Using Basu’s Theorem to show that for a random sample drawn from a normal distribution N (μ, σ2), the sample mean ¯X and sample variance S2 are independent of each other.
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Q: State the null and alternate hypotheses (write it mathematically) andwrite your claim. Find the…
A: x1 =473x2 = 459 s1 = 39.7s2 =24.5 n1 = 8n2 =18
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Q: A sample of n = 9 scores has SS = 72. The variance for this sample is s2 = 9. O True O False
A: Given information- Sample size n = 9 Sum of squares,SS = 72 We have given that the variance for this…
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A: Hey there! Thank you for posting the question. Since your question has more than 3 parts, we are…
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A: X~N(μ,σ2)
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A: The mean is calculated as follows:
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A: Null Hypothesis: A hypothesis which is tested for plausible rejection is called the Null Hypothesis…
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A: Given Z=2 Mean=60, variance=100, sd=10, n=16 Z=(X-mean)/sd Z=(Xbar-mean)/sd/√n
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Q: variance
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A: Given: Sample sizes: n1=8n2=18 Sample means: X¯1=473X¯2=459 Sample standard deviations: Significance…
Using Basu’s Theorem to show that for a random sample drawn from a
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- Rods are produced in large quantities in a factory. The masses of these rods are normally distributed with mean 250g and variance 9g. A random sample of 100 rods is selected. Find the probability that the mean mass of the rods in the sample will lie between 249g and 251g. If the rods are produced in batches of n and a batch is selected at random, find the least value of n such that the probability that the mean mass of the rods in the batch will lie between 249g and 251g is greater than 0.95.A researcher takes sample temperatures in Fahrenheit of 16 days from Miami and 14 days from Atlanta. Use the sample data shown in the table. Test the claim that the mean temperature in Miami greater than the mean temperature in Atlanta. Use a significance level of α=0.10α=0.10.Assume the populations are approximately normally distributed with unequal variances.Note that list 1 is longer than list 2, so these are 2 independent samples, not matched pairs. Miami Atlanta 68.3 73.6 83.1 69.3 79.1 54.9 72 81.1 72.8 78.6 83.3 54 82.7 36.1 80.7 44.3 87 58.4 83.1 50.8 77.4 60.5 86.1 61.2 76.3 46.8 74.5 54.4 83.3 78.5 The Null Hypotheses is: H0: μ1 - μ2 = 0 What is the alterative hypothesis? Select the correct symbols for each space. (Note this may view better in full screen mode.)HA: μ1 - μ2 Based on these hypotheses, find the following. Round answers to 4 decimal places. Test Statistic = p-value = The p-value is The correct…The University of Florida is interested in determining if there is a difference in the amount of money spent on food every two weeks between male and female students. They take a random sample of 20 male students (group 2) and 20 female students (group 1). They also find that xbar2 is 106 with a standard deviation of 14, and xbar1 is 146 with a standard deviation of 39. Do not assume equal variances. Find the test statistic for the difference in the amount of money spent. (Round your answer to one number after the decimal.)
- Suppose you drew a random sample,n of 100 from a population and found mean =30, standard deviation = 0.2.How is the variance sampling distribution of X changed when the sample size is increased from100 to 200? A. variance will increase В. variance will decreaseThere are two samples. Sample 1 has n=10 and a sample variance of 4. Sample 2 has n=8 and a sample variance of 9. Calculate the standard error of the difference between the two sample means (to 2 decimal points). Assume that the variances in the two populations that produced the samples are equal.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 State the null and alternate hypotheses (write it mathematically) and write your claim. Find the test statistic Identify the Rejection region (critical region) and fail to reject region. Show this by drawing a curve and separate the rejection region from the fail to reject region using the critical values
- Assume the scores on a standardized test are known to follow a bell-shaped distribution with a mean of 90 and a variance of 9. Suppose this test is administered to a group of 1250 students. Use the empirical rule to determine approximately how many students would you expect to score less than 87 or greater than 99?Independent simple random samples are taken to test the difference between the means of two populations whose variances are not known. The sample sizes are n1 = 12 and n2 = 14. Which is the correct distribution to use?A sample of n = 25 scores has a mean of x̅ = 65 and an estimated standard error of sM = 2 points. What is the sample variance?
- A biased die is thrown thirty times and the number sixes seen is eight. If the die is thrown a further twelve times find the expected numbers of sixes and the variance of the number of sixes. * E(X)=3.1 and Var.=2.346 None of the choices E(X)=3.2 and Var.=2.346 E(X)=3.2 and Var.=2.347Consider an engine parts supplier and suppose the supplier has determined that the mean and variance of the population of all cylindrical engine part outside diameters produced by the current machine are, respectively, 2.5 inches and .00075. To reduce this variance, a new machine is designed. A random sample of 20 outside diameters produced by this new machine has a sample mean of 2.5 inches and a variance of s 2 = .0002 (normal distribution). In order for a cylindrical engine part to give an engine long life, the outside diameter must be between 2.43 and 2.57 inches. If σ 2 denotes the variance of the population of all outside diameters that would be produced by the new machine, test H 0: σ 2 = .00075 versus H a: σ 2 < .00075 by setting α = .05.The average size of a farm in Pekan I is 185 acres. The average size of a farm in Pekan II is 100 acre. Assume that the data were obtained from two samples with standard deviations of 38 acres and 12 acres, and sample size of 8 and 9 respectively. Can it be concluded at α = 0.05 that the average size of the farms in Pekan I and Pekan II are different? (Assume equal variances)