Percentages of ideal body weight were determined for 18 randomly selected insuli

Question

Percentages of ideal body weight were determined for 18 randomly selected insulin-dependent diabetics and are shown below [11]. A percentage of 120 means that an individual weighs 20% more than his or her ideal body weight: a percentage of 95 means that the individual weighs 5% less than the ideal. 107 119 99 114 120 104 88 114 124 116 101 121 152 100 125 114 95 117 (%) (a) Compute a two-sided 95% confidence interval for the true mean percentage of ideal body weight for the population of insulin-dependent diabetics. (b) Does this confidence interval contain the value 100%? What does the answer to this question tell you?

Explanation / Answer

Here we have given 18 data values.

We have to find 95% confidence interval for true mean.

Here sample size is of 18 which is less than 30 so we use one sample t-interval.

95% confidence interval for population mean is,

Xbar - E < mu < Xbar + E

where Xbar is sample mean.

E is standard error

E = (tc * s) / sqrt(n)

where tc is critical value for t-distribution.

s is sample standard deviation.

n is sample size

We can do one sample t-interval in TI-83 calculator.

steps :

STAT --> ENTER data values --> STAT --> TESTS --> 8:TInterval --> ENTER --> Highlight on Data--> List : 2nd+1-->Freq : 1--> C-level : 0.95 --> Calculate --> ENTER

95% confidence interval for true mean is (105.6, 119.95)

We are 95% confident that the true mean is lies between 105.6 and 119.95

We see that 100 is not lie in the confidence interval.

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