Question

Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. (You may find it useful to reference the appropriate table: z table or t table)

H₀: μ₁ − μ₂ = 0
H_A: μ₁ − μ₂ ≠ 0

x−1x−1 = 57	x−2x−2 = 63
σ1 = 11.5	σ2 = 15.2
n1 = 20	n2 = 20

a-1. Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
  

a-2. Find the p-value.
  

• p-value < 0.01

• 0.01 ≤ p-value < 0.025

• 0.025 ≤ p-value < 0.05

• 0.05 ≤ p-value < 0.10

• p-value ≥ 0.10

a-3. Do you reject the null hypothesis at the 5% significance level?
  

• Yes, since the p-value is less than α.

• No, since the p-value is less than α.

• Yes, since the p-value is more than α.

• No, since the p-value is more than α.

a-4. Interpret the results at αα = 0.05.

• We conclude that the population means differ.

• We cannot conclude that the population means differ.

• We conclude that population mean 2 is greater than population mean 1.

• We cannot conclude that population mean 2 is greater than population mean 1.

Answer 1

a-1. Calculate the value of the test statistic. (Negative values should be indicated by a minus sign. Round all intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
-1.41

a-2. Find the p-value.
  

• p-value ≥ 0.10

a-3. Do you reject the null hypothesis at the 5% significance level?
  

• No, since the p-value is more than α.

a-4. Interpret the results at αα = 0.05.

• We cannot conclude that the population means differ.