Show that adding a constant K to a random variable increases the average by K but does not change the variance. Show that multiplying a random variable by K multiplies both the average and the standard deviation by K.

Find the F-test statistic to test the claim that the variances of the two populations are equal. Both distributions are normal. The populations are independent. The standard deviation of the first sample is 4.83295.8304 is the standard deviation of the second sample.

Why n-1 is used in the denominator for the variance for a normally distributed continuous RV?

Compute the standard score (Z-score) for x, when x = 42, the mean of the distribution = 26, and the standard deviation = 8. %3D %3D -2 2. We cannot tell because we don't know the value of the variance.

A toy manufacturer wants to know how many new toys children buy each year. Assume a previous study found the variance to be 1.44. She thinks the mean is 6.7 toys per year. What is the minimum sample size required to ensure that the estimate has an error of at most 0.14 at the 85% level of confidence? Round your answer up to the next integer.

maria has calculated the variance for a set of data and now takes the square root of that value. she has caculated the :  -standard deviation  -mean deviation  -mean  -mode

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…

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. ased on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Since the P-value > ?, we fail to reject the null hypothesis.Since the P-value > ?, we reject the null hypothesis.    Since the P-value ≤ ?, we reject the null hypothesis.Since the P-value ≤ ?, 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…

The sum of the squared deviations of scores from their mean: is computed the same for samples and populations. is computed by squaring each deviation to avoid a zero solution in the numerator. is the numerator for the sample variance and population variance. all of these

In a human population, the proportion of individuals with a certain disease is 0.10. if we select a sample of size 1000 from this population, determine the value of the variance of the sample proportion.