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<v Instructor>Dear students, this is our first example</v>

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for chapter six.

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In this example, we are going to learn

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how to calculate confidence interval

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for a small sample size of eight

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using t-distribution.

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Now, the problem here is from our textbook, problem 15.

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The problem states, a pilot study is run to investigate

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the feasibility of recruiting pregnant women

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into a study of risk factors for pre-term delivery.

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Women are invited to participate

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at their first clinical visit for prenatal care.

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The following represent the gestational ages in weeks

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of women who consented to participate in the study.

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Compute a 95% confidence interval

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for the mean gestational age

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of women enrolling in the study.

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So here,

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the numbers or values are given,

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and the first step is for us to calculate the mean

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and the standard deviation.

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Now, here, I have used the short formula

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to calculate the standard deviation,

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because the objective here is not to calculate

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the standard deviation or the mean,

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but rather, to learn how to calculate

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the confidence interval.

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Now, I also want to let you know that

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for this biostatistics

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ER problem, the solution here is typed

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because once I heard from a student

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that all of my biostat ER examples are solved by hand.

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Hence, I have used this typed solution here,

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but I am going to go through this step by step.

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So the next thing we have to see here is

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the degrees of freedom,

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because based on that, we have to obtain

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our t-value from the back of our book.

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So our degrees of freedom here is going to be n - 1.

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And what is our n?

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Our n is eight.

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So when we take eight and deduct one, we get seven.

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So based on 95% confidence interval

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and degrees of freedom of seven,

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we get the t-value again from the back of our book,

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which is 2.365.

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Now, once we have all the

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values at our

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hand, this is basically plugging it into the formula.

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And the formula here is X bar +/- t,

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which is the t we just obtained, the t-value.

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S divided by square root of n.

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So our X bar here is 14.8.

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The t-value here is 2.365.

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The standard deviation we calculated previously,

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which is five, and the sample size, n, is eight,

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so it is the square root of eight.

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So, when we perform the algebra,

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we get 14.8

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+/- 4.18.

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And when, again, we solve that,

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what we get is 10.6 and 19.0.

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So that is basically our 95% confidence interval

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for the mean gestational age

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of women enrolling in the study.