Final answer:
To test whether the mean days to wellness is less for naturopathic remedies compared to OTC remedies, establish null and alternative hypotheses, use a t-test for independent samples with df=17.8, and compare the t-statistic to the critical value at a 5% significance level.
Step-by-step explanation:
To conduct the appropriate hypothesis test to evaluate if the mean number of days to wellness is less for people who used a naturopathic remedy versus an over-the-counter (OTC) pharmaceutical remedy, we first establish our null hypothesis (H0) and alternative hypothesis (Ha). Given that the data is normally distributed and the degree of freedom (df) is 17.8, we will likely be using a t-test for independent samples.
The null hypothesis (H0) would be that there is no difference in the mean number of days to wellness between the two groups, while the alternative hypothesis (Ha) would be that the mean number of days to wellness for the naturopathic remedy group is less than that for the OTC remedy group. Following this, we would calculate the t-statistic for the given data, compare it to the critical t-value from the t-distribution with df=17.8 at the 5% significance level, and make a decision to reject or not reject the null hypothesis based on this comparison.