(4 points)

Teen weights ~ Public health officials in the state of Michigan want to investigate different health measures for teenagers in the state. As part of their work, they take a sample of 42 female 15-year-olds.The mean weight of these 42 teens was 60.81 kg with a standard deviation of 14.48 kg.Round all calculated values to 4 decimal places as appropriate.1. Consider the sample of 42 female 15-year-olds as a random sample of all such teenagers in Michigan. Calculate a 95% confidence interval for the mean weight of all female 15-year-olds in Michigan.( , )

2. If the public health officials wanted to estimate the mean weight with 95% confidence and a margin of error of no more than 2.7 kg, how large a sample size would they need?Use a t* value rounded to three decimal places and the sample information above to calculate your answer. Your answer should be an integer value.n=n=

As a continuation of their work the public health officials in Michigan collect a random sample of 49 female 19-year-olds in Michigan and construct a 90% confidence interval for the mean weight to be (61.79, 71.81) kg.

3. Assuming the officials performed the calculations correctly, which of the following statements are appropriate interpretations of this confidence interval scenario? Select all that apply. A. Approximately 90% of female 19-year olds in Michigan weigh between 61.79 and 71.81 kg. B. There is a 90% chance that a different random sample female 19-year olds in Michigan will have a mean weight between 61.79 and 71.81 kg. C. We can expect that 90% of confidence intervals created using the same method the public health officials used will contain the true mean weight of female 19-year olds in Michigan. D. We can be 90% confident that the true mean weight of female 19-year olds in Michigan is between 61.79 and 71.81 kg.