**Statistics 578 Assignemnt-3**

**Assignment-3-solution: (Chs. 7 and 8):Due by Midnight of Sunday, October 14 ^{th}, 2012: drop box 3: Total 70 points**

__True/False (1 point each)__

__Chapter 7__

1. A sample size of 1000 is large enough to conclude that the sampling distribution of p is a normal distribution, when the estimate of the population proportion is .996.

__FALSE__ Here, n(1-p) = 1000*0.004 = 4 which is less than 10 or even 5 (the liberal rule suggested in the book)

2. The standard deviation of all possible sample proportions decreases as the sample size decreases. __FALSE__**It increases when n gets smaller.**

3. If the population is normally distributed then the sample mean is normally distributed for any sample size.

** TRUE** (Instructions on Ch 7, property 4)

4. The reason sample variance has a divisor of n-1 rather than n is that it makes the standard deviation an unbiased estimator of the population standard deviation.

__FALSE__**Sample variance is unbiased but sample standard deviation is not.**

**5. **The mean of the sampling distribution of is always equal to the mean of the sampled population. __TRUE __

__Chapter 8__

**6**. First a confidence interval is constructed without using the finite population correction factor. Then, for the same identical data, a confidence interval is constructed using the finite population correction factor. The width of the interval with the finite population correction factor is wider than the confidence interval without the finite population correction factor.

** False**.

**Look at the formula for finite population correction. It reduces the standard deviation.**

7. When the population is normally distributed and the population standard deviation *s* is unknown, then for any sample size n, the sampling distribution of is based on the t distribution.

__TRUE__**When we substitute the estimated standard deviation in the formula, the distribution becomes t-distribution instead of Z distribution.**

8. When the level of confidence and sample standard deviation remain the same, a confidence interval for a population mean based on a sample of n=200 will be wider than a confidence interval for a population mean based on a sample of n= 150. __False__

9. When the level of confidence and the sample size remain the same, a confidence interval for a population mean *µ* will be narrower, when the sample standard deviation s is small than when s is large. __True__

10. When the level of confidence and sample proportion p remain the same, a confidence interval for a population proportion p based on a sample of n=100 will be narrower than a confidence interval for p based on a sample of n=400. __FALSE__

11. The sample mean, the sample proportion and the sample standard deviation are all unbiased estimators of the corresponding population parameters. ** FALSE** The Sample Standard Deviation is not an unbiased estimator (Clearly stated in Instructions on Ch8 page6)

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