Suppose x has a normal distribution with mean μ = 36 and standard deviation σ = 15. Describe the distribution of x values for sample size n = 4. (Round ox to two decimal places.) Mx = 0x = Describe the distribution of x values for sample size n = 16. (Round ox to two decimal places.) Mx = Describe the distribution of x values for sample size n = 100. (Round ox to two decimal places.) Hx= 0x = How do the x distributions compare for the various samples sizes? The standard deviations are the same, but the means are decreasing with increasing sample size. O The standard deviations are the same, but the means are increasing with increasing sample size. The means are the same, but the standard deviations are decreasing with increasing sample size. O The means and standard deviations are the same regardless of sample size. The means are the same, but the standard deviations are increasing with increasing sample size.

Suppose x has a normal distribution with mean ? = 53 and standard deviation ? = 7.Describe the distribution of x values for sample size n = 4. (Round ?x to two decimal places.) ?x =  ?x =  Describe the distribution of x values for sample size n = 16. (Round ?x to two decimal places.) ?x =  ?x =  Describe the distribution of x values for sample size n = 100. (Round ?x to two decimal places.) ?x =  ?x =

The two data sets in the table below are dependent random samples. The population of (x - y) differences is approximately normally distributed. A claim is made that the mean difference (x - y) is less than 29.3. X y DII For each part below, enter only a numeric value in the answer box. For example, do not type "z =" or "t=" before your answers. Round each of your answers to 3 places after the decimal point. (a) Calculate the value of the test statistic used in this test. Test statistic's value = -2.760 61 71 58 48 38 41 (b) Use your calculator to find the P-value of this test. P-value $ 4 44 48 66 43 32 30 29 33 (c) Use your calculator to find the critical value(s) used to test this claim at the 0.07 significance level. If there are two critical values, then list them both with a comma between them. Critical value(s) = -1.700 (d) What is the correct conclusion of this hypothesis test at the 0.07 significance level? O There is sufficient evidence to support the claim that the mean…

In a population of a certain species of newt, the mean length of the newts is μ= 63 inches and the standard deviation is σ= 3.4 inches. You collect a random sample of n=16 newts. The bell curve below represents the distribution of these sample means. The scale on the horizontal axis is the standard error of the sampling distribution. Complete the indicated boxes, correct to two decimal places. mean of distribution= standard error=       Note: The left box is 2 standard errors below the mean. The middle box is the mean. The right box is 2 standard errors above the mean.

The mean performance score of a large group of fifth-grade students on a math achievement test is 76. The scores are known to be normally distributed. What percentage of the students had scores more than 2.1 standard deviations above the mean? Click here for page 1 of the Areas under the Normal Curve Table Click here for page 2 of the Areas under the Normal Curve Table The percentage of the students that had scores more than 2.1 standard deviations above the mean is%. (Round to two decimal places as needed.)

P3. Show that the mle of unknown standard deviation when the mean is known is different from the sample standard deviation when the random sample is taken from a normal population characterized by two parameters, mean and variance. Which estimator is unbiased? Justify your answer. Show that a sample mean is a minimum variance unbiased estimator of the mean of a normal population with known variance.

When you take samples of size n - 100 from a normally distributed population, what will likely be the shape of the distribution of sample means? Right Skewed Left Skewed Normal

According to the US Census Bureau. the number of people in a household has amean of 2.6 and a standard deviation of 1.5. Suppose the census bureauinstead had estimated this mean using a random sample of 225 homes and that sample had a mean of 2.4 and standar deviation of 1.4. Describe the center and spreadof the sample mean for 225 homes. What does the distribution describe?