Question

To investigate the fluid mechanics of swimming, twenty swimmers each swam a specified distance in a water-filled pool and in a pool where the water was thickened with food grade guar gum to create a syrup-like consistency. Velocity, in meters per second, was recorded and the results are given in a table below. The researchers concluded that swimming in guar syrup does not change swimming speed. (Use a statistical computer package to calculate the P-value. Use ud = Uwater - Uguar syrup. Round your test statistic to two decimal places and the P-value to three decimal places.) Swimmer Velocity (m/s) Water Guar Syrup 1.87 1.10 1.52 1.35 1.59 1.70 1.51 1.41 1.60 1.09 1.36 0.91 1.09 1.55 1.74 1.53 1.46 1.72 1.62 1.97 0.94 1.78 1.53 1.22 1.89 1.82 1.22 1.43 1.91 1.33 1.37 1.78 1.82 1.27 1.91 1.07 1.031.00 1.00 1.31 20

Answer 1

Solution:

We can use the excel data analysis Paired t-test and the excel output is given below:

t-Test: Paired Two Sample for Means
	Water	Guar Syrup
Mean	1.499	1.417
Variance	0.099377895	0.093527368
Observations	20	20
Pearson Correlation	-0.058119063
Hypothesized Mean Difference	0
df	19
t Stat	0.81
P(T<=t) one-tail	0.21350845
t Critical one-tail	1.729132792
P(T<=t) two-tail	0.427
t Critical two-tail	2.09302405

t = 0.81

df = 19

p=0.427

Question 2:

Let S = event that friend drives small car

L = event that friend drives large car

T = event that friend is at work on time.

PS) = 0.25, P(L) = 0.75, P(TS) = 0.8, P(TL) = 0.5

We have to find

P(ST

We know that:

PTSP(S) P(T|S)P(S) + P(TL)(L)

0.2 0.8 x 0.25 0.8 x 0.25 +0.5 x 0.75 0.575

A friend who works in a big city owns two cars, one small and one large. One-quarter of the time he drives the small car to work, and three-quarters of the time he takes the large car. If he takes the small car, he usualy has little trouble parking and so is at work on time with probability 0.8. If he takes the large car he is on time to work with probability 0.5. Given that he was at work on time on a particular morning, what is the probability that he drove the small car? Give the answer to three decimal places. 0.348