Math  /  Data & Statistics

QuestionFrom a random sample of 51 adults who earned an associate's degree from a community college (but no education beyond), the mean lifetime earnings was $1.6\$ 1.6 million. The sample standard deviation was $0.5\$ 0.5 million. Construct a 95%95 \% confidence interval for the mean lifetime income of adults who earned an associate's degree and no formal education beyond.
A What type of inference problem is this? (iii) Confidence interval for a population mean (ii) Confidence interval for the population mean of paired differences (iii) Confidence interval for a population proportion (iv) Confidence interval for the difference in two population proportions
B Are the criteria for approximate normality met? Explain. Random sample C Compute the margin of error. Round to three decimal places. 140,627140,627
D Compute the lower limit and upper limit of the 95%95 \% confidence interval. Round to three decimal places.  Lower Limit =1,459,373 Upper Limit =1,740,627\text { Lower Limit }=1,459,373 \quad \text { Upper Limit }=1,740,627
E Interpret the confidence interval in the context of this situation.

Studdy Solution
E. Interpretation of the confidence interval:
We are 95% confident that the true population mean lifetime earnings for adults who have earned an associate's degree (and no formal education beyond) falls between 1,459,373and1,459,373 and 1,740,627.
In other words, if we were to repeat this sampling process many times and construct a 95% confidence interval each time, about 95% of these intervals would contain the true population mean lifetime earnings for adults with associate's degrees.

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