**Problem 1 - Setup:**D.C. Montgomery discusses a case in which the tensile strength of a synthetic fiber used to make cloth for men's shirts is of interest to a manufacturer. It is suspected that the strength is affected by the percentage of cotton in the fiber. Three levels of cotton percentage are considered, and five observations are taken at each level. The 15 experiments are run in random order.This dataset (Cotton.xlsx) is available on Blackboard. There is a header. Note that in order for cotton to be considered as a factor in R, it cannot just consist of numeric values, so the cotton percentages are listed as C20, C25, C35, instead of 20, 25, 35. The dataset is shown below.| % Cotton | pounds per square inch | \( \bar{Y_i} \) | \( \sum Y_{ij} \) | \( \sum Y_{ij}^2 \) | \( s_i^2 \) ||----------|------------------------|-----------------|-------------------|--------------------|------------|| 20 | 12 17 17 18 18 | 15.4 | 77 | 1225 | 9.8 || 25 | 13 18 18 19 19 | 17.4 | 87 | 1539 | 6.3 || 35 | 7 10 11 15 11 | 10.8 | 54 | 616 | 8.2 |If the cotton percentages are three levels randomly selected from a big set of cotton percentages, i.e., a model with a random factor should be considered for analysis.1. **Write down appropriate statistical models for the analysis with necessary assumptions.**2. **Complete the ANOVA Table:** | Source | SS | df | MS | F | |--------------|--------|----|-----|----| | % Cotton (Trt) | 114.53 | | | | | Error | 97.20 | | | | | Total | 211.73 | | | |3. **State the null and alternative hypotheses. Perform a hypothesis test and calculate its p-value. Use a 0.05 significance level

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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a. b. C. Name: 3. You have been provided the following regression summery output for the demand for Good X. F df Significance F 0.00000798529 53.29202 Regression Residual Total Intercept Price (Px) Income (1) Price Other (Py) 3 56 59 Coefficients 355.8130 -4.9835 0.8762 -1.4893 SS 824.897 209.662 1,034.559 Standard Error 0.632473 0.939474 0.487969 0.968633 MS 255.3953 4.792375 P-value 6.45E-05 0.001985 0.078924 0.027889 Using the estimates above, state the demand function rounded to two decimals (Format: Qx=do+a1 Px + a ₂1+ a 3Py): Is the product called X a normal or inferior good? (motivate) Is the "Price Other (Py)" referring to a complement or substitute good (motivate)
An engineer designed a valve that will regulate water pressure on an automobile engine. The engineer designed the valve such that it would produce a mean pressure of 5.5 pounds/square inch. It is believed that the valve performs above the specifications. The valve was tested on 24 engines and the mean pressure was 5.7 pounds/square inch with a variance of 0.49. A level of significance of 0.01 will be used. Assume the population distribution is approximately normal. Make the decision to reject or fail to reject the null hypothesis.
A psychologist examines retention of a learned task in monkeys. At 90 days 5 monkeys are trained on a discrimination task. Then their performance is tested again at 4 months, 6 months, and 1 year. A partial ANOVA summary table follows. The data were analyzed using a repeated-measures ANOVA. Answer the following: Describe the null and alternative hypotheses. Then complete the source table. Source Between treatments SS df MS F 11 Within treatments Between subjects Error 40 Total 143
Suppose the mean weight of King Penguins found in an Antarctic colony last year was 15.4 kg. In a sample of 35 penguins same time this year in the same colony, the mean penguin weight is 14.6 kg. Assume the population standard deviation is 2.5 kg. At .05 significance level, can we reject the null hypothesis that the mean penguin weight does not differ from last year? Use P-value approach.
If, in an analysis of variance, you find that MSTR is greater than MSE, why can you not immediately reject the null hypothesis without determining the F ratio and its distribution? Explain.
If the variance of Aeronautical Engineering board examination results is 144, what is the minimum number if takers needed to estimate the population mean with 95% confidence using a margin of error of 0.80.
A researcher wants to measure average cardiovascular health of university students and compare those scores to the average scores in the general population. Assuming that population variance is known, what statistical test is most appropriate for this study? independent-samples t-test single-sample t-test z-test for sample mean related-samples t-test
The electric cooperative needs to know the mean household usage of electricity by its non-commercial customers in kWh per day. They would like the estimate to have a maximum error of 0.1 kWh. A previous study found that for an average family the variance is 6.25 kWh and the mean is 15.6 kWh per day. If they are using a 98% level of confidence, how large of a sample is required to estimate the mean usage of electricity? Round your answer up to the next integer.
An automobile manufacturer has given its van a 50.6 miles/gallon (MPG) rating. An independent testing firm has been contracted to test the actual MPG for this van since it is believed that the van has an incorrect manufacturer's MPG rating. After testing 220 vans, they found a mean MPG of 50.5. Assume the population variance is known to be 1.69. A level of significance of 0.01 will be used. Find the P-value of the test statistic. you may write the P-value as a range using interval notation, or as a decimal value rounded to four decimal places.
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