Question

Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 10 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows: Hours 3 2.6 2.4 2.8 2.4 2 2 2.4 2.2 2.9 a) What is a point estimate for the population mean length of time. (Round answer to 4 decimal places) b)What must be true in order to construct a confidence interval in this situation? Select an answer

E is yes or no option!!! Thank you

Answer 1

a)

x2 X 9 2 6.76 2.6 5.76 2,4 7.84 2,8 5.76 2.4 4 2 2 5.76 2.4 4.84 2,2 8.41 2.9 62.13 24.7 Sum

The sample mean X is computed as follows: 1 X 24.7 2.47 10 n i-1 Also, the sample variance S IS 24.72 1 1 62.13 0.125 10 1 1 10 n (03)-»3) Therefore, the sample sandartd deviation s is - V0.125 0.353 8 = 8

a) The point estimate for the population mean is :

T = 2,47

B) The population must be approximately normal for calculating the confidence interval.

C)we will use the t distribution to calculate the confidence interval for the mean

CI T Ta( 2

for 95% confidence n = 10

degree of freedom:n-1=10-1=9

Ta2.2621

0.353 CI 2.47 t 2.2621 /10

CI 2.47 + 0.25

CI (2.22, 2.72)

d) option D is right.

e) Is this Possible?

answer is yes

Is this likely?

the answer is No, since 2 lies outside the confidence interval calculated