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Chapter 8 Questions
Complete the following questions. The questions may include pictures or graphics to illustrate or aid in solving the problem. You can check your answer by clicking View Answer. If the question is unclear, confusing, or if you need further clarification, send me an email.
1. Activity
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2. What are the three elements of the Central Limit Theorem and what do they mean?
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a) As N increases, the distribution of the sample means approaches normality regardless of the shape of the population distribution. In other words, the means taken from samples will be generally similar to one another, with some being higher than average and some being lower. The larger the sample size, the more the sample means will cluster around an average value in a generally normally distributed fashion.
b) The mean of the sampling distribution of sample means will equal the population mean
.c) The standard deviation of the sampling distribution will equal the standard deviation of the population divided by the square root of the sample size
. The larger the sample size, the less variability there will be among the sample means. 3. What is a Standard Error and how does it relate to Hypothesis Testing?
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The standard error 
is the standard deviation of the sampling distribution of sample means. In other words, it is how far on average we would expect any sample mean to deviate from the mean of the sample means. In hypothesis testing, it allows us to compare an obtained difference to what we would expect that difference to be on average. In other words, it tells us whether our obtained difference is likely to have occurred by chance.
is the standard deviation of the sampling distribution of sample means. In other words, it is how far on average we would expect any sample mean to deviate from the mean of the sample means. In hypothesis testing, it allows us to compare an obtained difference to what we would expect that difference to be on average. In other words, it tells us whether our obtained difference is likely to have occurred by chance. 4. Imagine that we wanted to predict the final exam grades of future 301 classes on the basis of last semester's grades. Use the following data for questions 5 through 7 below:
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See the following questions.
5. Between what two scores will 99% of future scores fall?
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6. Between what two scores will 68% of future scores fall?
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7. Between what two scores will 95% of future scores fall?
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8. Imagine I thought your class would perform better than previous classes on the final exam. What would the null and alternative hypotheses be for this comparison? What would the null and alternative hypotheses be if I thought that your class would perform differently on the final exam than previous classes?
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Better:
Different:
Different: