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Consider a tech company that wants to offer free breakfast to its employees if their confidence interval shows it will decrease the proportion of employees who skip breakfast.

Each interval shows the difference in proportion of [tex]p_1 - p_2[/tex] where [tex]p_1[/tex] represents the employees who skip breakfast when free breakfast is offered and [tex]p_2[/tex] represents the employees who skip breakfast when free breakfast is not offered. Determine if there is enough evidence to suggest that offering free breakfast results in an increase in the proportion of employees who don't skip breakfast.

1. Confidence Interval: (-0.44, -0.16)
- Yes, we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
- Or
- No, our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.

2. Confidence Interval: (-0.25, 0.05)
- Yes, we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
- Or
- No, our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.

3. Confidence Interval: (-0.23, 0.15)
- Yes, we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.
- Or
- No, our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.

Answer :

Final answer:

The confidence intervals provide information on whether there is enough evidence to suggest that offering free breakfast results in a decrease in the proportion of employees who skip breakfast.

Explanation:

The confidence interval (-0.44, -0.16) indicates that there is enough evidence to suggest that offering free breakfast results in a decrease in the proportion of employees who skip breakfast. The lower limit of the confidence interval, -0.44, means that at the minimum, the proportion of employees who skip breakfast when free breakfast is offered is 0.44 less than when it's not offered. The upper limit of the confidence interval, -0.16, means that at the maximum, the proportion of employees who skip breakfast when free breakfast is offered is 0.16 less than when it's not offered.

The confidence interval (-0.25, 0.05) indicates that there is not enough evidence to suggest that offering free breakfast results in a difference in the proportion of employees who skip breakfast. The entire confidence interval ranges from negative to positive values, indicating that the proportion of employees who skip breakfast when free breakfast is offered could either be higher or lower than when it's not offered.

The confidence interval (-0.23, 0.15) indicates that there is not enough evidence to suggest that offering free breakfast results in a difference in the proportion of employees who skip breakfast. The entire confidence interval ranges from negative to positive values, indicating that the proportion of employees who skip breakfast when free breakfast is offered could either be higher or lower than when it's not offered.

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Answer:

Step-by-step explanation:

In this scenario, the confidence interval represents the possible range of differences in the proportion of employees who skip breakfast when free breakfast is offered and when it's not. A confidence interval that does not include zero indicates that there is statistically significant evidence to suggest a difference in proportions between these two groups.

Therefore, for the first interval (-0.44,-0.16), since it does not include zero, we can be confident that offering free breakfast results in a decrease in the proportion of employees who skip breakfast.

For the second interval (-0.25, 0.05), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

Similarly, for the third interval (-0.23, 0.15), since it contains zero, we cannot be confident that there is a difference in the proportion of employees who skip breakfast between the two groups.

So, the correct answer is:

For the interval (-0.44,-0.16), we can be confident that employees will skip breakfast less when free breakfast is offered than when it's not.

For the intervals (-0.25, 0.05) and (-0.23, 0.15), our confidence interval shows that there could be no difference in the proportion of employees who skip breakfast.

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