This week you will begin working on Phase 2 of your course project. Using the same data set and variables for your selected topic, add the following information to your analysis:
1. Discuss the importance of constructing confidence intervals for the population mean.
What are confidence intervals?
What is a point estimate?
What is the best point estimate for the population mean? Explain.
Why do we need confidence intervals?
2. Find the best point estimate of the population mean.
3. Construct two confidence intervals for the population mean: a 95% confidence interval and a 99% confidence interval. Assume that your data is normally distributed and the population standard deviation is unknown.
Please show your work for the construction of these confidence intervals and be sure to format your equations to fit the appropriate form (may need editing here).
4. Write a paragraph that correctly interprets the confidence intervals in context of your selected topic.
5. Compare and contrast your findings for the 95% and 99% confidence intervals.
Did you notice any changes in your interval estimate? Explain.
What conclusion(s) can be drawn about your interval estimates when the confidence level is increased? Explain.
Be sure to number your responses to these questions using the same numbers as above for your sections.
This assignment should be formatted using APA guidelines and a minimum of 2 pages in length.
Statistics Task 2 – Confidence Intervals
The Gallup Organization conducted a poll in which a simple random sample of 1,022 Americans 18 and older were asked, “Do you consider yourself financially better off than you were a year ago?” Of the 1,022 adult Americans surveyed, 450 said yes.
- Obtain a point estimate for the proportion of American adults who believe they are better off financially than they were one year ago.
- Find for a 95% confidence interval.
- Determine the margin of error for the Gallup survey based on a 95% confidence interval.
A researcher wants to know if the proportion of teenage drivers who get into an accident is different. She surveys 10,000 teenage drivers and finds that 614 got into an accident in the last year.
- Find the 99% confidence interval for the population proportion of teenage drivers that will get into an accident.
- Find the 90% confidence interval for the population proportion of teenage drivers that will get into an accident.
- Which confidence interval has a larger margin of error? Explain why it may have a larger margin of error.
A researcher wants to know the proportion of teens (16 and 17-year-olds) who have texted while driving. What size sample should the researcher use if she wants an estimate within 2 percentage points of the true population proportion with 90% confidence if
- The researcher uses a prior estimate of 34%?
- The researcher does not use any prior estimates.
- Find the t-value such that the area under the t-distribution to the right of the t-value is 0.10, assuming 20 degrees of freedom (df). That is, find t10with 20 degrees of freedom.
- Suppose for a simple random sample of 100 Americans age 15 or older, the mean time spent eating or drinking per day is 1.22 hours with a standard deviation of 0.65 hours. A histogram of time spent eating or drinking each day is skewed right. Use this result to explain why a large sample size is needed to construct a confidence interval for the mean time spent eating and drinking each day.
- Determine a 95% confidence interval for the mean amount of time Americans age 15 or older spend eating and drinking each day.