A population, T is normally distributed with unknown mean, u and variance 49. A sample of size 9 gave a sample mean of 20. Find the 99% C.I. for the population mean. А. [16,24] В. [15,25] С. [27,33] D. [14,26] A. A В. В С. С D. D
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- Suppose that the amount of protein in certain type of energy bar is Normally Distributed with a mean of 8.1 grams with a standard deviation of 0.64 grams. Suppose that a random sample of 25 of these bars is selected. d. Find the 90th percentile of the sample means of the grams of protein in these bars. e. Find the values v and w such that the middle 90% of the sample means of protein amounts fall between v and w.The desired percentage of SiO2 in a certain type of aluminous cement is 5.5. To test whether the true average percentage is 5.5 for a particular production facility, 16 independently obtained samples are analyzed. Suppose that the percentage of SiO2 in a sample is normally distributed with σ = .3. Assume that the sample mean is 5.25. (a) Does this indicate that the true average percentage differs from 5.5? Carry out a test at α = .01. (b) If the true average percentage is µ = 5.6, what is the probability of type II error?A variable of two populations has a mean of 20and a standard deviation of 18 for one of the populations and a mean of 20 and a standard deviation of 40 for the other population. a. For independent samples of size 9 and 25, respectively, find the mean and standard deviation of x1−x2. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of x1−x2 is _______________. (Type an integer or a decimal. Do not round.)
- A variable of two populations has a mean of 20and a standard deviation of 18 for one of the populations and a mean of 20 and a standard deviation of 40 for the other population. a. For independent samples of size 9 and 25, respectively, find the mean and standard deviation of x1−x2. (Assume that the sampling is done with replacement or that the population is large enough.) The mean of x1−x2 is 0 (Type an integer or a decimal. Do not round.) The standard deviation of x1−x2 is ___________. (Round to four decimal places as needed.)Suppose a random sample of exponential random variables X1, ..., Xn is taken. Find the meanand standard deviation of the sample mean.A discrete random variable X has the following probability distribution: Value of X 1 2 3 4 5 6 Probability 0.30 0.20 0.15 0.15 0.10 0.10 Find the probability that X is a multiple of 2. ["", "", "", ""] Find the probability X is greater than 1, or P(X > 1). ["", "", "", ""] Find the mean of the random variable X, μX. ["", "", "", ""] Find the variance of the random variable X, σ2XσX2 . ["", "", "", ""] Find the standard deviation of the random variable X, σX.
- The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…A normally distributed random variable has a mean of 449: a. If a score of 325 has a standard normal score - 1.38, compute for the variance of the X.b. If a score has 404 is three standard deviations below the mean, find standard deviation of X.c. If a score of 433 lies two standard deviations above the mean, find the variance of X.A certain population has a mean of 200 and standard deviation of 50. If all random samples of size 100 are drawn from this population, the resulting distribution of X will have a mean of _________.
- Suppose that average male weight in the US is 175 pounds with a standarddeviation of 25 pounds. Suppose you randomly select 1,000 male Americans and ask their weight, and average the 1,000 numbers to compute a sample mean Xn. What is the variance of the sample mean Xn?Suppose that the general fertility rate, g f rt , is following an AR(1) process shown in the image below A) if y1<1, what is the expression for the mean and variance of g f t rt showing any assumptions that were made . b) suppose that Var (€|gfrt-1)= as shown in the image below. explain why you may not obtain a best linear unbiased estimator of y0 and y1 by estimating (3) using OLS.Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the correlation coefficient between X and Y.