(Weights of Children) Listed below are the weights (in pounds) of 20 children randomly selected from a group of one million. 70 98 85 75 90 95 77 80 73 60 63 72 53 69 83 89 71 77 80 100 (a) Construct a stem-and-leaf plot and make your comment on the shape of the distribution.

(b) Calculate the mean and standard deviation of these sample data.

(c) Based on these data with a 0.05 significance level to test the claim that the mean weight for all children in the group is at least 80 lb. (assuming the weights of all children in the group are approximately normal). Conduct a hypothesis test following the steps: Step 1. Write the null and alternative hypotheses in symbolic form. What type of test is it (Left-, right-, or two-tailed)? Step 2. Assuming the null hypothesis is true, check the requirements and determine the mean and standard deviation of the sampling distribution of the sample statistic. What test statistic should be used Step 3. Determine the type of test, find the critical value and sketch the rejection region Step 4. Calculate the sample statistic value and make your decision Step 5. State your conclusion in plain English