Find variance that be used in the pooled-variance t test

Question

Hypothesis testing mean and proportion.

1.      If we are testing for the difference between the means of 2 related populations with samples of n₁ = 20 and n₂ = 20, number of degrees of freedom is equal to

a)      39.

b)      38.

c)      19.

d)      18.

2. If we are testing for difference between the means of 2 independent populations presuming equal variances with samples of n₁ = 20 and n₂ = 20, the number of degrees of freedom is equal to

a)      39.

b)      38.

c)      19.

d)      18.

3.      Given the following information, estimate s_p², pooled sample variance that should be used in the pooled-variance t test.

s₁² = 4  s₂² = 6

n₁ = 16 n₂ = 25

a)      s_p² = 6.00

b)      s_p² = 5.00

c)      s_p² = 5.23

d)      s_p² = 4.00

4. A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctor's results in 83 who indicate that they suggest aspirin. The value of the test statistic in this problem is approximately equal to:

a)      - 4.12

b)      - 2.33

c)      - 1.86

d)      - 0.07