A researcher would like to test the effectiveness of a newly developed growth hormone. The researcher knows that under normal circumstances laboratory rats reach an average weight of µ = 950 grams at 10 weeks of age. The distribution of weights is normal with σ = 30. A random sample of n = 25 newborn rats is obtained, and the hormone is given to each rat. When the rats in the sample reach 10 weeks old, each rat is weighed. The mean weight for this sample is M = 974. Sketch the appropriate distribution, and locate the critical region for .05. Calculate the test statistic ( z- score) for the sample. What decision should be made about the null hypothesis, and what decision should be made about the effect of the hormone?
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!
- A researcher would like to test the effectiveness of a newly developed growth hormone. The researcher knows that under normal circumstances laboratory rats reach an average weight of µ = 950 grams at 10 weeks of age. The distribution of weights is normal with σ = 30. A random sample of n = 25 newborn rats is obtained, and the hormone is given to each rat. When the rats in the sample reach 10 weeks old, each rat is weighed. The mean weight for this sample is M = 974.
- Sketch the appropriate distribution, and locate the critical region for .05.
- Calculate the test statistic ( z- score) for the sample.
- What decision should be made about the null hypothesis, and what decision should be made about the effect of the hormone?
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