Lesson 2 Assignment 3

# Lesson 2 Assignment 3 - Marcie DeGiovine 258—10-0153...

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Unformatted text preview: Marcie DeGiovine 258—10-0153 February I, 20i3 — May 20, 2013 BA635 Lesson #2, Assignment #3: Chapter 3 Problems 1. Conﬁdence Intervals: 1 tests. Digital Switches, Inc, produces a product called the C390 with an advertised 0.5% failure rate. A test of products shipped from the factory to the company's testing lab found a sample average failure rate of 0.45% with a sample standard deviation of 0.15% when a sample of n = 64 observations was studied. A. Calculate the range within which the population average failure rate can be found with 95% conﬁdence. B; Assuming that s = 0.15% cannot be reduced, and a sample size of n = 64, what is the minimum range within which the sample average faiiure rate must be found to justify with 95% conﬁdence the advertised failure rate of 0.5%? 2. Hypothesis Testing: t tests. Durable Products, Inc., has received a bid from a foreign supplier to fill the company's needs for additional mineral solution. Durable's current supplier provides materiai that is, on average, 99% pure. Sixteen samples provided by the foreign supplier have an average purity of 98%, with a standard deviation of 1%. A. Calculate the 95% conﬁdence interval within which you would expect to find the true mean purity level for solution provided by the foreign supplier. B. Is it iikely that solution provided by the foreign supplier is typical of the purity level provided by Durable's current supplier? Explain why or why not. 3. Correlation and Simple Regression. May Brothers Department Store has conducted a survey to learn the buying intentions of a sample of 62 department store customers. The survey asked each customer their household gross incomelin \$ thousands), and their number of shopping trips per year. A. Interpret the coefﬁcient of correlation between the TRIPS and INCOME variables of 0.8. B. interpret the following results for a simple regression over this sample where TRIPS is the dependent Y variable and INCOME is the independent X-variable: The regression equation is: TRlPs = 0.5 + 0.1 lNCOME iNCOME — F statistic = 105.7 Answer: 1. Confidence intervals: 2 tests A. Relevant test statistic is the 2 statistic where the known sample standard deviation 5 = 0.15% is substituted for the unknown population standard deviation. 95% conﬁdence interval for the population mean is from 0.41% to 0.49%: “LB/VF?) : 0.4:»Latent/ﬂit) -‘ 0M ">2...2_[5/.{ﬁ”3__ Cugrraaw-rf/QZQ). (j; am". B. Relevant test statistic is the 2 statistic where the known sample stande deviation 5 = 10 is substituted for the unknown population standard deviation. To justify an advertised life of 1,500 hours, the sample mean must fall within the minimum range of 0.46% to 0.54%: “flats/o"): aviators/4:12) a cum... arms/Wm . or was Lott/(Erik 05” 2. Hypothesis Testing: t tests. A. r test with die n - l : 16 - l : 15 is used to determine the 95% conﬁdence interval where you would expect to find the true population mean. Conﬁdence interval is from 97.47% to 98.53% purity, and calculated by: rte/Va“): at cons; GMT»): 97.9”? 7o 3? H15/“): (it: is. wig/m) ~. 99.533 3:. B. Based on the 95% conﬁdence interval estimated in part A, there is a less than 5% chance that the true mean for product purity from the foreign supplier meets the 99% purity (quality) ievel obtained from the domestic supplier. 3. Correlation and Simple Regression. A. A correlation coefﬁcient r = 0.8 means that there is a strong direct relation between the TRIPS and iNCOME variables. If the correlation coefﬁcient falls in the range between 1 and -l; it'r = 1, there is a perfect direct linear relation between the dependent Y-variabie and the independent X-variable; ifr = -1 and there is a perfect inverse linear relation between Y and X. For both, actual values for Y all fail exactly on the regression line. The regression equation expiains all of the underlying variation in the dependent Y variable in tenns of variation in the independent X variable. If r = 0, zero correlation exists between the dependent and independent variables; they are autonomous. When r = 0, there is no relation at ail between actual Y observations and ﬁtted fishes. B. Usually the constant in this type ot‘a regression has no meaning. The intercept should not be used to suggest the number of planned trips for a department customer with zero income. The INCOME coefficient is statistically signiﬁcant at the a = 0.05 level with a calculated t statistic value of 2; so it is possible to be 95% confident that income affects the number of planned department store trips. The probability is less than 5% of encountering such a iarge t-statistic for ENCOME since the variable is not a factor on TRIPS. The iNCOME coefﬁcient value of 0.1 means that a one-unit (thousand dollar) increase in INCOME results in an average increase of 0.1 units in the TRIPS variable. R2 = 64 "/o: the variation in the number of pianned trips can be explained using the INCOME independent variable. R2 = 64%: 63.4% of the variation in the # of planned trips can be explained using just the INCOME independent variable. (when controlling for both sample size (n=62) and the it of estimated coefﬁcients) F Static of 106.7: this level of explained variation is statisticaliy significant at more than the 99% conﬁdence level. (chances are less than 1% of encountering such a large F statistic when no relation exists between X & Y variables) SEE 0.3: can be used to indicate the range where the actual number of planned trips might be found for a customer with a given income level. (usually the # of TRIPS equals :l: (j; ' SEE) with 95% confidence) ...
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