Let Y₂ represent the ith normal population with unknown mean 4, and unknown varianceof for i=1,2. Consider independent random samples, Y₁₁, Yi2,,Yin, of size ni, fromthe ith population with sample mean Y, and sample variance S?=²-1₁-1(Y - Y₁².(a) What is the distribution of Y;? State all the relevant parameters of the distribution.(b) Find a level a test (that is, the rejection region) for testing Ho: ₁ = o versusHa Hiio when of is unknown and n; is small.(c) In the context of the test in part (b), state the Type I error and give a probabilitystatement for the level of significance, a.

T- test is used under the assumptions Variances are equal and not equal

Answered: Let Y, represent the ith normal…

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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The amount of chlorine in 100 cm3 water taken from a water tank was measured, the average was 2.15 mg was found. The expert claims that the amount of chlorine in the water is greater than that measured. For this reason, 100 households were randomly selected, with an average chlorine content of 2.55mg and a variance of 0.49 mg. According to this data, find the account value z. 13 - O A) 8,15 O B) 5,71 O C) -5,71 O D) -8, 15 O E) 0.54
You are testing the claim that having lights on at night increases weight gain (abstract). A sample of 10 mice lived in an environment with bright light on all of the time and 8 mice who lived in an environment with a normal light/dark cycle is given below. Test the claim using a 10% level of significance. Assume the population variances are unequal and that the weight changes are normally distributed. Give answers to 3 decimal places. Data available at StatKey, choose Mice Wgt Gain-2e data set Light (x₁) 1.71 4.67 4.99 5.33 5.43 6.94 7.15 9.17 10.26 11.67 What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem. Ho: Select an answer ? V Select an answer V Ha: Select an answer ✓ Based on the hypotheses, find the following: Test Statistic = Dark (₂) 2.27 2.53 2.83 4 4.21 4.6 5.95 6.52 p-value = ? V Select an answer V (Hint: difference in means from Ha) The correct decision is to Select an answer…
Warming and Ice Melt The average depth of the Hudson Bay is 305 feet. Climatologists were interested in seeing if the effects of warming and ice melt were affecting the water level. Fifty-five measurements over a period of weeks yielded a sample mean of 306.2 feet. The population variance is known to be 3.6. Can it be concluded that the average depth has increased with a=.05 ? a)Use the P-value Method b) Use the Critical Value Method
You are testing the claim that having lights on at night increases weight gain (abstract). A sample of 10 mice lived in an environment with bright light on all of the time and 8 mice who lived in an environment with a normal light/dark cycle is given below. Test the claim using a 6% level of significance. Assume the population variances are unequal and that the weight changes are normally distributed. Give answers to 3 decimal places. Data available at StatKey, choose Mice Wgt Gain-2e data set Light (x1x1) Dark (x2x2) 1.71 2.27 4.67 2.53 4.99 2.83 5.33 4 5.43 4.21 6.94 4.6 7.15 5.95 9.17 6.52 10.26 11.67 H0: μ₁ = μ₂Ha: μ₁ > μ₂ Based on the hypotheses, find the following:Test Statistic = __________ (Hint: difference in means from Ha)p-value = ___________________
The variability in the amounts of impurities present in a batch of chemical used for a particular process depends on the length of time the process is in operation. A manufacturer using two production lines, 1 and 2, has made a slight adjustment to line 2, hoping to reduce the variability as well as the average amount of impurities in the chemical. Samples of 25 and 25 measurements from the two batches yield 1.04, respectively 0.51 variances. Do the data present sufficient evidence to indicate that the process variability is less for line 2? Use 5% significance level. Conduct a hypothesis test of the airline executive’s belief. [α = 0.05]
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Suppose a sample 30 observations is drawn from a population with variance population with variance population is 4.55 and the sample variance is 6.7. Test the hypothesis that the sample comes from a population with a variance greater than 4.55 at a 5% level of significance.
You are testing the claim that having lights on at night increases weight gain (abstract). A sample of 10 mice lived in an environment with bright light on all of the time and 8 mice who lived in an environment with a normal light/dark cycle is given below. Test the claim using a 2% level of significance. Assume the population variances are unequal and that the weight changes are normally distributed. Give answers to 3 decimal places. Data available at StatKey, choose Mice Wgt Gain-2e data set Light (1) 1.71 4.67 4.99 5.33 5.43 6.94 7.15 9.17 10.26 11.67 What are the correct hypotheses? Note this may view better in full screen mode. Select the correct symbols in the order they appear in the problem. Ho: ₁ Test Statistic = Dark (₂) 2.27 2.53 2.83 4 4.21 4.6 5.95 6.52 Ha: ₁ Based on the hypotheses, find the following: p-value = = V Select an answer ✓ Select an answer (Hint: difference in means from H₂) The correct decision is to fail to reject the null hypothesis The correct summary…

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