4 Suppose a simple random sample (X; i.i.d. observations) of size n = 40 was taken from a distribution with PDF(0xº 1, if 0 < I< 1f(x) =0,otherwise.where the parameter 0 is unknown. From the sample, the following summary statistic was computed:E, In X; = -9.2945.Find the 98% confidence interval for the parameter 0 :Note: Here the confidence interval is taken to be the one based on a pivot and the pivot here is based on the fact that- In X; has an exponential (0) distribution. Further a certain multiple of sum of i.i.d. exponential random variableshas a chi-sq distribution.Note: Use at least 4 decimal places (rounded) in all the intermediate computations and in the answer submissions.

We are given the following pdf from X1,X2....Xn where n=40 f(x) = θxθ-1 if 0≤x≤1 here θ is unknown…

Answered: Suppose a simple random sample (X;…

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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For a 98% confidence interval of the population mean based on a sample of n = 20 with s = 0.05, the critical value of t is:
b) Find the critical value of t for a 90% confidence interval with df=58.
For a random sample of 50 measurements of X1, sample mean x ̄1 = 200, sample standard deviation s1 = 10. For X2, from a random sample of 50, sample mean x ̄2 = 190 and sample standard deviation s2 = 15. Assume that population distributions are approximately independent normal with unequal variances. Answer the following questions 1 through 3. 1. Construct a 90% confidence interval for μ1 − μ2. (i) State the assump- tions, (ii) show your work, and (iii) interpret the result in context of the problem. 2. Using the same samples, you want to test whether the difference between two population means is 5 or not at the significance level α = 0.1. H0 : μ1 − μ2 = 5 vs H1 : μ1 − μ2 ̸= 5. What would your conclusion be? Support your answer briefly. You don’t need to conduct the hypothesis test.
A random sample of size n1=23, taken from a normal population with a standard deviation σ1=5, has a mean x1=77. A second random sample of size n2=37, taken from a different normal population with a standard deviation σ2=3, has a mean x2=38. Find a 96% confidence interval for μ1−μ2.
To test H0: σ=4.5 versus H1: σ≠4.5, a random sample of size n=14 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s=6.7, compute the test statistic. (b) If the researcher decides to test this hypothesis at the α=0.10 level of significance, determine the P-value. (c) Will the researcher reject the null hypothesis?
A random sample of n measurements was selected from a population with unknown mean μ and standard deviation σ=35 for each of the situations in parts a through d. Calculate a 95% confidence interval for μ for each of these situations. a. n=50, x=27 b. n=150, x=118 c. n=120, x=15 d. n=120, x=5.36 a. (enter your response here,enter your response here)
A random sample of n measurements was selected from a population with unknown mean μ and standard deviation σ=15 for each of the situations in parts a through d. Calculate a 90% confidence interval for μ for each of these situations. a. n=50, x=26 b. n=150, x=115 c. n=80, x=18 d. n=80, x=4.76 e. Is the assumption that the underlying population of measurements is normally distributed necessary to ensure the validity of the confidence intervals in parts a through d? Explain. a. ( , ) b. ( , ) c. ( , ) d. ( , ) e.
A random sample of n measurements was selected from a population with unknown mean μ and standard deviation σ=15 for each of the situations in parts a through d. Calculate a 99% confidence interval for μ for each of these situations n=60, x=36 b. n=200, x=120 c. n=110, x=16
A sample of 20 items is chosen from a normally distributed population with a sample mean of ?̅ = 11.5 and a sample standard deviation of sx = 2.8. At the 0.05 level of significance test the null hypothesis that the population mean, µ is 14. H0: µ = 14 H1: µ < 14 ( ?̅ = 11.5 is less than 14) with α = 0.05.
1. For a random sample of size n = 100 from a normally distributed population has a sample mean of x ̅ = 20.85 and a sample standard deviation of s = 13.41. Find: a. 95% confidence interval for the population mean μ
A random sample of nn measurements was selected from a population with standard deviation σ=17.9 and unknown mean μ. Calculate a 99 % confidence interval for μ for each of the following situations: (a) n=40, x⎯⎯⎯=102.1≤μ≤ (b) n=55, x⎯⎯⎯=102.1≤μ≤ (c) n=80, x⎯⎯⎯=102.1≤μ≤
A random sample of size n1=22, taken from a normal population with a standard deviation σ1=6, has a mean x1=80. A second random sample of size n2=37,taken from a different normal population with a standard deviation σ2=4, has a mean x2=33. Find a 92% confidence interval for μ1−μ2

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Suppose a simple random sample (X; i.i.d. observations) of size n = 40 was taken from a distribution with PDF Soz0!, iro