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Chapter 7 QUIZ

TRUE OR FALSE

Question 7.191

1. True or false: For a normal population, the sampling distribution of the sample mean is always normal.

Question 7.192

2. True or false: The Central Limit Theorem takes effect at n=30, so it doesn't make sense to get larger samples.

FILL IN THE BLANK

Question 7.193

3. The distance between the point estimate and its target parameter is called the __________ __________ [two words].

Question 7.194

4. If the population is either non-normal or of unknown distribution and the sample size is large, then the sampling distribution of ˉx is __________ __________ (two words).

SHORT ANSWER

Question 7.195

5. If the population is either non-normal or of unknown distribution and the sample size is small, then do we know the sampling distribution of ˉx?

Question 7.196

6. The sampling distribution of the sample proportion ˆp may be considered approximately normal only if both the following conditions hold: (1) __________ and (2) __________.

CALCULATIONS AND INTERPRETATIONS

Soybean Crop. Protein content in a particular farmer's soybean crop is normally distributed, with a mean of 40 grams and a standard deviation of 20 grams. Suppose we take samples of size 100 soy plants. Use this information for Exercises 7 and 8.

Question 7.197

7.

  1. Find the probability that the sample mean protein content will be less than 38 grams.
  2. Find the probability that the sample mean protein content will be between 36.08 and 43.92 grams.
  3. Find the probability that the sample mean protein content will be greater than 42.5 grams.

Question 7.198

8. Refer to Exercise 7.

  1. Find the sample mean protein content higher than 95% of all such sample means.
  2. Find the sample mean protein content lower than 95% of all such sample means.
  3. Between which two values does the middle 90% of sample mean protein content lie?

Comparing Per Capita Incomes. Use this information for Exercises 9 and 10. According to the U.S. Census Bureau, the mean per capita income in Texas is $25,800, whereas the mean per capita income in Florida is $26,500. Suppose both distributions are normal, each with a standard deviation of $8000. Suppose we take samples of 100 residents of each state.

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Question 7.199

9.

  1. Find the probability that the sample mean per capita income in Texas will exceed $27,000.
  2. Find the probability that the sample mean per capita income in Florida will exceed $27,000.

Question 7.200

10.

  1. Find the 95th percentile of sample mean per capita income in Texas.
  2. Find the 95th percentile of sample mean per capita income in Florida.

Question 7.201

11. Men and Depression. According to the National Institute for Mental Health, 6.6% of men are affected by a depressive disorder each year.

  1. If we take samples of 400 men, find P(ˆp<0.066).
  2. If we take samples of 400 men, find P(0.05<ˆp<0.066).
  3. If we take samples of 400 men, find the 2.5th and 97.5th percentiles of the sample proportion.
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