3. Given a random sample \(\{X_i\}_{i=1}^n\) from \(\mathcal{N}(\mu, \sigma^2)\), let \((L, U)\) denote the \((1-2\alpha) \times 100\%\) confidence interval of the \(t\) interval for \(\mu\). In testing hypotheses\[H_0: \mu = \mu_0 \quad \text{versus} \quad H_a: \mu < \mu_0,\]show that the rejection rule of the one-sample \(t\) test is equivalent to rejecting \(H_0\) at the significance level \(\alpha\) if \(U < \mu_0\).

Given random sample X1,X2,......,Xn from Nμ,σ2 Here, we need to test H0:μ=μ0 vs…

Answered: Given a random sample {X₂}_₁ from N(µ,…

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 x,~ N(µ1, 0;²) and x2 ~ N(µ2, 02²), and that x, and x, are independent. Develop a procedure for constructing a 100(1 – a)% confidence interval on µ1 - H2, assuming that o and o, are unknown and cannot be assumed equal.
from each population with bivariate normal distribution, samples were taken with each size n = 4, as follows. 6 5 8 5 Population | X₁ = 10 6 9 8 Population II X₂ = (₁ 5 45, 11 10 12 11' By using a = 5% a). in population 1, test the hypothesis Ho : μ = (₁ Is this Ho rejected? 5 b). in population II, test the hypothesis Ho:μ=(₁). Is this Ho rejected? 10 c). test the hypothesis Ho: E₁ = ₂. Is this Horejected?
Let X equal the number of female children in a three-child family. We shall use a chi-square goodness-of-fit statistic to test the null hypothesis that the distribution of X is b(3, 0.5) (a) Define the test statistic and critical region, using an a = 0.05 significance level. (b) Among students who were taking statistics, 52 came from families with three children. For these families, x = 0, 1, 2, and 3 for 5, 17, 24, and 6 families, respectively. Calculate the value of the test statistic and state your conclusion, considering how the sample was selected.
A random sample of nn measurements was selected from a population with unknown mean μμ and standard deviation σσ. Calculate a 90% confidence interval for μ for each of the following situations: (a) n=90, x¯¯¯=27, s=3.92n=90, x¯=27, s=3.92 ≤μ≤ (b) n=75, x¯¯¯=48.1, s=3.72n=75, x¯=48.1, s=3.72 ≤μ≤ (c) n=90, x¯¯¯=67.7, s=4.12n=90, x¯=67.7, s=4.12 ≤μ≤ (d) n=105, x¯¯¯=100.3, s=3.21n=105, x¯=100.3, s=3.21 ≤μ≤
find the p-value for the hypothesis test with the standard test statistic z. decide whether to reject H0 for the level of significanceα 14. Left-tailed test (z=-1.55, α=0.05) 16. Right-tailed test (z=1.23, α=0.10) 18. Two-tailed test (z=1.95, α=0.08)
Suppose you perform the hypothesis test Ho: u = 80 versus H1:µ + 80. The population variance, o, is unknown. The sample size isn = 13. Assume the significance level is 0.09. Part 1: 1) Should you use z or t to find the critical value? t Part 2 of 4 Part 2: 2) Choose the correct critical region. Reject Ho if t > ta Reject Ho if t ta Reject Ho if t ta Reject Ho if t ta O Reject Ho if t 2 tę Reject Ho if t s - ta or t > ta O Reject Ho if t t Reject Ho if t < – ta O Reject Ho if t < - t; ort 2 tę
An economist believes he can show that the average starting salary for electrical engineer's exceeds the average starting salaries for computer science majors. We test the hypotheses Ho: µ1 - 42 = gersus H;: µ1 – H2 > 0 at 2% level of significance. Here, lithe average starting salary of electrical engineers, and Mz denotes the average starting salary of a computer science major. We test these hypotheses by obtaining a random sample of 500 electrical engineer's starting salaries and independently, we obtain a random sample of 500 starting salaries for computer science majors. The results of the two-sample are recorded in the table below: Electrical Computer Majors Engineers Sample Size 500 500 Sample average 60000 59,000 Sample Standard 8,000 13,000 Deviation Compute the p-value
Assume that you have a sample of n₁ = 8, with the sample mean X₁ = 42, and a sample standard deviation of S₁ = 7, and you have an independent sample of n₂ = 13 from another population with a sample mean of X₂ = 33, and the sample standard deviation S₂ = 8. Construct a 99% confidence interval estimate of the population mean difference between μ₁ and μ₂. Assume that the two population variances are equal. ≤11-1₂5 (Round to two decimal places as needed.) (...
15
A random sample of 144 recent donations at a certain blood bank reveals that 86 were type A blood. Does this suggest that the actual percentage of type A donations differs from 40%, the percentage of the population having type A blood? Carry out a test of the appropriate hypotheses using a significance level of 0.01. In USE SALT State the appropriate null and alternative hypotheses. O H: p = 0.40 H:p 0.40 O Ho: p + 0.40 H: p = 0.40 O H: p = 0.40 H:p + 0.40 Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.) Z = P-value = State the conclusion in the problem context. O Reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%. O Do not reject the null hypothesis. There is sufficient evidence to conclude that the percentage of type A donations differs from 40%. O Do not reject the null hypothesis. There is not sufficient…

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