College football is a rough sport Unfortunately it can be as

College football is a rough sport! Unfortunately, it can be associated with decreased mobility beyond the age of 60. A study is being planned to compare the mobility at age 60 between men who played football in college and men who did not play football in college. The gait velocity test measures the speed of walking a 6-meter course and is reported in meters/second. For 60-year-old men the standard deviation of the gait velocity test is 0.3 meters/second.

Solution

Manual calculation

For 0.05 level, z = 1.96

d = = 0.1

sd=0.3

for \\beta =0.20, z =0.842

n = 2* \\frac{( z_\\alpha +z_\\beta)^2*s^2} {d^2^}

n = 2* \\frac{( 1.96+0.842)^2*0.3^2} {0.1^{^2}}

= 141.32

The required sample size for each group =142

MINITAB output ( there is difference in the result)

Power and Sample Size

2-Sample t Test

Testing mean 1 = mean 2 (versus ?)

Calculating power for mean 1 = mean 2 + difference

? = 0.05 Assumed standard deviation = 0.3

            Sample Target

Difference    Size   Power Actual Power

       0.1     143     0.8      0.802083

The sample size is for each group. =143