A broker, who works for an e-trading company, is investigating retirement portfolios. The broker would like to test the claim that portfolios consisting mostly of bonds have smaller annual returns than portfolios consisting mostly of stocks. They collected a random sample of predominantly bond portfolios and a random sample of predominantly stock portfolios. The summary statistics (in percents) are shown in the following table.

Assume that the percents are normally distributed and that the population variances are not equal. At the 0.01 level of significance, is there sufficient evidence that the mean annual return is less for portfolios consisting of bonds than stocks?

Let 1 represent the mean annual return for portfolios with bonds and 2 represent the mean annual return for portfolios with stocks.

Annual returns for bond-heavy portfolios (in percents)	Annual returns for stock-heavy portfolios (in percents)
x1=4.7	x2=5.6
s1=0.6	s2=1.4
n1=18	n2=17

Using the table below, find the degrees of freedom and the approximate range for the p-value given thatthe test statistic is 2.45. Enter the p-values in order from smallest to largest.

Probability	0.10	0.05	0.025	0.01	0.005
Degrees of Freedom
16	1.337	1.746	2.120	2.583	2.921
17	1.333	1.740	2.110	2.567	2.898
18	1.330	1.734	2.101	2.552	2.878
19	1.328	1.729	2.093	2.539	2.861
20	1.325	1.725	2.086	2.528	2.845
21	1.323	1.721	2.080	2.518	2.831
22	1.321	1.717	2.074	2.508	2.819

Provide your answer below:

degrees of freedom = 16

p-value is between and .