Question

Match the confidence level with the confidence interval for μ. _______ _____ 1. x̄ ± 2.575( σ ) √? _____ 2. x̄ ± 1.96( σ ) √? _____ 3. x̄ ± 1.645( σ ) √? A. 90% B. 95% C. 99%

Answer 1

Confidence level can be determined from the critical value of the confidnce interval.

a)

2.575 / sqrt(n)

Here, critical value = 2.575

From the Z table, confidence level for the two tailed critical value of 2.575 is 0.99

So,

Confidence level = 99%

b)

1.96 / sqrt(n)

Here, critical value = 2.575

From the Z table, confidence level for the two tailed critical value of 1.96 is 0.95

So,

Confidence level = 95%

c)

1.645 / sqrt(n)

Here, critical value = 1.645

From the Z table, confidence level for the two tailed critical value of 1.645 is 0.90

So,

Confidence level = 90%