Question

a.) Given: 3.01 < μ < 3.69. Find the margin of error.

b.) Find the critical value t_α/2 that corresponds to a confidence level of 90% and a sample size of 10.

c.) Find the positive critical value z_α/2 that corresponds to a confidence level of 98.02%.

Answer 1

Solution :

Given that,

a.

Lower confidence interval = 3.01

Upper confidence interval = 3.69

  = (Lower confidence interval + Upper confidence interval ) / 2

= (3.01 + 3.69) / 2

= 6.7 / 2 = 3.35

= 3.35

Margin of error = E = Upper confidence interval -   = 3.69 - 3.35 = 0.34

Margin of error = 0.34

b.

sample size = n = 10

Degrees of freedom = df = n - 1 = 10 - 1 = 9

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t /2,df = t0.05,9 = 1.833

The critical value tα/2 = 1.833

c.

At 98.02% confidence level the z is ,

= 1 - 98.02% = 1 - 0.9802 = 0.0198

/ 2 = 0.0198 / 2 = 0.0099

Z/2 = Z 0.0099 = 2.33

The positive critical value zα/2 = 2.33