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 18.1 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) O Part (b) O Part (c) O Part (d) O Part (e) O Part () O Part (g) O Part (h) O Part (i) 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.) 95% C.I.

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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 37 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.)

- Part (a)
- Part (b)
- Part (c)
- Part (d)
- Part (e)
- Part (f)
- Part (g)
- Part (h)

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 of the Diagram:

The diagram shows a bell-shaped curve representing the normal distribution of the data. The peak of the curve indicates the point estimate (sample mean), while the shaded region in the center represents the 95% confidence interval (C.I.). 

The bounds of this interval and the point estimate should be labeled on the graph. The x-axis likely represents the possible mean ages for the data set, while the y-axis shows the probability density. The 95% confidence interval is depicted as the central range under the curve, indicating where the true mean is likely to lie with 95% certainty.
Transcribed Image Text: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 18.1 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.) - Part (a) - Part (b) - Part (c) - Part (d) - Part (e) - Part (f) - Part (g) - Part (h) 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 of the Diagram: The diagram shows a bell-shaped curve representing the normal distribution of the data. The peak of the curve indicates the point estimate (sample mean), while the shaded region in the center represents the 95% confidence interval (C.I.). The bounds of this interval and the point estimate should be labeled on the graph. The x-axis likely represents the possible mean ages for the data set, while the y-axis shows the probability density. The 95% confidence interval is depicted as the central range under the curve, indicating where the true mean is likely to lie with 95% certainty.
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