-12.5 points My Notes Ask Your Teacher From generation to generation, the mean a

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-12.5 points My Notes Ask Your Teacher 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 41 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.) E Part (c) E Part (a) E Part (b) State the null hypothesis. State the alternative hypothesis. In words, state what your random variable Xrepresents. Xrepresents the average age of the sample of smokers. Ho: 19 Ha: 19 O Xrepresents the age of a person when he or she first began smoking. Ho: 19 Ha: 19 Xrepresents the average number of cigarettes for each smoker Ho: 19 Ha: H 19 Xrepresents the average age when smokers first start to smoke. Ho: 19 Ha: 219 E Part (d) State the distribution to use for the test. (Round your answers to four decimal places.) 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 Part What is the p value? (Round your answer to four decimal places.) Explain what the p-value means for this problem. lf 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 18.1 years or less 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. 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. 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 not 18.1 years or less.

Explanation / Answer

here Ho: mu>=19

Ha: mu<19

Xbar -- average age when a smoker first start to smoke

Xbar~N(19,1.32)

test stat is t (as we do not know population std deviation)

here std error =std deviation/(n)1/2 =0.203

hence test stat t=(X-mean)/std error =-4.4329

for above p vlaue =0.0000

for p value-option 2 is correct

reject the null hypothesis.

since alpha> p value , we reject the null

there is sufficient evidence ............

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