A researcher wants to see if gender plays a role in where we sit in a restaurant. An analysis of survey data yields the following contingency table, chi-squared value, and p-value:
Tabulated statistics: Gender, Seating
Rows: Gender Columns: Seating
Back Front Middle All
Female 14 28 84 126
Male 18 18 63 99
All 32 46 147 225
Pearson Chi-Square = 2.469, DF = 2, P-Value = 0.291
a. What is the interpretation of the p-value for the Chi-Squared Statistic value of 2.469?
my answer:
There is no realtionship in this population
b. What is the conclusion based on the p-value?
my answer: the p value is a probability
c. What are the null and alternative hypotheses for this Chi-Squared Test?
My answer: the null- More males sit in the front and middle in restaurant
Alternative : the females sit in the back of the restaurant
b. What level of significance are you using? If P ≤ .05, then there is a relationship. You reject the null hypothesis. If P ≤ .01, you do not reject.
c. Ho(null): There is no relationship between gender and where people sit in a restaurant.
Ha: There is a relationship between gender and where people sit in a restaurant.
What is the interpretation of the p-value for the Chi-Squared Statistic value of 2.469?
-- were do I go from here on this one??
a. The interpretation of the p-value for the Chi-Squared Statistic value of 2.469 is that there is no significant relationship between gender and seating preference in this population. The p-value provides a measure of the strength of evidence against the null hypothesis. In this case, a p-value of 0.291 suggests that there is a 29.1% probability of observing a chi-square statistic as extreme as 2.469 (or more extreme) under the assumption that there is no true relationship between gender and seating preference. Since the conventional threshold for statistical significance is usually set at a p-value of 0.05, the p-value of 0.291 is greater than 0.05, indicating that we do not have enough evidence to reject the null hypothesis.
b. Based on the p-value of 0.291, the conclusion would be that there is not enough evidence to reject the null hypothesis. In other words, there is insufficient evidence to conclude that gender has a significant effect on where people sit in this restaurant.
c. The null hypothesis for this Chi-Squared Test is that there is no relationship between gender and seating preference in the population. The alternative hypothesis is that there is a relationship between gender and seating preference in the population. In this research question, the null hypothesis would state that gender does not play a role in where individuals choose to sit in the restaurant, while the alternative hypothesis would state that gender does play a role in determining seating preference.