Statistics Assignment Page 1 of 2 Creating Intervals 1. Define confidence interval and confidence level. (2 points) 2. What is a critical z-value, and how is it related to the confidence level? Describe how you would look up the critical z-value for a 72% confidence interval on a normal curve table. What is the critical z-value for a 72% confidence interval? (3 points) 3. Fill in the table below. (1 point) Confidence Critical z- Level value (z*) 90 95 99 4. What is the formula for a confidence interval? A. Write the answer in words, not math symbols. (1 point) B. Write the answer symbolically, using x , z*, o, and n. (1 point) 5. Define unbiased estimator. Why are unbiased estimators useful? (2 points) 6. The TreeDropp'd Fruit Company wants to sell its apples overseas in attractive pink and yellow gift boxes. To design the boxes, the company needs to estimate the average diameter of their apples. A random sample of 50 apples has a mean of 4.1 inches. Using previous research, you assume a population standard deviation o of .4 inches. (As you continue to study statistics you will look at how to estimate o, which is what researchers do in the real world. For now, assume you know it.) A. What is the point estimate in this scenario? Is it an unbiased estimator? (1 point) B. What is the critical z-value for a 95% interval? (1 point) C. What is the margin of error for a 95% interval in this scenario? Show your work. (1 point) D. What is the 95% confidence interval for this scenario? Show your work. (2 points) E. If you wanted to construct a 99% confidence interval with a margin of error of 1% of the point estimate, what is the minimum number of apples you will need in your sample? (3 points)