A study of the effect of exposure to color (red or blue) on the ability to solve puzzles used 42 subjects. Half the subjects (21) were asked to solve a series of puzzles while in a red-colored environment. The other half were asked to solve the same series of puzzles while in a blue-colored environment. The time taken to solve the puzzles was recorded for each subject. The 21 subjects in the red-colored environment had a mean time for solving the puzzles of 9.64 seconds with standard deviation 3.43; the 21 subjects in the blue-colored environment had a mean time of 15.84 seconds with standard deviation 8.65.
The two-sample t statistic for comparing the population means has value (± 0.001).

The two-sample t statistic for comparing the population means is -3.053.

Step-by-step explanation:

We are given that the time taken to solve the puzzles was recorded for each subject.

The 21 subjects in the red-colored environment had a mean time for solving the puzzles of 9.64 seconds with standard deviation 3.43; the 21 subjects in the blue-colored environment had a mean time of 15.84 seconds with standard deviation 8.65.

Let = average time taken to solve the puzzle in red-colored environment.

= average time taken to solve the puzzle in blue-colored environment.

So, Null Hypothesis, :      {means that there is no difference in time taken to solve both the puzzles}

Alternate Hypothesis, :      {means that there is difference in time taken to solve both the puzzles}

The test statistics that would be used here Two-sample t test statistics as we don't know about the population standard deviation;

                     T.S. =   ~

where, = sample average time for solving the puzzles in the red-colored environment = 9.64 seconds

= sample average time for solving the puzzles in the blue-colored environment = 15.84 seconds

= sample standard deviation for red-colored environment = 3.43 seconds

= sample standard deviation for blue-colored environment = 8.65 seconds

= sample of subjects in the red-colored environment = 21

= sample of subjects in the blue-colored environment = 21

Also,    =   = 6.58

So, test statistics  =    ~

                               =  -3.053

The value of two-sample t test statistics is -3.053.

12

step-by-step explanation:

12 + 5 = 17

12x2=24

24-7=17

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.