# Is the claim of 18mg of nicotine per cigarette accurate?

• tzx9633
In summary, the conversation discusses testing a claim about the average nicotine content in a certain brand of cigarettes. Using a significance level of 0.05 and a sample size of 12, the sample mean of 19.1 is compared to the claimed average of 18mg. The appropriate null hypothesis should be that the population mean is less than or equal to 18, and the correct calculation for the t statistic should be (19.1-18)/(2/sqrt(12)), which would result in a larger t value and a stronger rejection of the null hypothesis. This could potentially indicate an error in the book or a non-standard approach to the problem.
tzx9633

## Homework Statement

An advertisement for a certain brand of cigarettes claimed that on average there's no more than 18mg of nicotine per cigarettes . A test of 12 cigarettes gave a sample mean of 19.1 . Assuming varience is 4 , test the claim with a significance level of α = 0.05

## The Attempt at a Solution

My ans is
Ho = µ_0 = 18
H1 = µ_0 <18

Since n < 30 , and standard deviation of population unknown , so , i use t-distribution

t test = (19.1-18) / ( 2 /sqrt(2) ) = 1.905

t α = 0.05 , v =11 = 1.796

Since t test > t critical , so i reject the Ho , but accroding to the ans , i should not reject the Ho ,

Is my ans wrong ?

tzx9633 said:

## Homework Statement

An advertisement for a certain brand of cigarettes claimed that on average there's no more than 18mg of nicotine per cigarettes . A test of 12 cigarettes gave a sample mean of 19.1 . Assuming varience is 4 , test the claim with a significance level of α = 0.05

## The Attempt at a Solution

My ans is
Ho = µ_0 = 18
H1 = µ_0 <18

Since n < 30 , and standard deviation of population unknown , so , i use t-distribution

t test = (19.1-18) / ( 2 /sqrt(2) ) = 1.905

t α = 0.05 , v =11 = 1.796

Since t test > t critical , so i reject the Ho , but accroding to the ans , i should not reject the Ho ,

Is my ans wrong ?
Your null hypothesis should be ##H_0: \mu_0 \le 18##
In addition, your calculation of the t statistic looks wrong to me.
https://en.wikipedia.org/wiki/Student%27s_t-test said:
In testing the null hypothesis that the population mean is equal to a specified value μ0, one uses the statistic

where
is the sample mean, s is the sample standard deviation of the sample and n is the sample size.

tzx9633 said:

## Homework Statement

An advertisement for a certain brand of cigarettes claimed that on average there's no more than 18mg of nicotine per cigarettes . A test of 12 cigarettes gave a sample mean of 19.1 . Assuming varience is 4 , test the claim with a significance level of α = 0.05

## The Attempt at a Solution

My ans is
Ho = µ_0 = 18
H1 = µ_0 <18

Since n < 30 , and standard deviation of population unknown , so , i use t-distribution

t test = (19.1-18) / ( 2 /sqrt(2) ) = 1.905

t α = 0.05 , v =11 = 1.796

Since t test > t critical , so i reject the Ho , but accroding to the ans , i should not reject the Ho ,

Is my ans wrong ?

You want to distinguish between values of ##\mu## that are ##\leq 18## and ##> 18##, so you should use ##H_0: \mu= 18## vs. ##H_1: \mu > 18##.

Are you sure you should use ##\sigma = 2?## If this refers to the sample variance, it is the estimated variance of ##X##, not of ##\bar{X}_{12}## = sample mean. The appropriate standard deviation for ##\bar{X}_{12}## is ##\sigma/\sqrt{12} = 2/\sqrt{12}.## That would give an even larger value of ##t## than the one you used, making ##H_0## even more strongly rejected than you indicate. This seems to be another instance of a wrong answer in the book (or possibly, the book having a weird, non-standard way of doing things).

Last edited:

## 1. Is the claim of 18mg of nicotine per cigarette accurate?

The accuracy of the claim of 18mg of nicotine per cigarette can vary depending on the brand and type of cigarette. The amount of nicotine in a cigarette can range from 8mg to 20mg, with an average of 12mg. It is important to note that this amount is not always absorbed by the smoker, as some nicotine is lost through the smoke and filters. Additionally, the accuracy of this claim can also be affected by the manufacturing process and the consistency of nicotine levels in each cigarette.

## 2. How is the amount of nicotine in a cigarette measured?

Nicotine levels in cigarettes are measured by conducting laboratory tests on multiple samples of a particular brand and type of cigarette. These tests analyze the amount of nicotine in the tobacco and the amount that is released when the cigarette is smoked. The results are then averaged to determine the amount of nicotine per cigarette.

## 3. Is there a difference in nicotine levels between regular and light cigarettes?

Yes, there is a difference in nicotine levels between regular and light cigarettes. Light cigarettes typically contain less nicotine than regular cigarettes, with an average of 8mg per cigarette. However, this does not mean that light cigarettes are a healthier option, as smokers may compensate for the lower nicotine levels by smoking more or inhaling deeper, resulting in similar nicotine intake as regular cigarettes.

## 4. Does the amount of nicotine in a cigarette affect its addictive potential?

Yes, the amount of nicotine in a cigarette can affect its addictive potential. Nicotine is a highly addictive substance, and the more nicotine a cigarette contains, the more addictive it can be. However, factors such as smoking behavior and individual sensitivity to nicotine also play a role in addiction.

## 5. Are there any regulations or standards for the amount of nicotine in cigarettes?

In many countries, there are regulations and standards for the amount of nicotine in cigarettes. For example, in the United States, the Federal Trade Commission requires cigarette manufacturers to disclose the amount of nicotine and tar in their products. The European Union also has regulations in place for the maximum amount of nicotine allowed in cigarettes. However, these regulations may vary by country and are constantly evolving.

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