(Hypothetical study) A researcher wants to test whether women's average body temperature is higher than men's. Suppose it is known that standard deviation of both men and women's is W = M = 0.7 (W : population standard deviation of women's body temperature, M: population standard deviation of men's body temperature). 100 men and 100 women's body temperature was measured and it was found that xw xm = 0.1, that is women's sample mean body temperature was 0.1 degree higher than men's. Use = 0.01.

a) State null and alternative hypotheses.

b) Test statistic of this study is 1.01. Do you think the observed difference is unusual if the null hypothesis is true?

c) Use R to find P-value. Interpret the p-value in context of the problem.

d) Make a decision (whether to reject the null or not) and draw a conclusion in context of the problem

e)95% confidence interval of _wmis (-0.09, 0.29). (i) Does this confidence interval agree with your conclusion from Problem 5? (ii) what additional information do we learn from the confidence interval that we didn't get from Problem 5 conclusion?