 individuals surveyed, of which 64 knew the product.The goal is to test whether there is a significant difference in the recognition rates between these two states at a significance level of 0.05.#### Hypotheses- **Null Hypothesis (\(H_0\)):** \( p_T = p_C \) - The proportion of product recognition in Texas ( \( p_T \) ) is equal to that in California ( \( p_C \) ).- **Alternative Hypothesis (\(H_a\)):** \( p_T \neq p_C \) - The proportion of product recognition in Texas ( \( p_T \) ) is not equal to that in California ( \( p_C \) ).#### Test StatisticParticipants are required to compute the test statistic using their data inputs. Enter the test statistic accurate to four decimal places:```plaintexttest statistic = ____```#### p-valueParticipants must also calculate the p-value from the test statistic above. Enter the p-value accurate to four decimal places:```plaintextp-value = ____```#### p-value ComparisonCompare the p-value to the significance level (\( \alpha = 0.05 \)) to check: - \( \ \) If the p-value <= \( \alpha \) - \( \ \) If the p-value > \( \alpha \)#### Decision RuleBased on the p-value:- \( \ \) Reject the null hypothesis.- \( \ \) Accept the null hypothesis.- \( \ \) Fail to reject the null hypothesis.#### ConclusionFrom the decision made, conclude the findings: - \( \ \) There is not sufficient evidence to conclude product recognition between Texans and Californians is the same. - \( \ \) There is sufficient evidence to conclude product recognition between Texans and Californians is the same. - \( \ \) There is sufficient evidence to conclude there is a significant difference in product recognition between Texans and Californians. - \( \ \) There is not sufficient evidence to conclude there is a significant difference in product recognition between Texans and Californians.This structured approach guides

Denote pT is true proportion of people, who recognize product from State T and pC is the true…

A marketing survey involves product recognition in Texas and California. Of 366 Texans surveyed, 78 knew the product while 64 out of 449 Californians knew the product. Use a significance level of 0.05 to test if there is a difference in recognition rates. Ho:PT = PC На: рт + рс What is the test statistic? (Report answer accurate to four decimal places.) test statistic = What is the p-value? (Report answer accurate to four decimal places.) p-value = The p-value is... O less than (or equal to) a O greater than a The p-value leads to a decision to... O reject the null O accept the null O fail to reject the null The conclusion is that... O There is not sufficient evidence to conclude product recognition between Texans and Californians is the same. O There is sufficient evidence to conclude product recognition between Texans and Californians is the same. O There is sufficient evidence to conclude there is a significant difference in product recognition between Texans and Californians. O There is not sufficient evidence to conclude there is a significant difference in product recognition between Texans and Californians.