Question

A researcher believes that women today weigh less than in previous years. To investigate this belief, she randomly samples 41 adult women and records their weights. The scores have a mean of 111 lbs. and a standard deviation of 12.4. A local census taken several years ago shows the mean weight of adult women was 115 lbs.

	a.	What is the alternative hypothesis?
	b.	What is the null hypothesis?
	c.	What is your conclusion, using á = 0.011 tail?
	d.	What type error may you be making because of your conclusion in part c?   Please show all work.

Answer 1

a. Here claim is that mean is less than 115

As null hypothesis always have equality sign, alternative hypothesis is

b. Null hypothesis is

c. Here sample size is 41>30, so distribution is normal and we can use t test statistics

P value is TDIST(2.07,40,1)=0.0225

As P value is greater than alpha=0.011, we fail to reject the null hypothesis

Hence we do not have sufficient evidence to support the claim that mean is less than 115