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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4) A set of measurements is given as follows. X = [0.1, 0.3, 0.8, 12,4, 7,9] We want to approximate the source of this data with Gamma distribution, i.e., X~Gamma(a, B). For Gamma distribution, the mean and variance can be found from the below equations. a Hx a o = Find the parameters of Gamma distribution to fit the data. Come up with two other distributions that you think are good representation of this data. Justify your answer.
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.
The distribution of certain test scores is a nonstandard normal distribution with a mean of 80 and a standard deviation of 9. What are the values of the mean and a standard deviation after all test scores have been standardized by converting them to z-scores using z=(x-µ)/σ? A) The mean is 100 and the standard deviation is 10 B) The mean is 0 and the standard deviation is 1 C) The mean is 1 and the standard deviation is 0 D) The mean is 10 and the standard deviation is 100
Use the following data to answer question 8 - 12. A number of studies have claimed evidence that the first-born in a family is, on the whole, more likely to be "successful" than later-borns. A study along this direction compared the IQs of a random sample of 80 first-borns with those of an independent random sample of 105 later-borns. The data are summarized below: Sample size Sample mean Sample SD First-borns 80 112 7.2 Later-borns 105 108 8.0
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…
With a sample size of 5, the P(t<x)=0.57P(t<x)=0.57. What is xx
A sample of n = 8 scores has a mean of M = 16. For this sample, ΣX = 128. Is this true or false?
Suppose you have a normally distributed population such that o? = 7. Using the sampling distribution of S?, we find that from a random sample of size n = 11, s² = 16.053. Does our population variance seem || reasonable? Note: We will consider our population variance reasonable if our x value falls within the interval x0.975 (df), x'o.025 (df)]. 1) Find the values of the interval [xo.975(df), x²o.025(df)]. x°0.975(df) = (Round to 3 decimals.) x'0.025(df) - (Round to 3 decimals.) 2) Find the value of x that comes from the data you collected in the problem statement. (Round to 3 decimals.) 3) Is the population variance reasonable? Yes O No
Estimate ff e+y“ dA with R = [0, 3] × [0, 3] using m = n = 2 and midpoints as your R sample points.
We have a random sample of 36 data palrs where the sample mean of the differences is 1.18 and the sample standard devlation of the differences Is 3. Then the sample test statistic Is d = 1.18 Using these values, along with u = 0, we calculate the corresponding t value for the test statistic. 1.18 - 0 V V36 0.065
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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