Usin7) An employer polled its employers to see if they agree with the proposed new store hours and whether or not their present shift made a difference in their answers. The customers answered 1 for agree, 2 for don't know, and 3 for disagree. Nine first shift employees answered "agree", 15 second shift employees answered "agree", and 20 third shift employees answered agree. With a 95% confidence level determine whether or not the employees' present shift played a role in their responses to the pollg the chi squared distribution.

To determine whether the employees' present shift played a role in their responses to the poll, we can conduct a chi-squared test of independence. This test allows us to assess whether there is a significant association between the two categorical variables (present shift and response to the poll).

To perform the chi-squared test, we need to set up the null and alternative hypotheses. The null hypothesis (H0) assumes that there is no association between the two variables, meaning the present shift does not affect the employees' responses. The alternative hypothesis (Ha) assumes that there is an association between the two variables.

H0: There is no association between present shift and response to the poll.
Ha: There is an association between present shift and response to the poll.

Next, we need to create a contingency table, also known as an observed frequency table. The contingency table will display the observed frequencies of each combination of present shift and response categories.

| | Agree | Don't Know | Disagree |
|------------|-------|------------|----------|
| 1st Shift | 9 | - | - |
| 2nd Shift | 15 | - | - |
| 3rd Shift | 20 | - | - |

Since we don't have the frequencies for "Don't Know" and "Disagree," we can calculate them by subtracting the frequencies of "Agree" from the total number of employees in each shift. For example:

Number of 1st shift employees = 9 (Agree) + "Don't Know" + "Disagree"
Number of 2nd shift employees = 15 (Agree) + "Don't Know" + "Disagree"
Number of 3rd shift employees = 20 (Agree) + "Don't Know" + "Disagree"

Now, we can complete the contingency table:

| | Agree | Don't Know | Disagree |
|------------|-------|------------|----------|
| 1st Shift | 9 | x | y |
| 2nd Shift | 15 | w | z |
| 3rd Shift | 20 | u | v |

The next step is to perform the chi-squared test. We calculate the expected frequencies based on the assumption of independence, which can be determined using the formula:

Expected Frequency = (row total) * (column total) / (total number of observations)

Using the expected frequencies, we can then calculate the chi-squared statistic:

χ^2 = Σ ((Observed Frequency - Expected Frequency)^2 / Expected Frequency)

Finally, we need to determine the critical value or p-value associated with the chi-squared statistic. The critical value helps us decide whether to reject or fail to reject the null hypothesis. The p-value, on the other hand, gives the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.

If the p-value is less than the significance level (e.g., 0.05), we reject the null hypothesis. If the p-value is greater than the significance level, we fail to reject the null hypothesis.

By comparing the calculated chi-squared statistic to the critical value or p-value, we can determine if there is a significant association between the present shift and employees' responses to the poll.

Note: To calculate the exact values, we need additional information, such as the total number of employees in each shift and the responses of "Don't Know" and "Disagree."