110. Sampling Distributions and the Central Limit Theorem

1. As the sample size increases,

(a) the population mean decreases.

(b) the population standard deviation decreases.

(c) the standard deviation for the distribution of the sample means increases.

(d) the standard deviation for the distribution of the sample means decreases.

2. The concept of sampling distribution applies to

(a) only discrete probability distributions from which random samples are obtained.

(b) only continuous probability distributions from which random samples are obtained.

(c) only the normal probability distribution.

(d) any probability distribution from which random samples are obtained.

3. When we consider sampling distributions, if the sampling population is normally distributed, then the distribution of the sample means

(a) will be exactly normally distributed.

(b) will be approximately normally distributed.

(c) will have a discrete distribution.

(d) will be none of the above.

4. The expected value of the sampling distribution of the sample mean is equal to

(a) the standard deviation of the sampling population.

(b) the mean of the sampling population.

(c) the mean of the sample.

(d) the population size.

5. The sample statistic is the point estimate of

(a) the population standard deviation σ.

(b) the population median.

(c) the population mean µ.

(d) the population mode.

6. If repeated random samples of size 40 are taken from an infinite population, the distribution of sample means

(a) will always be normal because we do not know the distribution of the population.

(b) will always be normal because the sample mean is always normal.

(c) will always be normal because the population is infinite.

(d) will be approximately normal because of the Central Limit Theorem.

7. The mean TOEFL score of international students at a certain university is normally distributed with a mean of 490 and a standard deviation of 80. Suppose groups of 30 students are studied. The mean and the standard deviation for the distribution of sample means will respectively be

(a) 490, 8/3.

(b) 16.33, 80.

(c) 490, 14.61.

(d) 490, 213.33.

8. A certain brand of light bulb has a mean lifetime of 1500 hours with a standard deviation of 100 hours. If the bulbs are sold in boxes of 25, the parameters of the distribution of sample means are

(a) 1,500, 100.

(b) 1,500, 4.

(c) 1,500, 2.

(d) 1,500, 20.

9. Samples of size 49 are drawn from a population with a mean of 36 and a standard deviation of 15. Then P( < 33) is

(a) 0.5808.

(b) 0.4192.

(c) 0.1608.

(d) 0.0808.

10. A tire manufacturer claims that its tires will last an average of 40,000 miles with a standard deviation of 3,000 miles. Forty-nine tires were placed on test and the average failure miles was recorded. The probability that the average failure miles was less than 39,500 is

(a) 0.3790.

(b) 0.8790.

(c) 0.1210.

(d) 0.6210.

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