Question

Consider a study designed to compare different joystick types on the time it takes to complete a navigation mission.

A group of technology students is interested in whether haptic feedback (forces and vibrations applied through a joystick) is helpful in navigating a simulated game environment they created. To investigate this, they randomly assign 20 students to each of three joystick controller types and record the time it takes to complete a navigation mission. The joystick types are (1) a standard video game joystick, (2) a game joystick with force feedback, and (3) a game joystick with vibration feedback.

The three joystick types are designated 1, 2, and 3 and the parameters of the model are

μ₁, μ₂, μ₃,

and σ. The following table summarizes the time (seconds) data.

Joystick	x	s	n
1	279	72	20
2	245	62	20
3	258	82	20

(a)

Is it reasonable to pool the standard deviations for these data? Explain your answer.

Yes, the smallest s is half the largest s.

Yes, the largest s is less than twice the smallest s.    

No, the largest s is more than twice the smallest s.

No, the largest s is exactly twice the smallest s.

There is not enough information.

(b)

For each parameter,

μ₁, μ₂, μ₃,

and σ, give the estimate. (Round your answer for σ to three decimal places.)

μ₁=

μ₂=

μ₃=

σ=

Answer 1

a)

Yes, the largest s is less than twice the smallest s.    

b)

from above:

Group	ni				SS=(ni-1)*s2
1	20				98496.0000
2	20				73036.0000
3	20				127756.0000
	grand mean=				299288.0000
					SSE

μ₁= 279

μ₂= 245

μ₃= 258

σ= sqrt(SSE/(N-k))=sqrt(299288/57) =5250.667