Censored Data Data Set 15 “Presidents” in Appendix B lists the numbers of years that U.S. presidents lived after their first inauguration. As of this writing, five of the presidents are still alive and after their first inauguration they have lived 37 years, 25 years, 21 years, 13 years, and 5 years so far. We might use the values of 37+ , 25+, 21+ ,13+, and 5+, where the positive signs indicate that the actual value is equal to or greater than the current value. (These values are said to be censored at the current time that this list was compiled.) If you use the values in Data Set 15 and ignore the presidents who are still alive, what is the mean ? If you use the values given in Data Set 15 along with the additional values of 37+, 25+, 21+, 13+,and5 + , what do we know about the mean? Do the two results differ by much?
Censored Data Data Set 15 “Presidents” in Appendix B lists the numbers of years that U.S. presidents lived after their first inauguration. As of this writing, five of the presidents are still alive and after their first inauguration they have lived 37 years, 25 years, 21 years, 13 years, and 5 years so far. We might use the values of 37+ , 25+, 21+ ,13+, and 5+, where the positive signs indicate that the actual value is equal to or greater than the current value. (These values are said to be censored at the current time that this list was compiled.) If you use the values in Data Set 15 and ignore the presidents who are still alive, what is the mean ? If you use the values given in Data Set 15 along with the additional values of 37+, 25+, 21+, 13+,and5 + , what do we know about the mean? Do the two results differ by much?
Solution Summary: The author compares the mean number of years that U.S. presidents lived after their first inauguration with the additional values.
Censored Data Data Set 15 “Presidents” in Appendix B lists the numbers of years that U.S. presidents lived after their first inauguration. As of this writing, five of the presidents are still alive and after their first inauguration they have lived 37 years, 25 years, 21 years, 13 years, and 5 years so far. We might use the values of 37+ , 25+, 21+ ,13+, and 5+, where the positive signs indicate that the actual value is equal to or greater than the current value. (These values are said to be censored at the current time that this list was compiled.) If you use the values in Data Set 15 and ignore the presidents who are still alive, what is the mean? If you use the values given in Data Set 15 along with the additional values of 37+, 25+, 21+, 13+,and5 + , what do we know about the mean? Do the two results differ by much?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
During busy political seasons, many opinion polls are conducted. In apresidential race, how do you think the participants in polls are generally selected?Discuss any issues regarding simple random, stratified, systematic, cluster, andconvenience sampling in these polls. What about other types of polls, besides political?
Please could you explain why 0.5 was added to each upper limpit of the intervals.Thanks
28. (a) Under what conditions do we say that two random variables X and Y are
independent?
(b) Demonstrate that if X and Y are independent, then it follows that E(XY) =
E(X)E(Y);
(e) Show by a counter example that the converse of (ii) is not necessarily true.
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