In the manufacture of a chemical product, several different layers of ink are deposited onto the surface. The thickness of these layers is critical if specifications regarding the final color are to be met. The thicknesses of two different layers of ink are considered random variables jointly distributed by the bivariate normal.

It is known that the first layer has a mean of 0.1 millimeters and a standard deviation of 3.1 millimeters, and the second layer has a mean of 0.23 millimeters and a standard deviation of 1.7 millimeters. Also, the correlation among the layers is 0.8. Moreover, specifications call for a product to have a thickness of the first layer in the range of 0.099 to 0.200 millimeters and for the second layer in the range of 0.230 to 0.250 millimeters (mm). Define random variables in your notes.

What is the variance of the sum of the two layers' thicknesses?

What is the covariance between layers?

QUESTION 2 Which of the following describes a sampling distribution? O a. distribution of individual responses in a single sample O b. distribution of individual responses in a population O c. probability distribution of individual responses in a single sample O d. probability distribution of a sample statistic QUESTION 3 Knowledge of the sampling distribution of a statistic enables researchers to a. draw a smaller sample than ordinarily would be necessary. b. estimate the probable margin of error (MoE) of a sample statistic. c. calculate the population value. d. calculate the difference between a population value and a sample estimate.Question 9 1 pts A p-value is O The probability of rejecting the null hypothesis assuming that the null hypothesis is true. 0 The probability of rejecting the null hypothesis assuming that the null hypothesis is false. 0 The probability that the observed test statistic is statistically signicant. 0 The probability of observing a test statistic at least as extreme as the observed test statistic assuming that the alternative hypothesis is true. 0 None of the above Question Completion Status: QUESTION 3 The sampling distribution of a statistic gives all the values a statistic can take O gives the probability of getting each value of a statistic under the assumption it had resulted due to chance alone is a probability distribution O all of these 3 points Save Arriwer QUESTION 4 Assuming that the population mean is 47.2 and the population deviation is 6.4, what is the zobt value for a sample mean of 52.1 if N = 8? O 1.96 O 2.17 O 1.73 0.77 3 points Save Answer Click Save and Submit to save and submit. Click Save All Answers to save all answers. Save All Answers Save and SubmitQUESTION 7 The confidence level is denoted by 1 - a. a is On the probability that a confidence interval will contain the estimated population parameter. Ob. the probability that a confidence interval will not contain the estimated population parameter. the probability that a confidence interval will contain the sample statistic. Od. the probability that a confidence interval will not contain the sample statistic. QUESTION 8 The sample mean is an unbiased point estimator of the population mean. True False QUESTION 9 The larger the p-value, the more we doubt the null-hypothesis. True False Click Save and Submit to save and submit. Click Save All Answers to save all answers