a the gym i notice women tend to work out together more then men. males together at gym 5 alone 7 women alone 6 together 6 what statistical test should i use what is the Ha and Ho what is the appropriate analysis and should the Ho be rejected
To determine if there is a significant difference between men and women working out alone or together at the gym, you can use a Chi-square test for independence. This test is appropriate when analyzing categorical data to determine if there is a relationship between two variables.
In this case:
- The null hypothesis (Ho) is that there is no association between gender and working out alone or together. In other words, the proportion of men and women working out alone or together is the same.
- The alternative hypothesis (Ha) is that there is an association between gender and working out alone or together. This means that the proportion of men and women working out alone or together is different.
The next step is to perform the Chi-square test for independence. This test will calculate a p-value, which will help determine if we can reject the null hypothesis or not. If the p-value is less than the chosen significance level (e.g., 0.05), we can reject the null hypothesis and conclude that there is a significant association between gender and working out alone or together.
Note: To perform the actual calculations, you will need to create a contingency table with the observed frequencies for men and women working out alone or together. This table will look like this:
Alone Together Total
Men
Women
Total
Fill in the table with the given information and use it to perform the Chi-square test for independence. Once you have the test statistic and p-value, compare the p-value to the chosen significance level to make a decision on rejecting or failing to reject the null hypothesis.