Basic Statistics

80 ESTIMATION OF POPULATION MEANS: CONFIDENCE INTERVALS

Table 7.1 Weight Gain Under Supplemented and Standard Diets

Supplemented Diet Standard Diet

Infant Number Gain in Weight (g) Infant Number Gain in Weight (g)

1 2 3 4 5 6 7 8 9

10

11

12

13

14

15

16

448

229

316

105

516

496

130

242

470

195

389

97

458

347

340

212

232

200

184

75

265

125

193

373

21 1

• n1 = 16 Xi =311.9
  s: = 20: 392


• 
  

  722 = 9 X:! = 206.4
  S; = 7060

  
  

Section 7.2 the sample size needed to obtain a confidence interval of a specified length
is given. We need to know 0 in order to obtain a confidence interval using the normal
distribution. Often, 0 is unknown. A distribution that can be used when 0 is unknown
is introduced in Section 7.3. This distribution is called the t distribution or the Student
t distribution. The formula for the confidence interval for a single mean using the t
distribution is presented in Section 7.4. Confidence intervals for the differences in
two means when the data come from independent populations is given in Section 7.5.
The case of paired data is discussed in Section 7.6. Note that in this chapter we are
assuming interval or ratio data or, as it is often called, continuous data.

7.1 CONFIDENCE INTERVALS

First, we illustrate how to compute a confidence interval for p, the population mean
gain in weight when we assume that 0 is known.

7.1.1 An Example

To simplify the problem as much as possible, suppose that we have been studying
the diet of infants for some time and that from the large amount of data accumulated,
we have found the standard deviation of gains in weight over a 1-month period to
be 120g. It seems rather reasonable to believe that the standard deviation of the