Imagine that we are interested in studying whether or not college students are more motivated to succeed than the general public. To test this, we've developed a measure that ranks motivation on a scale of 0-100. We know that the average score of the population is 50, and we know that the population standard deviation is 6. To test whether college students are more motivated than the general public, I choose a sample of N=1, and have this person complete my measure. She does, and gets a score of 62. Use p<.05. Step 1: Restate the question as a research hypothesis and a null hypothesis: Research Hypothesis: Null Hypothesis: Step 2: Determine the characteristics of the comparison distribution: Mean = ________ Standard Deviation = __________ Step 3: Determine the cutoff Z-score for rejecting the null hypothesis (use a 0.05 p value): Is this a 1- or 2-tailed test? __________ Z cutoff sample score = __________ Step 4: Determine your sample's score on the comparison distribution: Sample Z-score = __________ Step 5: Make a decision about the hypothesis. (What do we do with the null hypothesis?) Plot the Z-score mean, cutoff score, and sample Z-score on a normal curve:
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!
Imagine that we are interested in studying whether or not college students are more motivated to succeed than the general public. To test this, we've developed a measure that ranks motivation on a scale of 0-100. We know that the average score of the population is 50, and we know that the population standard deviation is 6. To test whether college students are more motivated than the general public, I choose a sample of N=1, and have this person complete my measure. She does, and gets a score of 62. Use p<.05.
Step 1: Restate the question as a research hypothesis and a null hypothesis:
- Research Hypothesis:
- Null Hypothesis:
Step 2: Determine the characteristics of the comparison distribution:
- Mean = ________
- Standard Deviation = __________
Step 3: Determine the cutoff Z-score for rejecting the null hypothesis (use a 0.05 p value):
- Is this a 1- or 2-tailed test? __________
- Z cutoff sample score = __________
Step 4: Determine your sample's score on the comparison distribution:
- Sample Z-score = __________
Step 5: Make a decision about the hypothesis. (What do we do with the null hypothesis?)
- Plot the Z-score mean, cutoff score, and sample Z-score on a normal curve:
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