Final answer:
Given the t-statistic of 4.21 and df of 85, in comparison to the critical t-value at the .05 significance level, which is usually close to 2 for large df, we reject the null hypothesis as the obtained t-statistic is much higher, indicating a significant result.
Step-by-step explanation:
To decide whether to reject the null hypothesis that the population mean equals 100, we compare the obtained t-statistic to the critical t-value at the .05 significance level (alpha = 0.05) for a one-tailed or two-tailed test. Given that the researcher's obtained t-statistic is 4.21 with degrees of freedom (df) of 85, we need to compare this to the critical t-value for df=85 at the .05 significance level.
Using a t-distribution table or calculator function TTEST, we can ascertain the critical value. If this t-statistic of 4.21 is greater than the critical value, we reject the null hypothesis. Given the information and assuming a two-tailed test (which is more common when the alternative hypothesis does not specify a direction), and considering the t-distribution table usually provides a critical value close to 2 for large df at the .05 level, a t-statistic much larger than that (like 4.21) would lead us to reject the null hypothesis due to the significant result.
Therefore, since the t-statistic is substantially higher than the typical critical value at the .05 significance level, we reject the null hypothesis and conclude that there is significant evidence that the population mean is not 100.