Question

Based on experience, you believe that less than 15% of the population of your city dislike the taste of cilantro. Two-hundred people were randomly selected from your city and questioned about their like or dislike of the taste of cilantro. Thirty-two of those questioned stated they disliked the taste of cilantro.

Complete the tasks and answer the questions.

• Use the 2SD method to estimate the true proportion of the population of your city that dislikes the taste of cilantro. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.
• Write the interpretation of this confidence interval.
• Use the theory-based method to estimate the true proportion of the population of your city that dislikes the taste of cilantro with a 95% confidence interval. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.
• Write the interpretation of this confidence interval.
• Use the theory-based method to estimate the true proportion of the population of your city that dislikes the taste of cilantro with an 88% confidence interval. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.
• Write the interpretation of this confidence interval.

Answer 1

Solution:

We are given:

Use the 2SD method to estimate the true proportion of the population of your city that dislikes the taste of cilantro. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.

Answer:

The 2SD confidence interval is given below:

Therefore, the interval notation is:

And the sample proportion ± the margin of error notation is:

Write the interpretation of this confidence interval.

Answer: There is a 95% confidence that the confidence interval calculated contains the true
population proportion.

Use the theory-based method to estimate the true proportion of the population of your city that dislikes the taste of cilantro with a 95% confidence interval. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.

Answer: The 95% confidence interval is given below:

Therefore, the interval notation is:

And the sample proportion ± the margin of error notation is:

Write the interpretation of this confidence interval.

Answer: There is a 95% confidence that the confidence interval calculated contains the true
population proportion.

Use the theory-based method to estimate the true proportion of the population of your city that dislikes the taste of cilantro with an 88% confidence interval. State the resulting confidence interval in both forms – the interval notation and the sample proportion ± the margin of error notation.

Answer: The 88% confidence interval is given below:

Therefore, the interval notation is:

And the sample proportion ± the margin of error notation is:

Write the interpretation of this confidence interval.

Answer: There is an 88% confidence that the confidence interval calculated contains the true
population proportion.