## Educational Content: Statistical Analysis of Two Variables### Observations for Two Variables, \( x \) and \( y \)Given are five observations:| \( x_i \) | 3 | 12 | 6 | 20 | 14 ||-----------|----|----|----|----|----|| \( y_i \) | 55 | 40 | 55 | 10 | 15 |### Questions**(a)** Estimate the standard deviation of \( \hat{y}^* \) when \( x = 10 \). **Answer:** [ ]**(b)** Develop a 95% confidence interval for the expected value of \( y \) when \( x = 10 \). **Answer:** [ ] to [ ]**(c)** Estimate the standard deviation of an individual value of \( y \) when \( x = 10 \). **Answer:** [ ]**(d)** Develop a 95% prediction interval for \( y \) when \( x = 10 \). **Answer:** [ ] to [ ]

Given,xy355124065520101415we will first find the necessary calculation xyxy…

Answered: (a) Estimate the standard deviation of…

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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One consumer wants to know if the average number of chips is less than 45 in a bag of Red Bird potato chips. A random sample of 100 was selected and the sample statistics werex=41.6 and s = 7.6. (i) What is the standard error of x? (ii) Using one or two sentences, briefly describe the Central Limit Theorem (CLT) for the sample mean. (ii) Does CLT hold for this test? Explain your reasoning. (iv) State the hypotheses for the test. (v) Give a 90% CI (3 d.p.) for the average amount of chips in each bag (The margin of error is 1.262). (vi) Interpret your Cl in part (iv) in context. (vii) Make a decision and conclusion based on your Cl in part (v).
A sample of 66 night-school students' ages is obtained in order to estimate the mean age of night-school students. x = 24.7 years. The population variance is 18. (a) Give a point estimate for u. (Give your answer correct to one decimal place.) (b) Find the 95% confidence interval for u. (Give your answer correct to two decimal places.) Lower Limit Upper Limit (c) Find the 99% confidence interval for u. (Give your answer correct to two decimal places.) Lower Limit Upper Limit
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A normal distribution has μ = 30 and σ = 5. (a) Find the z score corresponding to x = 25. (Enter an exact number.) (b) Find the z score corresponding to x = 44. (Enter a number.) (c) Find the raw score corresponding to z = −3. (Enter an exact number.) (d) Find the raw score corresponding to z = 1.5. (Enter a number.)
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1. In the past, a chemical company produced 880 pounds of a certain type of plastic per day. Now, using a newly developed and less expensive process, the mean daily yield of plastic for the first 50 days of production is 871 pounds; the standard deviation is 21 pounds. Do the data provide sufficient evidence to indicate that the mean daily yield for the new process is less than that of the old procedure? (Use α=0.05) (d) Conclusion of the test above is Reject the null hypothesis and the mean daily yield for the new process is less than that of the old procedure. Reject the null hypothesis and the mean daily yield for the new process is not less than that of the old procedure. Do not reject the null hypothesis and the mean daily yield for the new process is less than that of the old procedure. Do not reject the null hypothesis and the mean daily yield for the new process is not less than that of the old procedure.
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Use the sample information x⎯⎯x¯ = 42, σ = 7, n = 16 to calculate the following confidence intervals for μ assuming the sample is from a normal population. (a) 90 percent confidence. (Round your answers to 4 decimal places.) (b) 95 percent confidence. (Round your answers to 4 decimal places.) (c) 99 percent confidence. (Round your answers to 4 decimal places.) (d) Describe how the intervals change as you increase the confidence level.multiple choice The interval gets narrower as the confidence level increases. The interval gets wider as the confidence level decreases. The interval gets wider as the confidence level increases. The interval stays the same as the confidence level increases.

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(a) Estimate the standard deviation of ŷ* when x = 10. (b) Develop a 95% confidence interval for the expected value of y when x = 10. to (c) Estimate the standard deviation of an individual value of y when x = 10. (d) Develop a 95% prediction interval for y when x = 10. to