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Calculation of Confidence Interval using STATDISK

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1. Mendelian Genetics?When Mendel conducted his famous genetics experiments with peas, one sample of offspring consisted of 428 green peas and 152 yellow peas.
a. Use statdisk to find the following confidence interval estimates of the percentage of yellow peas.
99% confidence interval_______________
98% confidence interval_______________
95% confidence interval_______________
90% confidence interval_______________

b. After examining the pattern of the above confidence intervals, complete the following statement. As the degree of confidence decreases, the confidence interval limits__________________.

b. Explain why the preceding completed statement makes sense. Why should the confidence intervals behave as described?
___________________________________________________

2. Internet shopping?In a Gallup poll, 1025 randomly selected adults were surveyed and 29% of them said that they used the Internet for shopping at least a few times a year.
a. Find the point estimate of the percentage of adults who use the Internet for shopping____________
b. Find a 99% confidence interval estimate of the percentage of adults who use the Internet for shopping________________
c. Based on the result from part (b), if a traditional retail store wants to estimate the percentage of adult Internet shoppers in order to determine the maximum impact of Internet shoppers on its sales, what percentage of Internet shoppers should be used? ___________________________________

3. Credit Rating?When consumcers apply for credit, their credit is rated using FICO scores. Credit ratings are given below for a sample of applicants for car loans.
661 595 548 730 791 678 672 491 492 583 762 624 769 729 734 706 Using the sample data to construct a 99% confidence interval for the mean FICO score of all applicants for credit._____________

If one bank requires a credit rating of at least 620 for a car loan, does it appear that almost all applicants will have suitable credit ratings?

4. Stimulated Data?Randomly generate 500 IQ scores from a population having a normal distribution, a mean of 100, and a standard deviation of 15. Record the sample statistics here.
N=__________________x=______________________s=__________-

Confidence intervals are typically constructed with confidence levels around 90%, 95%, or 99%. Instead of constructing such a typical confidence interval, use the generated values to construct a 50% confidence interval. ________________________________

Does the above confidence interval have limits that actually do contain the true population mean, which we know is 100?________________

Repeat the above procedure 9 more times and list the resulting 50% confidence intervals__________ _________ __________ ______
________ _________ __________ ___________ __________

Among the total of the confidence intervals constructed, how many of them actually do contain the true population mean of 100? Is this result consistent with the fact that the level of confidence used is 50%?
________________________________________________________

Quality Control of Doughnuts?The Hudson Valley Bakery makes doughnuts that are packaged in boxes with labels stating that there are 12 doughnuts weighing a total of 42 oz. If the variation among the doughnuts is too large, some boxes will be underweight (cheating consumers) and others will be overweight (lowering profit). A consumer would not be happy with a doughnut so small that it can be seen only with an electron microscope, nor would a consumer be happy with a doughnut so large that it resembles a tractor tire. The quality control supervisor has found that he can stay out of trouble if the doughnuts have a mean of 3.50 oz and a standard deviation of 0.06 oz or less. Twelve doughnuts are randomly selected form the production line and weighted, with the results given in ounces.
3.43 3.37 3.58 3.50 3.68 3.61 3.42 3.52 3.66 3.50 3.36 3.42

Construct a 95% confidence interval for σ, then determine whether the quality control supervisor is in trouble.

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Solution Summary

The solution gives step by step procedure for the calculation of confidence interval using STATDISK.

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Correlation and Regression Questions

In this problem set you will get some practice performing a linear regression analysis. If you use Statdisk or Excel to perform any portion of these analyses, please include the results, label them, and refer to them accordingly in your interpretations.

Listed below are the overhead widths (in cm) of seals measured from photographs and the weights of the seals (in kg). The data are based on "Mass Estimation of Weddell Seals Using Techniques of Photogrammetry," by R. Garrott of Montana State University. The goal of the study is to explore the relationship between the overhead widths and the weights of the seals and to determine whether there is enough evidence to conclude that it is reasonable to use the overhead width to estimate the weight of a seal.

Overhead Width (cm) 7.2 7.4 9.8 9.4 8.8 8.4
Weight (kg) 116 154 245 202 200 191

1. Find the correlation coefficient and the critical value of r at the 5% significance level. Is there sufficient evidence to conclude that there is a linear relationship between the overhead width and the weight of the seals? Explain this using the value of the correlation coefficient and the critical value of r.

2. Find the explained variation. Explain the meaning of the explained variation in the context of this situation.

3. Find the unexplained variation. Explain the meaning of the unexplained variation in the context of this situation.

4. Find the total variation. Demonstrate and explain the relationship between the explained variation, the unexplained variation, and the total variation in the context of this situation.

5. Find the coefficient of determination. Demonstrate and explain the relationship between the explained variation, the total variation, and the coefficient of determination in the context of this situation. Explain the meaning of the coefficient of determination in the context of this situation.

6. Find the standard error of estimate.

7. Write the equation for the regression line. Explain the meaning of the slope of this line in the context of this situation. Find the predicted weight in kg of a seal given that the width from an overhead photograph is 9.0 cm.

8. Use the prediction interval spreadsheet to find both a 95% prediction interval estimate and a 95% confidence interval estimate of the weight in kg of a seal given that the width from an overhead photograph is 9.0 cm. Explain the meaning of these interval estimates in the context of this situation. Explain the difference between a 95% prediction interval estimate and a 95% confidence interval estimate for any given situation.

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