# Discussion: Statistical Methods Content of Zirconium Worksheet

Discussion: Statistical Methods Content of Zirconium Worksheet ORDER NOW FOR CUSTOMIZED AND ORIGINAL ESSAY PAPERS ON Discussion: Statistical Methods Content of Zirconium Worksheet I need support with this Statistics question so I can learn better. The University of Tampa MAT 152 Statistical Methods Content of Zirconium Worksheet this is Homework for statistics class the question is attached below with format examples for question 3 module_10_assingment.pdf abet_format.pdf abet_format2.pdf Statistical Methods (MET E 3070) Module 10: Chapter 11 1. As an engineer, you are asked to investigate the relationship between steel strength and content of zirconium. To find some meaningful information: a) Compute: ?????? and ?????? ?0 and ?? ?1 b) Compute: ?? c) Compute: ????? d) Compute: ?????? , ?????? and ?????? e) Test the significance of the regression at ?? = 0.05. Whats your conclusion? (??0 = 53.24) f) Test the hypothesis ??0 : ??1 = 4 & ??0 : ??1 ? 4 g) Compute: ?? 2. What does it say about your regression? h) Find a 95% confidence interval on the ??1 and ??0 i) Find a 95% confidence interval for the mean response for a zirconium % of 5 j) Find a 95% confidence interval on a future observation at ??0 = 7. Strength (Kpa) % Zr 85 5 89 4 90 6 90 8 90 4 90 5 94 7 100 9 100 7 100 6 60 1 63 0 65 1 70 2 70 5 70 1 80 4 90 6 2. In another engineer job, you were asked to interpret the relationship between temperature and the grow of bacteria. To find some meaningful information: a) Compute: ?????? and ?????? ?0 and ?? ?1 b) Compute: ?? c) Compute: ????? d) Compute: ?????? , ?????? and ?????? e) Test the significance of the regression at ?? = 0.05. Whats your conclusion? (??0 = 44.03) f) Test the hypothesis ??0 : ??1 = 12 & ??0 : ??1 ? 12 g) Compute: ?? 2. What does it say about your regression? h) Find a 95% confidence interval on the ??1 and ??0 i) Find a 95% confidence interval for the mean response for a temperature of 55 C ? j) Find a 95% confidence interval on a future observation at ??0 = 45. The University of Tampa MAT 152 Statistical Methods Content of Zirconium Worksheet Temperature (C) 40 42 49 46 44 48 46 43 53 52 54 57 58 # of bacteria 400 405 465 470 465 485 490 535 565 585 587 605 625 3. JJ works for a large automobile plant. For one of her assignments, she will need to investigate a claimed, which was discussed in meeting with her manager, and present the results found. The claimed is that heavier autos will give lesser gasoline mileage and lighter autos will give higher gasoline mileage. She will be working at the manufacturing area with cars that could weight from 2500 to 6000 lbs. How should she go about collecting data needed to prove or disprove the claim? How would she go about using the collected data to determine if there is a linear relationship between the gasoline mileage and weight of the car? Goal: Confirm that the proportion of defective chips has been reduced. Statistical Method: To examine the proportion of defective chips manufactured, a confidence interval can be implemented. In this specific case since the population of chips is binomial, a proportion confidence interval will be calculated. This interval will give the range of the proportion of the defective chips to the normal chips. Here, an upper bound of a 95% or 99% confidence interval will be examined. The University of Tampa MAT 152 Statistical Methods Content of Zirconium Worksheet Thus, this upper bound will yield the highest percentage of defective chips for any given sample. Procedure: Constructing the confidence interval begins with setting the probability equal to the confidence interval, as if it were normally distributed. Thus, the probability is formed as seen below: ? ? ? = (1 ? ?) Equation 1 Equation 1 is the basis for this calculation since a binomial distribution becomes normally distributed as n is increased. However, for a binomial population, approximated as a normal distribution, the Z value is as seen in Equation 2. = ( ) = ( Equation 2 ) Substituting Equation 2 into Equation one and rearranging to solve for the bounds of p yields the following equation. ( ( ? ) ? ? + ( ) ) ? (1 ? ?) Equation 3 Similar to the proportion confidence interval seen in equation 3, the upper most bound will be examined. This upper bound will be examined using a 95% or 99% confidence interval. When calculating the upper bound, z? is used. ? + ( ) Equation 4 Solution: JJ can use the above statistical method to determine if the proportion of defective chips was truly reduced. Starting by taking a various number of samples, the more the better, JJ will determine the proportion of defective chips.The University of Tampa MAT 152 Statistical Methods Content of Zirconium Worksheet Following the methods listed above, JJ can examine the uppermost bound of the proportion confidence interval. She will be able to see the highest percent of defective chips any sample may contain. In this case it would be most beneficial to evaluate this proportion with a 95% or 99% confidence interval. She will know the proportion has decreased if Equation 4 yields a number smaller than 0.045. The problem is that she needs to test to make sure the number of defectives is reduced. The methodology here should be to test for a specified proportion. This methodology will show us whether the proportion of defective chips to functioning chips had become less than 4.5%. Let the proportion of defective chips in a sample be P. Let P0 denote the actual proportion of defective chips (4.5%). where After obtaining the critical value of Z for the confidence interval, if the calculated value of Z is greater than the critical value, the number of defectives is not reduced. If the calculated value of Z is less than the critical value, the number of defectives is reduced. Get a 10 % discount on an order above $ 100 Use the following coupon code : NURSING10