Question

Decide whether you would reject or fail to reject the null hypothesis in the following situations:

= 3.50, sD = 1.10, n = 12, a = .05, two-tailed test

Answer 1

Hence, We REJECT the NULL HYPOTHESIS, Which means there is a SIGNIFICANT DIFFERENCE.

• Explanation:

• Solve the problem:

Set up the Hypothesis

Null Hypothesis (H0): There is no significant difference ( μ = 0 )

Alternative Hypothesis (H1): There is a significant difference ( μ ≠ 0 )

• Calculate the test Statistics:

Given: x = 3.50, s = 1.10, n = 12, ∝ = 0.05 ( two-tailed -test)

• Calculate the t - value using the formula:

t = x - μ / s /√n

t = 3.50 - 0 / 1.10 /√12

t ≈ 9.57

• Determine the critical value:

For a Two-Tailed Test with ∝ = 0.05 and degrees of freedom

(df) = n - 1 = 12 - 1 = 11, We can look up the critical value in a t-distribution table or use a calculator.

• The critical value is approximately:

± 2.201

• Compare Test Statistic to Critical Value:

Since the calculated t- value (9.57) is greater than the critical value (2.201), We Reject the Null Hypothesis.

• Final Answer:

Hence, We REJECT the NULL HYPOTHESIS, Which means there is a SIGNIFICANT DIFFERENCE.

I hope this helps!