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| 1 | |
Following is a random sample of the heights of students in a class: 5'3", 5'9", 6'1", 5'8", 5'11", 6'5", 6'2", 5'7", 5'1", 6', 5'6", 5'9". Compute a point estimate of the mean and the standard deviation of the heights of the students. |
| | A) | 5'9.8", 2.9" |
| | B) | 5'10.3", 3.44" |
| | C) | 5'9.8", 2.8" |
| | D) | 5'10.3", 3.31" |
| | E) | none of the above |
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| 2 | |
A new shampoo is introduced in the market. The manufacturer interviews 25 different individuals for their opinion. Eighteen individuals like the shampoo. Compute a point estimate for the proportion of the population liking the shampoo. |
| | A) | 0.36 |
| | B) | 0.72 |
| | C) | 0.28 |
| | D) | 0.56 |
| | E) | 0.64 |
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| 3 | |
In which of the following situations is the Central Limit Theorem not applicable? |
| | A) | When the sample is small and the population is normal. |
| | B) | When the sample is large and the population is normal. |
| | C) | When the sample is large, above 30, and the population is not normal. |
| | D) | When the sample is small, below 30, and the population is not normal. |
| | E) | none of the above |
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| 4 | |
A certain brand of electric bulbs has an average life of 300 hours with a standard deviation of 25. A random sample of 100 bulbs is tested. What is the probability that the sample mean will be less than 295? |
| | A) | 0.0548 |
| | B) | 0.1096 |
| | C) | 0.4452 |
| | D) | 0.0793 |
| | E) | 0.0228 |
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| 5 | |
When sampling from a population with a standard deviation of 14, using a sample size of 144, what is the probability that the sample mean will be at least 3 units away from the population mean? |
| | A) | 0.0051 |
| | B) | 0.0257 |
| | C) | 0.2157 |
| | D) | 0.0102 |
| | E) | 0.0514 |
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| 6 | |
It is found that on average, 9% of the population recycles its garbage, with a standard deviation of 3% over the country. If a random sample of 49 households is taken, what is the probability that more than 4 households recycle their garbage? |
| | A) | 0.4744 |
| | B) | 0.9488 |
| | C) | 0.0256 |
| | D) | 0.9744 |
| | E) | 0.0512 |
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| 7 | |
Which of the following statements does not refer to the Central Limit Theorem? |
| | A) | The expected value of the mean of the distribution of sample means is μ. |
| | B) | The distribution of sample means is approximately normally distributed. |
| | C) | The Central Limit Theorem is true for any distribution, when the sample size is at least 30. |
| | D) | The standard deviation of the distribution of sample means is equal to σ. |
| | E) | When a non-normal population is sampled, the distribution of sample means is still normally distributed, as long as the sample size is large. |
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| 8 | |
If the Central Limit Theorem is applicable, this means that the sampling distribution of a ___________ population can be treated as normal since the ___________ is ___________. |
| | A) | Non-normal; sample size; small |
| | B) | Non-symmetrical; variance; large |
| | C) | Platy-kurtotic; sample size; large |
| | D) | Binomial; variance; large |
| | E) | Non-normal; standard error; large |
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| 9 | |
If a particular population characteristic is normally distributed with a mean of 80 and a variance of 64, given a sample size of 16, approximately ________% of sample averages will be larger than 77.5 but not larger than 82.5 |
| | A) | 11% |
| | B) | 22% |
| | C) | 44% |
| | D) | 79% |
| | E) | 89% |
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| 10 | |
If, over the long run, a particular estimator's expected value is equal to the population parameter it's supposed to estimate, it is considered to be ____________ |
| | A) | Efficient |
| | B) | Sufficient |
| | C) | Unbiased |
| | D) | Consistent |
| | E) | Freely Estimated |
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| 11 | |
Population parameter Alpha can be estimated with either of two estimators, Beta and Gamma. Because both Beta and Gamma become more likely to be close to Alpha's true value as sample size grows, they are considered ______________; if Beta's variance is half the size of Gammas, however, it would be considered more ______________ than Gamma. |
| | A) | Consistent; Efficient |
| | B) | Unbiased; Efficient |
| | C) | Efficient; Unbiased |
| | D) | Efficient; Consistent |
| | E) | Sufficient; Unbiased |
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| 12 | |
In attempting to estimate a population mean, a researcher has taken four random samples of 50 observations each, calculating a sample mean in each case. What is the total number of degrees of freedom for deviations from the means? |
| | A) | Not more than 10 |
| | B) | More than 10 but not more than 50 |
| | C) | More than 50 but not more than 100 |
| | D) | More than 100 but not more than 150 |
| | E) | None of the above |
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