The mean blood sodium concentration of these 38 cases was 115 mmol/l, with standard deviation of 12 mmol/l. Assuming that blood sodium concentration is normally distributed what is the 95% confidence interval within which the mean of the total population of such cases may be expected to lie? (Table value = 1.96)
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
- The mean blood sodium concentration of these 38 cases was 115 mmol/l, with standard deviation of 12 mmol/l. Assuming that blood sodium concentration is
normally distributed what is the 95% confidence interval within which the mean of the total population of such cases may be expected to lie? (Table value = 1.96) - In two wards for elderly women in a geriatric hospital the following levels of haemoglobin were found:
Ward A: 12.2, 11.1, 14.0, 11.3, 12.5, 12.7, 13.4, 13.7 g/dl;
Ward B: 11.9, 10.7, 12.3, 13.9, 11.4, 12.0, 11.1 g/dl.
What is the 95% confidence interval for the difference in treatments?
(Table value = 2.16)
- Suppose that a market research firm is hired to estimate the percent of adults living in a large city who have not cell phones. Five hundred randomly selected adult residents in this city are surveyed to determine the results. Of the 500 people sampled, 421 responded that they own cell phones. Using a 95% confidence level, compute a confidence
interval estimate for the true proportion of adult residents of this city who have not cell phones. (Table value = 1.96)
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