Question

10.2 Practice Exercise 10.10 (Self-Test) Algorithmic Video Consider the following hypothesis test The following results are from independent samples taken from two populations Sample 1 n1 35 X 113.6 S1 5.1 a. What is the value of the test statistic (to 2 decimals)? Sample 2 n 240 X 210.1 S2 8.5 2.19 b. What is the degrees of freedom for the t distribution? (Round down your answer to the whole number) 34 c. What is the p-value? Use z-table The area in the upper tail is Select d. At α .05, what is your conclusion? p-value is Select ; two-tailed p-value is between Select

Answer 1

Ans:

a)

Test statistic:

t=(13.6-10.1)/SQRT((5.1^2/35)+(8.5^2/40))

t=2.19

b)

$df=\frac{(n_1-1)\cdot(n_2-1)}{(n_2-1)C^2+(1-C)^2(n_1-1)}$

where,

$C=\frac{s_1^2/n_1}{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}$

df=65.06$\approx 65$

c)

Area in the upper tail=tdist(2.19,65,1)=0.0161

Two tailed p-value is between 0.01 to 0.05

d)

As,p-value is less than 0.05,So Reject H₀.