Please help with the following assignment (will give helpful rating):

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)T. The Ground Nugget Potato Company wants to sell its potatoes overseas in brown octagonal gift boxes. To create the design and make sure the boxes have the proper thickness, researchers need to estimate the average weight of the oompany's potatoes. A random sample of 10-0 potatoes has a mean of 700 grams. Using previous research, you assume a population standard deviation oof .39 grams. {As you continue to study statistics you will look at how to estimate a, which is what researchers do in the real world. For now, a55ume you know it.) A. Create a 95% condence Interval for the mean weight of the potatoes. {3 points) B. Give the minimum sample size for creating a 95% oondenoe interval with a margin of error of .5 grams. (2 points) C. F\" part 3,- Why could the "WIN! size DB SO much \"I'M? than the \"WING Sill In part SE