**Stats-578-Midterm-solutions**

BA 578-Fall2012: Midterm Test

Total 250 points

__True/False (__3 points each)

1. When determining the sample size n, if the value found for n is 79.2, we would choose to sample 79 observations. (Ch8)

F We always round up

2. If we examine selected items from the population, we are not conducting a census of the population. (Ch1)

T We are conducting sample

3. For a continuous distribution, Probability of (X greater than or equal to 10) is greater than the probability of (X greater than 10) (Ch6)

F They are equal for continuous distribution.

4. When the population is normally distributed and the population standard deviation *s* is unknown, then for any sample size n, it is appropriate to build the confidence interval of the sample mean X-bar based on the t distribution. (Ch8)

T This is true although for very large samples we "may" use Z distribution as approximation.

5. If the population is normally distributed with known variance then the sample mean may not be normally distributed for a very small sample size. (Ch7)

F In this case the sample mean is Normally distributed for any sample size.

6. We do not need to perform the continuity correction even if the population is 20 times or more than the sample size. (Ch6)

F The size of population is relevant only for "Finite Population Correction". For continuity correction, the sample size matters.

7. If the random variable of X is normally distributed, 99.73% of all possible observed values of X will be within three standard deviations of the mean. (Ch3)

T The "Empirical Rule"

8. If the Union (that is, the Probability using the conjunction "or") of two events equals 1, they are called complements. (Ch. 4)

F They are called "Exhaustive". To be complements they need additional property of being mutually exclusive.

9. When establishing the classes for a frequency table it is general rule that the more classes you use the better your frequency table will be. (Ch2)

F Having too many classes is not good: it beats the purpose of grouping. That is why we have the 2^k rule.

10. The reason sample variance has a divisor of n-1 rather than n is that it makes the standard deviation an unbiased estimate of the population standard deviation. (Chs. 3 and 7)

F The sample variance is an unbiased estimator but the sample standard deviation is not.

11. For a binomial probability experiment, with n=150 and p=.1, we can use the normal approximation to the binomial distribution even without continuity correction. (Ch6)

T Here np(1-p) = 13.5 > 10

12. 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 wider than a confidence interval for p based on a sample of n=150. (Ch8)

T The larger the sample size the smaller is the standard error. Hence the result.

13. If the population is normal and its standard deviation is known, then the t- distribution is appropriate for a sample size of 20. (Ch8)

F The Z distribution is appropriate if the standard deviation is known.

14. The sampling distribution of the sample mean is always normally distributed according to the Central Limit Theorem (Chaps. 6 and 7)

F It is always normally distributed if the parent population is normal, but is approximately normal for sufficiently large samples only if the parent distribution is not normal.

15. For a given sample size the variance of the sample proportion will be larger if p = 0.5 than if p = 0.6 (Ch7)

T This is obvious from the formula for the variance of p which involves p(1-p).

16. If a population is known to be normally distributed, then it follows that the sample mean must equal the population mean.(Ch7)

F The mean of the sample mean is equal to the population mean, but the sample mean for any sample may be greater than or less than the population mean.

__Multiple Choices__ (7 points each)

1. A fair die with six faces is rolled 10 times. What is the probability that an even number (2, 4 or 6) will occur between 2 and 4 times (inclusive)? (Ch5)

A. 0.6123

B. 0.1709

C. 0.1611

D. 0.3662 correct

E. 0.3223

For discrete distribution, P(2<= X <= 4) = P(X <=4) - P(X<= 1) = 0.37695 -0.01074 = 0.36621 using Binomdist function. You can also use the binomial table to add probabilities P(X= 2) + P(X =3) + P(X = 4) to get the same result for n= 10 and p = 0.5.

2. A person's telephone area code is an example of a(n) _____________

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