Question

A study of the ability of individuals to walk in a straight line reported the accompanying data on cadence (strides per second) for a sample of n = 20 randomly selected healthy men.

0.95	0.85	0.92	0.95	0.93	0.87	1.00	0.92	0.85	0.81
0.78	0.93	0.93	1.03	0.93	1.06	1.07	0.96	0.81	0.95

A normal probability plot gives substantial support to the assumption that the population distribution of cadence is approximately normal. A descriptive summary of the data from Minitab follows.

Variable	N	Mean	Median	TrMean	StDev	SEMean
cadence	20	0.9250	0.9300	0.9250	0.0798	0.0178
Variable		Min	Max	Q1	Q3
cadence		0.7800	1.0700	0.8600	0.9550

(a) Calculate and interpret a 95% confidence interval for population mean cadence. (Round your answers to four decimal places.)

- With 95% confidence, the value of the true mean cadence of all such men falls below the confidence interval.

- With 95% confidence, the value of the true mean cadence of all such men falls inside the confidence interval.   

- With 95% confidence, the value of the true mean cadence of all such men falls above the confidence interval. strides per second

Interpret this interval.

(b) Calculate and interpret a 95% prediction interval for the cadence of a single individual randomly selected from this population. (Round your answers to four decimal places.), strides per second

Interpret this interval.

- If this bound is calculated once, there is a 5% chance that these bounds will capture a future individual value of cadence for a healthy man.

- If this bound is calculated once, there is a 95% chance that these bounds will capture a future individual value of cadence for a healthy man.    

- If this bound is calculated sample after sample, in the long run, 95% of these bounds will capture a future individual value of cadence for a healthy man.

- If this bound is calculated sample after sample, in the long run, 95% of these bounds will fail to capture a future individual value of cadence for a healthy man.

Answer 1

Here we have

(a)

Degree of freedom : df n -1=19

Critical value of t for 95% confidence interval is 2.093.

So requried confidence interval is

So requried confidence interval is (0.8877, 0.9623).

correct option is :

With 95% confidence, the value of the true mean cadence of all such men falls inside the confidence interval.   

(b)

So requried prediction interval is

So requried confidence interval is (0.7539, 1.0961).

Correct option:

If this bound is calculated sample after sample, in the long run, 95% of these bounds will capture a future individual value of cadence for a healthy man.