Question

Construct the indicated confidence interval for the population mean y using a t-distribution. C=0.90, x = 115, s = 10, n= 18 The confidence interval is ( CD. (Round to the nearest tenth as needed.)

Answer 1

Confidence Interval is used to describe the amount of uncertainty associated with a sample estimate of a population parameter.

We are given,

Sample mean = 115

Sample standard deviation(s) = 10

n = 18

We can calculate the CI using the following formula,

Confidence interval = sample statistic + Margin of error

Margin of error = Critical value * Standard error

Critical value at 0.90 confidence level at 17(18-1) df = 1.74.

Standard error(SE) = s / sqrt( n ) = 10 / sqrt(18) = 10/4.2426 = 2.35

Margin of error = 1.74 * 2.35 = 4.10

Confidence interval = 115 + 4.10 = 110.90 to 119.10

Hence Confidence interval is 115 + 4.10 or [110.90 , 119.10].

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