A confidence interval for the difference of population means is calculated as the difference of the point estimates plus or minus themargin of error. A point estimate for the difference was found to be x₁ - x₂ = -1.4 so now the margin of error needs to be found.2The margin of error is calculated as follows where t is the value of t that corresponds to an upper tail area of a with a calculateddegrees of freedom, s, is the sample standard deviation from population 1, n, is the sample size from population 1, s2 is the samplestandard deviation from population 2, and n, is the sample size from population 2.ta/2 √OF2S₁2F3+17₂Before finding the margin of error, the values for t/2 and the standard deviations for both samples must be found.α2The value of ta/2 can be found on a table, but the values for and the degrees of freedom are needed. Recall that a is found bysetting the confidence level equal to (1 a) and solving for a. The margin of error for 90% confidence is to be found. Expressing 90%as a probability, gives 0.90, so we have 1 - a = 0.90. Therefore, a =andSubmit Skip (you cannot come back)S₂2F4F5XF64F7DELLF8n2F9α2pulation means.F1074°F SunnyF118:F1203PrtScr7:14 PM4/14/2023Insert

We have given the margin of error formula of two samples. tα/2s12n1+s22n2 Confidence level = 90% =…

Answered: A confidence interval for the…

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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Heights for teenage boys and girls were calculated. The mean height for the sample of 73 boys was 167 cm and the variance was 71. For the sample of 47 girls, the mean was 180 cm and the variance was 66. There is no reason to assume the variances would be equal. Estimate how much taller teenage boys are using a 96% confidence level. Express this in the (point estimate) ± (margin of error) format. Round answers to 2 decimal places. H
Researchers conducted a study to determine whether magnets are effective in treating back pain. Pain was measured using the visual analog scale, and the results shown below are among the results obtained in the study. Higher scores correspond to greater pain levels. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) to (c) below. Reduction in Pain Level After Magnet Treatment (u): n=22, x=0.58, s=0.89 Reduction in Pain Level After Sham Treatment (H2): n=22, x=0.51, s = 1.29 OA. Ho: H₁₂ H₁₁₂ H₁₁
A Show Time Remaining A The body lengths of deer mice are known to vary approximately normally, with mean 86 mm and standard deviation 8 mm. A research group is interested whether vitamin supplements will increase deer mouse body length. They select a random sample of 100 deer mice from the population of all deer mice that would ever receive vitamin supplements and observe their body lengths. Suppose the sample mean is calculated as 87.2 mm. Let u be the mean body length of deer mice who receive vitamin supplements. Provide the null and alternative hypotheses most appropriate for this situation. O A. Ho: H = 86 vs. Ha: P> 86 B. Họ: H = 87.2 vs. Hạ: µ 87.2 Reset Selection
Two samples of 6 and 5 items respectively gave the following data : Mean of 1st sample 40 Standard deviation of 1st sample Mean of the second sample 50 Standard deviation of the 2nd sample 10 Is the difference of means significant ? The value of t for 9 degress of freedom at 5% level is 2.26
Heights for teenage boys and girls were calculated. The mean height for the sample of 47 boys was 185 cm and the variance was 58. For the sample of 66 girls, the mean was 174 cm and the variance was 69. There is no reason to assume the variances would be equal. Estimate how much taller teenage boys are using a 87% confidence level. Express this in the (point estimate) ± (margin of error) format. Round answers to 2 decimal places. H
Listed below are systolic blood pressure measurements (mm Hg) taken from the right and left arms of the same woman. Assume that the paired sample data is a simple random sample and that the differences have a distribution that is approximately normal. Use a 0.10 significance level to test for a difference between the measurements from the two arms. Identify the test statistic and p-value. Right arm Left arm 144 167 OA.T-3.07, p-value = 0.037 OB. T = -2.32, p-value = 0.081 OC. T = -1.93, p-value = 0.127 OD. T = -4.01, p-value = 0.016 133 161 132 179 138 145 136 144
A test was made of Ho: u, = H, versus H,: µ, < µ,. The sample means were x, = 7 and 14, the sample standard deviations were s 5 and s, = 6, and the sample sizes 14 and n, 19. were n
Data on the weights (lb) of the contents of cans of diet soda versus the contents of cans of the regular version of the soda is summarized to the right. Assume that the two samples are independent simple random samples selected from normally distributedpopulations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.01 significance level for both parts. Diet Regular μ μ1 μ2 n 33 33 x 0.78488 lb 0.80356 lb s 0.00444 lb 0.00744 lb a. Test the claim that the contents of cans of diet soda have weights with a mean that is less than the mean for the regular soda. i) What are the null alternative hypothesis? ii) What's the test statics? iii) What's the P-value? iv) State the conclusion vi) construct a confidence interval suitable suitable for testing the claim that the two samples are from populations with the same mean vii) Does the confidence interval…
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The mileage in miles per gallon of several cars when they were new and when they were 3 years old is listed below. New 27 17 33 28 24 18 22 20 29 3 years 24 15 29 25 22 16 20 18 26 The mean of the sample of new car mileages is x = 23.9 with a sample standard deviation of sx 5.2, and The mean of the sample of three year old car mileage is ỹ = 21.4 with a sample standard deviation of sy = 4.6. The linear correlation coefficient is r = 0.998, which suggests linear correlation. Find the regression line and use it to predict the mileage a car will have after 3 years, if it gets 26 miles per gallon when it is new.
Heights for teenage boys and girls were calculated. The mean height for the sample of 51 boys was 183 cm and the variance was 66. For the sample of 71 girls, the mean was 173 cm and the variance was 61. There is no reason to assume the variances would be equal. Estimate how much taller teenage boys are using a 87% confidence level. Express this in the (point estimate) ± (margin of error) format. Round answers to 2 decimal places. H
let x be a ramdom variable with mean= 150 and standard deviation =4.2. Ramdom samples of fixed size n=30 are drawn from the distribution of x. determine the distribution, mean, and standard deviation of sample mean

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