3. A random variable that can be used to find a 0.954 confidence interval for u, the mean of the gamma distribution is (-48) 5x 10-t(n-1) %3D V48/25 28
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- The results of a state mathematics test for random samples of students taught by two different teachers at the same school are shown below. Can you conclude there is a difference in the mean mathematics test scores for the students of the two teachers? Use α = 0.01. In addition, assume the populations are normally distributed and the population variances/standard deviations are not equal. Teacher 1 Teacher 2 ?̅1 = 473 ?̅2 = 459 S1 = 39.7 S2 = 24.5 n 1 = 8 n 2 = 18 a. State the null and alternate hypotheses (write it mathematically) and write your claim. b. Find the test statistic c. Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and…A random sample of 25 students obtained a mean of 78 and a variance of s2 = 15 on a college entrance exam in engineering. Assuming the scores are normally distributed, construct a 98% confidence interval of σ2random sample of 10 subjects have weights with a standard deviation of 10.9919 kg. What is the variance of their weights? Be sure to include the appropriate units with the result.
- A sample of size 115 will be drawn from a population with mean 48 and standard deviation 12. Use the TI-83 Plus/TI-84 Plus calculator. Part 1 of 2 (a) Find the probability that x will be less than 45. Round the answer to at least four decimal places. The probability that x will be less than 45 is 0.0037 Part: 1/ 2 Part 2 of 2 (b) Find the 25 th percentile of x. Round the answer to at least two decimal places. The 25 th percentile is Skip Part Check Save For Later Subm © 2022 McGraw Hill LLC. All Rights Reserved. Terms of Use | Privacy Cente ......... .........a ... MacBook Air DII 80 F10 F7 F9 esc F4 F6 F2 F3 F1 @ 23 $ % & 1 2 3 4 6. 8.Suppose X is a random variable with standard beta distribution and parameters (alpha) = 8 and (beta) = 2 What is (PX>=0.6)?A statistics teacher taught a large introductory statistics class, with 500 students having enrolled over many years. The mean score over all those students on the first midterm was u = 88 with standard deviation o = 10. One year, the teacher taught a %3D much smaller class of only 25 students. The teacher wanted to know if teaching a smaller class was more effective and students performed better. We can consider the small class as an SRS of the students who took the large class over the years. The average midterm score was = 78. The hypothesis should be: a. Ho: H = 78 vs. Ha: H = 88. %3D O b. Ho: µ = 88 vs. Ha: µ 78 %3D Ο d. Ho: μ-88 νs. Ha: μ >88. %3D
- A two-sided test of hypothesis assumes that a normally distributed random variable X with mean of 102.83 and standard deviation of 12.23 with alpha - 5% for a sample of size 4. If the real mean is 115 compute the power of the test.A standardized exam’s score are normally distributed. In a recent year, the mean test score was 1477 and the standard was 315. The test scores of four students selected at random 1860 1230, 2160, and 1360. Find the Z- score that correspond to each value and determine wether any of the values are unusual. The Z-score for 1860 is-The Z-score for 1230 is-The Z-score for 2160 is-The Z-score for 1360is-(Mathematical Statistics) Let X1,X2,...,X5 be a random sample of the Gamma distribution with parameters a = and ß = 0, e > 0. Determine the 95% confidence interval for the parameter e based on the statistic E(i=1 - 5) Xi. 2
- A certain IQ test is known to have a population mean of 100 and standard deviation of 15 in the general population. You want to test whether psychology majors have a different average IQ than the population as a whole. Assume the variance of IQ is the same for Psych majors as it is in the general population. Suppose that Psychology majors actually have an average IQ of 108. If you do a 2-tailed test at α= .05 with a sample of 56 Psychology majors, you will be able to reject the null hypothesis if the mean IQ of your sample is below [L] or above [H]. Find L and H values. Options listed below. [L] answer choices: 96.08, 98.00, 103.92, 104.08, 110.00, 111.92. [H] Answer choices: 96.08, 98.00, 103.92, 104.08, 110.00, 111.92.Compute the standard score (Z-score) for x, when x = 21, the mean of the distribution = 27, and the variance (S2) = 9. Z = %3D O 2 -2 .67 -.67Suppose Y = 6x-8, where x is a random variable with mean 2 and a variance of 4/3. Determine the variance of the random variable y
