Question 3. A study suggested that hospital CEOs in the US have an average age of ?=57 years old (?=0.9 years old). The group of 7 hospital CEOs claims that their average age of 59 years old is significantly older than the US average. Use the five steps process to test the hypothesis and explain your result at significant level=0.01. Question 4. Before conducting a power calculation for a one-sample z-test, what statistical information do you need to know? Provide the symbols and definitions (Think about the formula to calculate power, there are six things you need to know). Question 5. Suppose the average weight of women in the US is ?=155 lbs with ?=35 lbs. If we proposed the weight should be 165 lbs, how large a sample do we need to have to detect the proposed difference in weight with 80% power and ?= 0.05 (one-sided)?
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Answer each question in two different ways – first by calculating the value of the test statistic (for #1 and #3) or the lower and upper confidence levels (LCL and UCL, for #2), and second by using Excel. The solution to each question should include the following: the appropriate calculations (showing all work), the Excel printout, and the blanks filled in. A diet doctor claims that the average North American is more than 20 pounds overweight. To test his claim, a random sample of 20 North Americans was weighed, and the difference between their actual and ideal weights was calculated. The data is listed below: 16 23 18 41 22 18 23 19 22 15 18 35 16 15 17 19 23 15 16 26 The sample statistics are: x̄=20.85, s=6.76. Can we infer, at the 5% significance level, that the doctor’s claim is true? Assume the required conditions are satisfied. H0: The average North American is not more than 20 pounds overweight. H1: The average North American is more than 20 pounds overweight. Conclusion: Reject H0 Reason for conclusion: The calculated test statistic (t-value) is greater than the critical value at the 5% significance level, indicating that there is enough evidence to reject the null hypothesis. The doctor's claim that the average North American is more than 20 pounds overweight is supported by the data.
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