Question

Suppose you were given a 95% confidence interval for the difference in two population means. What could you conclude about the population means if a) The confidence interval did NOT cover zero? b) The confidence interval did cover zero?

Answer 1

Answer:

a) The population means are unequal

b) The population means are equal

Step-by-step explanation:

Hypothesis testing is used to test the statistical significance of a statement. Null Hypothesis [H0] represents 'no significance' ; Alternate Hypothesis [H1] represents

For testing significance of difference between two population means

• H0 : No significant difference between two means ; M1 = M2
• H1 : Significant difference between two means ; M1 ≠ M2

Null Hypothesis is accepted, if the null hypothesis difference value is in the confidence interval. Null Hypothesis is rejected & alternate hypothesis accepted, if null hypothesis difference value is not in the confidence interval.

a) The confidence interval does not cover zero. Zero is the difference value as per null hypothesis, so it not included in confidence interval implies - rejection of null hypothesis. Alternate hypothesis acceptance implies 'there is significant difference between two means'  [ M1 ≠ M2 ]

b) The confidence interval does cover zero. Zero is the difference value as per null hypothesis, so it included in confidence interval implies - acceptance of null hypothesis. Null hypothesis acceptance implies 'there is no significant difference between two means' [ M1 = M2 ]

Answer 2

Answer:

(a) The population means are not same.

(b) The population means are same.

Step-by-step explanation:

The hypothesis to test whether there is a significant difference between two population means is:

H₀: There is no difference between the two population means, i.e.               μ₁ - μ₂ = 0.

Hₐ: There is no difference between the two population means, i.e.              μ₁ - μ₂ ≠ 0.

The decision rule based on confidence interval for the difference between two population means is:

If the confidence interval consists the null value of the difference, i.e. 0 then the null hypothesis will be accepted or else it will be rejected.

(a)

It is provided that the confidence interval for the difference between two population means does not contains 0.

Since the null value of the difference is not contained in the interval, it can be concluded that the null hypothesis will be rejected.

Thus, the population means are not same.

(b)

It is provided that the confidence interval for the difference between two population means does contains 0.

Since the null value of the difference is contained in the interval, it can be concluded that the null hypothesis will not be rejected.

Thus, the population means are same.