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- Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately ?2 = 47.1. However, a random sample of 18 colleges and universities in Kansas showed that x has a sample variance s2 = 86.1. Use a 5% level of significance to test the claim that the variance for colleges and universities in Kansas is greater than 47.1. Find a 95% confidence interval for the population variance. (a) What is the level of significance?State the null and alternate hypotheses. Ho: ?2 = 47.1; H1: ?2 < 47.1Ho: ?2 = 47.1; H1: ?2 > 47.1 Ho: ?2 = 47.1; H1: ?2 ≠ 47.1Ho: ?2 < 47.1; H1: ?2 = 47.1 (b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)What are the degrees of freedom?What assumptions are you making about the original distribution? We assume a uniform population distribution.We…A researcher prepared a figure showing sample quantiles as a function of the quantiles of a standard normal distribution, and concluded that the resulting line could be well-described using the linear equation: Xi = 1.2 Zi + 14.6 Based on this information, what value would you suggest as an estimate of the variance for this dataset?The lifetime X of a certain electronic component in hours is an exponential random variable with a mean of 4.3. Determine the variance of X. The answer should be a number rounded to five decimal places,
- A correlation of +.20 means that [blank] of the variance in the outcome variable is accounted for by the predictor variable.Let x represent the average annual salary of college and university professors (in thousands of dollars) in the United States. For all colleges and universities in the United States, the population variance of x is approximately o² = 47.1. However, a random sample of 17 colleges and universities in Kansas showed that x has a sample variance s² = 82.7. Use a 5% level of significance 1 test the claim that the variance for colleges and universities in Kansas is greater than 47.1. (a) What is the level of significance? State the null and alternate hypotheses. Ho: o²=47.1; H: o> 47.1 Ho: o²=47.1; H: o2 0.100 0.050 a, we fail to reject the null hypothesis. Since the P-value > x, we reject the null hypothesis. Since the P-values ∞, we reject the null hypothesis. Since the P-values a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. At the 5% level of significance, there is insufficient evidence to conclude the variance of annual salaries…2. Let X - tp. Verify the mean and variance formulas. (Hint: Let X = p/2UV-1/2.)
- please answerSuppose that contamination particle size (in microm- eters) can be modeled as f(x)=2x³ for 1 < x. Determine the mean of X. What can you conclude about the variance of X?Scores on a certain exam are normally distributed with a mean of 90 and a variance of 25. What is the z-value for a score of 80? -2.0 -0.4 1.0 2.0 0.4
- 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 -.67Consider the model (1-B)(1-0.2B)X_t = (1-0.5B)W_t find the forecasts for one, two and three steps ahead and calculate the variance of the one, two, and three steps ahead forecast errors
