Final answer:
To test the claim that the average number of cigarettes smoked by smokers has increased, a one-sample t-test can be used. The null hypothesis states that the average number of cigarettes smoked has not increased, and the alternative hypothesis states that it has. The test statistic is calculated using the sample mean, population mean, sample standard deviation, and sample size, and is compared to the critical value or p-value to make a decision.
Step-by-step explanation:
To test the claim that the average number of cigarettes smoked by smokers has increased, we can use a one-sample t-test.
1. Null hypothesis: The average number of cigarettes smoked by smokers is not increased.
2. Alternative hypothesis: The average number of cigarettes smoked by smokers has increased.
3. Calculate the test statistic using the formula: t = (sample mean - population mean) / (sample standard deviation / sqrt(sample size))
4. Determine the critical value or p-value using the t-distribution table or statistical software.
5. Compare the test statistic to the critical value or p-value. If the test statistic is greater than the critical value or if p-value is less than the significance level, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.
t = (34 - 30) / (sample standard deviation / sqrt(11))
Next, we need to determine the critical value or p-value using the t-distribution table or statistical software. This will depend on the significance level specified, in this case, 0.05.
Finally, we compare the test statistic to the critical value or p-value. If the test statistic is greater than the critical value or if p-value is less than 0.05, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.