Question

In an experiment related to "fast starts" — the acceleration and speed of a hockey player from a stopped position — sixty-three hockey players, varsity and intramural, from a local university were required to move as rapidly as possible from a stopped position to cover a distance of 6 meters. The means and standard deviations of some of the variables recorded for each of the 63 skaters are shown in the table.

	Mean	SD
Weight (kilograms)	71.270	9.170
Stride Length (meters)	1.010	0.235
Stride Rate (strides/second)	3.210	0.380
Average Acceleration (meters/second2)	3.062	0.579
Instantaneous Velocity (meters/second)	5.953	0.942
Time to Skate (seconds)	2.053	0.031

(a)

Give the formula that you would use to construct a 99% confidence interval for one of the population means (for example, mean weight).

x ± 1.645

s

n

x ± 1.28

s

n

    x ± 2.33

s

n

x ± 2.58

s

n

x ± 1.96

s

n

(b)

Construct a 99% confidence interval for the mean weight. (Round your answer to three decimal places.)

kg to  kg

(c)

Interpret this interval.

We are 99% confident that the population mean weight is within the interval.We are 99% confident that the population mean weight is directly in the middle of these two values.    There is a 99% probability that the mean weight for the sample is within the interval.There is a 99% probability that the population mean weight is within the interval.We are 99% confident that the mean weight for the sample is within the interval.

Answer 1

a)

x ± 2.58 *(s/sqrt(n))

b)

sample mean, xbar = 71.27
sample standard deviation, σ = 9.17
sample size, n = 63

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

ME = zc * σ/sqrt(n)
ME = 2.58 * 9.17/sqrt(63)
ME = 2.98

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))
CI = (71.27 - 2.58 * 9.17/sqrt(63) , 71.27 + 2.58 * 9.17/sqrt(63))
CI = (68.289 , 74.251)

c)

We are 99% confident that the population mean weight is within the interval