a) State the null and alternative hypotheses (b) How many degrees of freedom are there for testing the hypothesis? (c) Diagram the regions of acceptance and rejection for the test. Label the horizontal axis using the critical values of the test statistic, using an alpha = 0.01
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!
An experimenter wishes to test the hypothesis that a special vitamin supplement increases memory. To do this the experimenter randomly assigns subjects to either receive or not receive the vitamin supplement. After allowing a time period for the vitamin to work, the subjects are then given a memory test. The number of nonsense syllables correctly recalled serves as the dependent variable.
The data for the two groups are as follows:
Control Experimental
10 14
8 10
12 13
15 19
17 16
11 18
7 8
8 11
11 10
11 11
(a) State the null and alternative hypotheses
(b) How many degrees of freedom are there for testing the hypothesis?
(c) Diagram the regions of acceptance and rejection for the test. Label the horizontal axis using the critical values of the test statistic, using an alpha = 0.01
(d) What is the value of the estimated standard error? ___________________
(e) Calculate the appropriate test statistic to test the hypotheses ___________________________
(f) Based on the value of the test statistic you calculated in part (e), do you reject or fail to reject the null hypothesis? State the conclusion in your own words.
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