You are trying to find the average age of trees in Muir Woods. Someone claims the average of trees is 20 years, but you think it's older. In order to test, you take a sample size of 10 trees. The computed value of the sample average is 22 years. The underlying distribution of trees ages is assumed to be normal and stardard deviation is assumed known at 3 years.  Perform this test at the alpha=.1 level. Compute the test statistic for this test. Round to the nearest thousandth.

The distribution of the number of motor vehicles per household in the United States (the population) and sampling distributions of the mean for samples of size 4 and 10 are shown in below. A.Which distribution is which? Make a rough estimate of the mean and standard deviation of each distribution. Explain the reasons of your choices.b. The mean of the population is about 1.7. Theoretically, what is the mean of the sampling distribution for samples of size 4? Of size 10? Are these computed means consistent with your estimates of the means in the histograms? Briefly explain.c. The standard deviation of the population is about 1. Theoretically, what is the Standard Error (SE) of the sampling distribution for samples of size 4? Of size 10? Are these computed SEs consistent with your estimates of the SEs in the histograms? Briefly explain.d. Compare the shapes of the three distributions. Are the shapes consistent with the Central Limit Theorem? Briefly explain.

Consider a set of data in which the sample mean is 30.230.2 and the sample standard deviation is 7.87.8. Calculate the z-score given that x=31.4x=31.4. Round your answer to two decimal places.

Assume that the heights of women are normally distributed with a mean of 62.4 inches and a standard deviation of 1.6 inches. Find Q3 the third quartile that separates the bottom 75% from the top 25%

Consider the following data: −10, −10, 0, 3, −10, 3, 3  Step 1 of 3: Calculate the value of the sample Variance. Round your answer to one decimal place. Step 2 of 3: Calculate the value of the sample deviation. Round your answer to one decimal place. Step 3 of 3: Calculate the value of the range.

Suppose that the average number of Facebook friends users have is normally distributed with a mean of 136 and a standard deviation of about 45. Assume forty-two individuals are randomly chosen. Answer the following questions. Round all answers to 4 decimal places where possible.   Find the third quartile for the average number of Facebook friends