From generation to generation, the mean age when smokers first start to smoke va

Question

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 37 smokers of this generation was done to see if the mean starting age is at least 19. The sample mean was 18.2 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.)

A) State the distribution to use for the test. (Round your answers to four decimal places.)

X

~ ____ ( , )

B) What is the p-value? (Round your answer to four decimal places.)

C) Alpha (Enter an exact number as an integer, fraction, or decimal.)

=

D) Construct a 95% confidence interval for the true mean. Sketch the graph of the situation. Label the point estimate and the lower and upper bounds of the confidence interval. (Round your lower and upper bounds to two decimal places.)

Explanation / Answer

You need to set up the null hypothesis Ho (that the mean is >= 19) and the alternative Hypothesis, that the mean is < 19. Consequently you be using the 1-tailed t--test to see if the given values of the sample are within the ranger necessary for a 5% confidence.

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