ESTIMATES AND SAMPLE SIZES

Paper details:

To analyze the variation in weights of vitamin supplement tablets, a researcher randomly selects and weighs a sample of tablets. What confidence level would be appropriate for the confidence intervals? How would the intervals change (in size) as the level changes? How would the margin of error affect the outcome of the interval? What impact does the sample size have on the interval?

Module 6 Lab Assignment

Introduction

Finding relationships between variables can be very helpful, especially when it can help us make sound decisions.  In certain scenarios like knowing that a certain medication or method of treatment creates positive results can help many patients.  Upon completion of this class, you should have an understanding of correlation and regression, and how we can use it in inferential statistics. Finding a confidence interval is also useful in making decisions that affect a larger population.  Using technology to analyze the data is very important and highly useful.  This lab is your opportunity to take advantage of the tools in Excel.
Use Excel to complete the lab. Submit your document to the instructor through the link in Moodle by Sunday. Be sure to include your name in the document as well as in the name of your file.

1. Use the data in the table to complete the questions.

The IQ and brain size, as measured by the total point pixel count (in thousands) from an MRI scan, for nine female college students.

1. Construct a scatter plot for the data. Do the data appear to have a positive linear correlation, a negative linear correlation, or no linear correlation? Insert your scatter plot here and explain the visual representation of the correlation.

1. Calculate the correlation coefficient r. What can you conclude?
2. Find the equation of the regression line for the data.
3. Use the regression equation to predict the IQ of a female college student with a Pixel Count of 848.
4. You have been hired by a consortium of local car dealers to conduct a survey about the purchases of new and used cars.
5. If you want to estimate the percentage of car owners in your state who purchased new cars (not used), how many adults must you survey if you want 95% confidence that your sample percentage is in error by no more than four percentage points?

227. If you want to estimate the mean amount of money spent by car owners on their last car purchase, how many car owners must you survey if you want 95% confidence that your sample mean is in error by no more than $750? (Based on results from a pilot study, assume that the standard deviation of amounts spent on car purchases is $14,227.)

1. If you plan to obtain the estimates described in parts (a) and (b) with a single survey having several questions, how many people must be surveyed?

3. In a study designed to test the effectiveness of acupuncture for treating migraine, 142 subjects were treated with acupuncture and 80 subjects were given a sham treatment. The numbers of migraine attacks for the acupuncture treatment group had a mean of 1.8 and a standard deviation of 1.4.  The numbers of migraine attacks for the sham treatment group had a mean of 1.6 and a standard deviation of 1.2.
4. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those treated with acupuncture.

1. Construct the 95% confidence interval estimate of the mean number of migraine attacks for those given a sham treatment.

1. Compare the two confidence intervals. What do the results suggest abut the effectiveness of acupuncture?