From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 45 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) O Part (a)State the null hypothesis.Ο Ηρ μ< 19Ο Hg: μ+ 19Ho: H 2 19Ο H, μ= 19O Part (b)State the alternative hypothesis.Ο H μ+ 19Hai H2 19Ο H, μ< 19Ο H, μ= 19O Part (c)In words, state what your random variable X represents.O x represents the age of a person when he or she first began smoking.X represents the average number of cigarettes for each smoker.O X represents the average age when smokers first start to smoke.O X represents the average age of the sample of smokers.O Part (d)State the distribution to use for the test. (Round your answers to four decimal places.)O Part (e)What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)|---Select--- v = O Part (f)What is the p-value? (Round your answer to four decimal places.)Explain what the p-value means for this problem.If Ho is true, then there ischance equal to the p-value that the average age of people when they first begin to smoke is 18.1 years or less.O If Ho is true, then there is a chance equal to the p-value that the average age of people when they first begin to smoke is not 18.1 years or less.O If H, is false, then there is a chance equal to the p-value that the average age of people when they first begin to smoke is not 18.1 years or less.O If Ho is false, then there is a chance equal to the p-value that the average age of people when they first begin to smoke is 18.1 years or less.O Part (g)O Part (h)Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)a =(ii) Decision:O reject the null hypothesisO do not reject the null hypothesis(iii) Reason for decision:O Since a < p-value, we do not reject the null hypothesis.O Since a > p-value, we do not reject the null hypothesis.O Since a < p-value, we reject the null hypothesis.O Since a > p-value, we reject the null hypothesis.(iv) Conclusion:O There is sufficient evidence to conclude that the starting age for smoking in this generation is less than 19.O There is not sufficient evidence to conclude that the starting age for smoking in this generation is less than 19.

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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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From generation to generation, the mean age when smokers first start to smoke varies. However, the standard deviation of that age remains constant at around 2.1 years. A survey of 45 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.1 with a sample standard deviation of 1.3. Do the data support the claim at the 5% level?

Note: If you are using a Student's t-distribution for the problem, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

O Part (a)
State the null hypothesis.
Ο Ηρ μ< 19
Ο Hg: μ+ 19
Ho: H 2 19
Ο H, μ= 19
O Part (b)
State the alternative hypothesis.
Ο H μ+ 19
Hai H2 19
Ο H, μ< 19
Ο H, μ= 19
O Part (c)
In words, state what your random variable X represents.
O x represents the age of a person when he or she first began smoking.
X represents the average number of cigarettes for each smoker.
O X represents the average age when smokers first start to smoke.
O X represents the average age of the sample of smokers.
O Part (d)
State the distribution to use for the test. (Round your answers to four decimal places.)
O Part (e)
What is the test statistic? (If using the z distribution round your answers to two decimal places, and if using the t distribution round your answers to three decimal places.)
|---Select--- v =

O Part (f)
What is the p-value? (Round your answer to four decimal places.)
Explain what the p-value means for this problem.
If Ho is true, then there is
chance equal to the p-value that the average age of people when they first begin to smoke is 18.1 years or less.
O If Ho is true, then there is a chance equal to the p-value that the average age of people when they first begin to smoke is not 18.1 years or less.
O If H, is false, then there is a chance equal to the p-value that the average age of people when they first begin to smoke is not 18.1 years or less.
O If Ho is false, then there is a chance equal to the p-value that the average age of people when they first begin to smoke is 18.1 years or less.
O Part (g)
O Part (h)
Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write an appropriate conclusion.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
a =
(ii) Decision:
O reject the null hypothesis
O do not reject the null hypothesis
(iii) Reason for decision:
O Since a < p-value, we do not reject the null hypothesis.
O Since a > p-value, we do not reject the null hypothesis.
O Since a < p-value, we reject the null hypothesis.
O Since a > p-value, we reject the null hypothesis.
(iv) Conclusion:
O There is sufficient evidence to conclude that the starting age for smoking in this generation is less than 19.
O There is not sufficient evidence to conclude that the starting age for smoking in this generation is less than 19.

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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