A medical researcher wants to see whether a new herbal remedy helps people to sleep sounder. To do so,she randomly assigns half of the 50 volunteers inher study to a control group and half to an experimental group. The control group participants are given a placebo to take before bed, whilethe experimental group participants are given the herbal supplement. After six weeks, she finds that2/10 of the subjects in the control group reportsleeping sounder. (This appears to be due to the "placebo effect.") In contrast, 3/10 of the subjects in the experimental group (i.e., ~8)reportsleeping sounder. Does this result indicate strong evidence, weak evidence, or no evidence that the herbal remedy helps people to sleep sounder? *using standard mathematical notation.*

a) What is the null hypothesis?

b) What is the theoretical mean?

c) What is the theoretical standard deviation?

d) What is the significance level of the result? (e.g., >5% level, 5% level, 1% level, < 1% level,etc.)

e) What conclusion should be drawn from this study with respect to the null hypothesis?

a) The null hypothesis is that the herbal remedy does not help people to sleep sounder. This means that the herbal remedy has no effect on sleep. b) The theoretical mean is that the herbal remedy helps people to sleep sounder by a certain amount. This is the average amount that the herbal remedy is expected to help people sleep sounder. c) The theoretical standard deviation is the amount of variability in the results. This is the amount of variation that is expected in the results. d) The significance level of the result is the probability that the results are due to chance. The results of this study are not statistically significant, which means that the results are likely due to chance. e) The conclusion should be drawn from this study is that the herbal remedy does not help people to sleep sounder. There is not enough evidence to say that the herbal remedy helps people to sleep sounder.