What are the Statistical tests used to test the normality assumption of a variable. In which situations do we use these tests, which is more effective depending on whether the number of N units is greater or less than 50.) Please explain. Also, write down the hypotheses to be established (the null and alternative hypothesis for the normality assumption). How should the tests be interpreted at the decision stage (ie when comparing the p probability values according to the 5% (0.05) significance level). Please explain..

What are the Statistical tests used to test the normality assumption of a variable. In which situations do we use these tests, which is more effective depending on whether the number of N units is greater or less than 50.) Please explain. Also, write down the hypotheses to be established (the null and alternative hypothesis for the normality assumption). How should the tests be interpreted at the decision stage (ie when comparing the p probability values according to the 5% (0.05) significance level). Please explain..

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The table below shows the rank attained by male and female officers in the NYPD. Do these data indicate that gender and rank are independent? Rank Officer Detective Sergeant Lieutenant Captain Higher Ranks Male 21900 4058 3898 1333 359 218 Female 4281 806 415 89 12 10 a) Notice that this situation involves two categorical variables in which we have a table of observed values. Your calculator will give you a table of expected values when you run the test (see part (d) below). Give the name of the hypothesis test that would be appropriate for this situation. !, b) State the hypotheses in words. c) Use your calculator to perform the appropriate hypothesis test and report the test statistic, p- value, and degrees of freedom. Be sure to write out what you entered in your calculator. Use a significance level of a = 0.05.
A researcher wanted to determine if carpeted or uncarpeted rooms contain more bacteria. The table shows the results for the number of bacteria per cubic foot for both types of rooms. A normal probability plot and boxplot indicate that the data are approximately normally distributed with no outliers. Do carpeted rooms have more bacteria than uncarpeted rooms at the a = 0.01 level of significance? Full data set O Carpeted 14.3 9.8 10.7 12.2 Uncarpeted 9.5 9.5 10.9 2.1 15 3 15.8 5.4 6.4 15.2 4.3 10.6 - X Student t-distribution Area in right tail t-Distribution Area in Right Tail Degrees of Freedom 0.25 0.20 0.15 0.10 0.05 0.025 0.02 0.01 0.005 0.0025 0.001 0.0005 1.000 0.816 0.765 0.741 1.376 1.061 0.978 0.941 0.920 1.963 1.386 1.250 1.190 1.156 3.078 1.886 1.638 1.533 6.314 2.920 2.353 2.132 12.706 4.303 3.182 2.776 2.571 15.894 4.849 3.482 2.999 2.757 31.821 6.965 4.541 3.747 3.365 63.657 9.925 5.841 4.604 4.032 127.32 1 14.089 7453 5.598 318.309 636.619 31.599 12.924 8.610 6.869 22.327…
Do you think new package labeling or doing nothing is best? You will want to calculate the percent of bars produced that are within 5 grams of 1000 grams and the percent of bars produced that are within 5 grams of 990 grams. In other words, given a uniform distribution between 980 and 1000, what is the probability of being between 995 and 1005 and what is the probability of being between 985 and 995?
Suppose that you are interested in the number of people in each household in the U.S. Your sample includes 10 households, with a mean 2.5 and a standard deviation 1.2. Construct a 95% confidence interval (CI) of the mean number of household members. (A) 1.2-3.8 (B) 1.4-3.6 (C)1.6-3.4 (D) 1.7-3.3 (E) 1.8-3.2
A researcher has run an experiment on the effects of early cognitive simulation on children and their school success at age 10 years. He wants to compare his sample results to the normal distribution (z-distribution), but he is not sure whether the population distribution is normal or not. He comes to you as an expert in statistics for advice. Can he do this? Why or why not? What conditions must be met?
Choose the correct definition of a random variable from the list below. A random variable is one whose values correspond to a scale with a countable number of values. one that occurs in one of two possible states, labeled success and failure. one that is measured to explain changes in the response variable. one whose values describe the outcome of some chance process. O one whose effect in an experiment cannot be distinguished from the effects of other variables.
Match to the appropriate answer. You will not use all options and you may not use each option more than once. Dummy variable Coefficient (beta) Correlation coefficient Heteroscedasticity p-value R² + Residual A. Used with categorical variable B. Lower value means statistical significance at a higher confidence level. C. When the distribution of residuals does change as the independent variable changes. D. Higher value means statistical significance at a higher confidence level. E. Difference between the predicted and observed values. F. When the distribution of residuals does not change as the independent variable changes. G. Min=-1, Max=1 H. Min-0, Max=1 1. Used to determine how much dependent variables changes if independent variable changed.
The accompanying data represent the running times of files produced by two motion-picture companies. Assume that the running-time differences are approximately normally distributed. Construct a 90% confidence interval for 90% confidence interval for μ - μ were created, should it be assumed that o² = = If a Company | 106 96 105 Time (minutes) 91 99 II 101 78 123 89 171 89 120 Click here to view page 1 of the table of critical values of the F-distribution, for alpha = 0.05. Click here to view page 2 of the table of critical values of the F-distribution, for alpha = 0.05. The confidence interval is < (Round to three decimal places as needed.)
A telephone poll of 500 adult Americans was reported in an issue of Time Magazine. One of the questions asked was “What is the main problem facing the country?” Thirty percent answered “crime”. We are interested in the population proportion of adult Americans who feel that crime is the main problem. Define the random variables X and P’ in words. Which distribution should be used for this problem? Explain your choice. Construct a 97% confidence interval for the population proportion of adult Americans who feel that crime is the main problem. i. State the confidence interval, ii. Sketch the graph, iii. Calculate the error bound 4. Suppose we want to lower the sampling error. What is one way to accomplish that?