Question

Suppose that you run a two-sample study to compare two sets of instructions on how to assemble a new machine. You randomly assign each employee to one of the instructions and measure the time (in minutes) it takes to assemble. Here is the data:

Population	Sample size	Sample mean	Sample standard deviation
Instruction set #1	20	120	12
Instruction set #2	20	110	8

The null hypothesis is H₀: μ 1 = μ 2. The alternative hypothesis is H₀: μ 1 ≠ μ 2. Calculate the P-value. (Use the simple method to estimate degrees of freedom k.)

Group of answer choices

0.0211

0.1780

0.0349

0.0059

0.0178

Answer 1

The statistical software output for this problem is:

Two sample T summary hypothesis test:

μ₁ : Mean of Population 1
μ₂ : Mean of Population 2
μ₁ - μ₂ : Difference between two means
H₀ : μ₁ - μ₂ = 0
H_A : μ₁ - μ₂ ≠ 0
(without pooled variances)

Hypothesis test results:

Difference	Sample Diff.	Std. Err.	DF	T-Stat	P-value
μ1 - μ2	10	3.2249031	33.103093	3.1008684	0.0039

From above output:

Test statistic = 3.1009

Using simple method, degrees of freedom = Min(20-1, 20-1) = 19

So,

p value = 2*P(t(19) > 3.1009) = 2*0.00295 = 0.0059

Option D is correct.