A newspaper article noted that the mean life span for 35 male symphony conductors was 73.2 years with a standard deviation of 8.7 . Males in the general population have a mean life span of 69.5 years. Use a 0.05 significance level to test the claim that male symphony conductors have a mean life span that is greater than 69.5 years. a. Define the parameter A. mu = The mean life span of the 35 male symphony conductors in the sample B. p = The proportion of all male symphony conductors who life more than 69.5 years C. mu = The mean life span of all male symphony conductors D. mu = The mean life span of all males b. State the null and alternative hypotheses A. Upper H 0 : mu equals 73.2 Upper H 1 : mu greater than 73.2 B. Upper H 0 : mu equals 69.5 Upper H 1 : mu greater than 69.5 C. Upper H 0 : mu greater than 69.5 Upper H 1 : mu equals 69.5 D. Upper H 0 : mu not equals 69.5 Upper H 1 : mu equals 69.5 c. Use your calculator to find the P-value. Which of these options is closest to the P-value? A. 0.0041 B. 0.0103 C. 0.0084 D. 0.1087 d. State the technical conclusion A. Reject Upper H 0 B. Do not reject Upper H 0 e. State the final conclusion A. There is sufficient evidence to warrant rejection of the claim that male symphony conductors have a mean life span that is greater than 69.5 years. B. There is not sufficient sample evidence to support the claim that male symphony conductors have a mean life span that is greater than 69.5 years. C. The sample data support the claim that male symphony conductors have a mean life span that is greater than 69.5 years. D. There is not sufficient evidence to warrant rejection of the claim that male symphony conductors have a mean life span that is greater than 69.5 years.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

A newspaper article noted that the mean life span for 35 male symphony conductors was

73.2

years with a standard deviation of

8.7

Males in the general population have a mean life span of 69.5 years. Use a 0.05 significance level to test the claim that male symphony conductors have a mean life span that is greater than 69.5 years.

a. Define the parameter

= The mean life span of the 35 male symphony conductors in the sample

p = The proportion of all male symphony conductors who life more than 69.5 years

= The mean life span of all male symphony conductors

= The mean life span of all males

b. State the null and alternative hypotheses

Upper H 0 : mu equals

73.2

Upper H 1 : mu greater than

73.2

Upper H 0 : mu equals 69.5 Upper H 1 : mu greater than 69.5

Upper H 0 : mu greater than 69.5 Upper H 1 : mu equals 69.5

Upper H 0 : mu not equals 69.5 Upper H 1 : mu equals 69.5

c. Use your calculator to find the P-value. Which of these options is closest to the P-value?

0.0041

0.0103

0.0084

0.1087

d. State the technical conclusion

Reject Upper H 0

Do not reject Upper H 0

e. State the final conclusion

There is sufficient evidence to warrant rejection of the claim that male symphony conductors have a mean life span that is greater than 69.5 years.

There is not sufficient sample evidence to support the claim that male symphony conductors have a mean life span that is greater than 69.5 years.

The sample data support the claim that male symphony conductors have a mean life span that is greater than 69.5 years.

There is not sufficient evidence to warrant rejection of the claim that male symphony conductors have a mean life span that is greater than 69.5 years.

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 + ...

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