Final answer:
The hypothesis test performed is a one-sample t-test, involving the comparison of sample mean against a hypothesized population mean to see if nitrogen dioxide levels are greater than 34 ppb. It involves stating hypotheses, collecting data, calculating the t-statistic, determining the significance level, and interpreting results.
Step-by-step explanation:
The hypothesis test being performed in this scenario is a one-sample t-test, as the scientist is comparing the sample mean of nitrogen dioxide levels from 31 randomly selected days to the hypothesized population mean. The key steps involved in this hypothesis test are as follows:
- State the null hypothesis (H0) which would be that the mean nitrogen dioxide level is 34 parts per billion (m) and the alternative hypothesis (Ha) that it is greater than 34 ppb.
- Collect the data and calculate the sample mean and standard deviation.
- Determine the level of significance (α), typically set at 0.05.
- Calculate the t-statistic using the sample data.
- Determine the critical value from the t-distribution table based on α and the degrees of freedom (df = n - 1, where n is the sample size).
- Compare the calculated t-statistic with the critical value to decide whether to reject or fail to reject the null hypothesis.
- Interpret the results in the context of the research question.
Understanding the steps in performing a hypothesis test is crucial in fields such as environmental science and statistics, where assessing levels of pollutants like nitrogen dioxide is essential for public health and policy making.