Chapter 7 Statistical intervals based on a single sample - Devore Test Bank

Chapter 7 - Statistical Intervals Based on a Single Sample


COMPLETION
1. The formula used to construct a 95% confidence interval for the mean of a normal population when the value of the
standard deviation is known is given by .

ANS:

PTS: 1

2. If the random sample is taken from a normal distribution with mean value and standard deviation ,
then regardless of the sample size n, the sample mean is distributed with expected value and standard
deviation .

ANS: normally, ,

PTS: 1

3. The standard normal random variable has a mean value of and standard deviation of
.

ANS: 0, 1

PTS: 1

4. If a confidence level of 90% is used to construct a confidence interval for the mean of a normal population when
the value of the standard deviation is known, the z critical value is .

ANS: 1.645

PTS: 1

5. If you want to develop a 99% confidence interval for the mean of a normal population, when the standard deviation
is known, the confidence level is .

ANS: .99

PTS: 1

6. If we think of the width of the confidence interval as specifying its precision or accuracy, then the confidence level
(or reliability) of the interval is related to its precision.

ANS: inversely

PTS: 1

7. The ability of a confidence interval to contain the value of the population mean is described by the .

ANS: confidence level

PTS: 1

, 8. Let be a random sample from a population having a mean and standard deviation . Provided that
n is large, the Central Limit Theorem (CLT) implies that is distributed.

ANS: approximately normally

PTS: 1

9. A random sample of 50 observations produced a mean value of 55 and standard deviation of 6.25. The 95% confidence
interval for the population mean is between and . (two decimal places)

ANS: 53.27, 56.73

PTS: 1

10. The formula used to construct approximately confidence interval for a population proportion p when the
sample size n is large enough is given by , where is the sample proportion,
and


ANS:

PTS: 1

11. A large-sample lower confidence bound for the population mean .


ANS:

PTS: 1

12. When is the mean of a random sample of size n (n is small) from a normal population with mean , the random
variable has a probability distribution called t-distribution with n-1 .

ANS: degrees of freedom

PTS: 1

13. When is the mean of a random sample of size n (n is large) from a normal population with mean , the random
variable has approximately a distribution with mean value of and
standard deviation of .

ANS: standard normal, 0,1

PTS: 1
14. Let denote the density function curve for a t-distribution with degrees of freedom. As , the spread

of the corresponding curve decreases.

ANS: increases

, PTS: 1

15. The z curve is often called the t curve with degrees of freedom equal to .

ANS:

PTS: 1

16. The area under a t-density curve between the critical values is .

ANS:

PTS: 1

17. Let be a random sample from a normal distribution with mean and variance . Then the random
variable has a probability distribution with degrees of freedom.


ANS: chi-squared

PTS: 1


18. The chi-squared critical value, , denotes the number on the measurement axis such that of the area
under the chi-squared curve with degrees of freedom lies to the of .

ANS: right

PTS: 1

19. The 5th percentile of a chi-squared distribution with 10 degrees of freedom is equal to .

ANS: 3.94

PTS: 1

20. The 90th percentile of a chi-squared distribution with 15 degrees of freedom is equal to .

ANS: 22.307

PTS: 1

21. The area under a chi-squared curve with 10 degrees of freedom, which is captured between the two critical values
is .

ANS:

PTS: 1