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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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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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.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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