Multiple studies have found that speaking curse words can reduce the sensation of pain (Stephens et al., 2009). A researcher learns that the mean pain score in the population is 6.0 on a 10-point scale (where 1 is the lowest pain score, and 10 is the highest pain score), with a standard deviation of 1.0, when people submerge their hands into ice cold water without saying any curse words. The researcher selects a random sample of 81 college students and asks them to submerge their hands in ice cold water for 5 minutes while repeatedly saying their favorite curse word. The mean pain score for the sample of students who participated in this experiment was 5.7.

Based on the sampling distribution, what is the z score corresponding to the sample mean of 5.70?

What is the probability of observing a mean of 5.7 or lower with a sample of 81, if we assumed that speaking curse words had NO effect on pain scores? Please report your probability as a proportion and not a percentage.

Based on these data, do you think that saying curse words had an effect on pain scores? Explain your answer based on your understanding of the mean and standard error of the sampling distribution.

Based on the Central Limit Theorem, what is the effect of increasing sample size on standard error?