Question

From generation to generation, the average 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 40 smokers of this generation was done to see if the average starting age is at least 19. the sample average was 18.2 with a sample standard deviation of 1.3. do the data support the claim at the 5% level?

Answer 1

To determine if the data supports the claim at the 5% level, perform a one-sample t-test.

Step-by-step explanation:

To determine if the data supports the claim at the 5% level, we need to perform a hypothesis test. The null hypothesis (H0) is that the average starting age is at least 19, and the alternative hypothesis (Ha) is that the average starting age is less than 19.

We can perform a one-sample t-test using the sample mean, sample standard deviation, and the number of observations. The test statistic is calculated as (sample_mean - hypothesized_mean) / (sample_standard_deviation / sqrt(sample_size)).

Next, we can compare the test statistic with the critical value from the t-distribution at the chosen significance level of 5%. If the test statistic is less than the critical value, we can reject the null hypothesis and conclude that the data supports the claim.