Suppose you have a normally distributed population such that \(\sigma^2 = 8\). Using the sampling distribution of \(S^2\), we find that from a random sample of size \(n = 15\), \(S^2 = 16.09\). Does our population variance seem reasonable?Note: We will consider our population variance reasonable if our \(\chi^2\) value falls within the interval \([\chi^2_{0.975}(df), \chi^2_{0.025}(df)]\).1) Find the values of the interval \([\chi^2_{0.975}(df), \chi^2_{0.025}(df)]\).\[\chi^2_{0.975}(df) = \](Round to 3 decimals.)\[\chi^2_{0.025}(df) = \](Round to 3 decimals.)2) Find the value of \(\chi^2\) that comes from the data you collected in the problem statement.\[\](Round to 3 decimals.)3) Is the population variance reasonable?- [ ] Yes- [ ] NoNo work required for Part 1 or Part 3, but recommended on Part 2.If you do not have a table, DI Management's "Compute the inverse of the p-value for a chi-square distribution" is useful to get exact answers (to many decimals).[Add Work]

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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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Suppose that X1,..., X, is a random sample from a normal distribution with mean u and variance o?. Two unbiased estimators of o? are ởf = s° = E(x, - Xy°, and ô = (X1 - 2 Find the efficiency of ở relative to ôž.
6. The resting pulse rate, X, for a particular population of adult women is normally distributed w mean of 74 beats per minute (bpm) and a standard deviation of 6 bpm. a) Find P(66 s X s 78) b) Find the 60th percentile of women's resting heart rates. c) If a sample of four women is randomly selected, find P(X > 79). d) Suppose now that the sample size is greater than four. Will the probability P(X > 79) be greater than, less than or the same as the value found in part c)? Explain.
4.
12) A metal bar is heated, and then allowed to cool. Its temperature T (in °C) is found to be The time is in minutes. T=15+75e-0.25 t Find the time rate of change of temperature after 5.0 minutes. 13) The standard normal curve (sometimes called the bell curve) in statistics looks like: 1 -x² y = e 2 √2π Show that there are two inflection points at x = +1
The calibration of a scale is to be checked by weighing a 11 kg test specimen 25 times. Suppose that the results of different weighings are independent of one another and that the weight on each trial is normally distributed with o = 0.200 kg. Let u denote the true average weight reading on the scale. (a) What hypotheses should be tested? Ho: H = 11 Ha: u + 11 Ho: H + 11 H3i H 11 a (b) With the sample mean itself as the test statistic, what is the P-value when x = 10.83? (Round your answer to four decimal places.) What would you conclude at significance level 0.01? Conclude that the true mean measured weight differs from 11 kg. Conclude that the true mean measured weight is the same as 11 kg. (c) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 11.2? (Round your answer to four decimal places.) For a test with a = 0.01, what is the probability that recalibration is judged unnecessary when in fact u = 10.9? (Round your answer to…
A variable of two populations has a mean of 49 and a standard deviation of 14 for one of the populations and a mean of 54 and a standard deviation of 15 for the other population. a) For independent samples of sizes 34 and 45, respectively, find the mean and standard deviation of ₁ - 2. mean: standard deviation: b) Can you conclude that the variable 1 T2 is approximately normally distributed? (Answer yes or no) answer:
34) If a population exhibits a skew of -5.00 and an excess kurtosis of 5.00 which of the following is true? The population mean exceeds the median. The population variance exceeds the standard deviation. The population standard deviation exceeds the variance. The population median equals the mean. The population median exceeds the mean.
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ndependent random samples are selected from two populations and are used to test the hypothesis Hn: (H, - H2) = 0 against the alternative H,: (4, - H2) #0. An analysis of 232 observations from population 1 and 311 from population 2 yielded p-value of 0.113. Complete parts a and b below. a. Interpret the results of the computer analysis. Use as0.10. A. Since this p-value exceeds the given value of a, there is insufficient evidence to indicate that the population means are different. O B. Since the given a value exceeds this p-value, there is insufficient evidence to indicate that the population means are different. OC. Since the given a value exceeds this p-value, there sufficient evidence to indicate that the population means are different. O D. Since this p-value exceeds the given value of , there is sufficient evidence to indicate that the population means are different. b. If the alternative hypothesis had been Ha: (H1 - H2) <0, how would the p-value change? Interpret the p-value…

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