Questions About Probability and Samples (Ch. 7) and Hypothesis Testing (Ch. 8) 1

Question

Questions About Probability and Samples (Ch. 7) and Hypothesis Testing (Ch. 8)

1. The distribution of sample means is not always a normal distribution. Under what circumstances is the distribution of sample means not normal?

2. For a population with a mean of = 70 and a standard deviation of = 20, how much error, on average would you expect between the sample mean (M) and the population mean for each of the following sample sizes?

a. n = 4 scores

b. n = 16 scores

c. n = 25 scores

4. The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following:

a. Increasing the difference between the sample mean and the original population mean.

b. Increasing the population standard deviation.

c. Increasing the number of scores in the sample.

5. Consider what happens when the alpha level is changed from = .05 to =.01.

a. What happens to the boundaries for the critical region?

b. What happens to the probability of a Type 1 error?

Explanation / Answer

1, Central Limit Theorem. The central limit theoremstates that if you have a population with mean and standard deviation and take sufficiently large randomsamples from the population with replacement , then the distribution of the sample means will be approximately normally distributed.

So for n<30 it wont be normal

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