Question

In: Math

Answer true or false with a sentence or two explanation. 1. In order to construct a...

Answer true or false with a sentence or two explanation.

1. In order to construct a confidence interval estimate of the population mean, the value of the population mean is needed.

2. A confidence interval is an interval estimate for which there is a specified degree of certainty that the actual value of the population parameter will fall within the interval.

3. The larger the confidence level used in constructing a confidence interval estimate of the population mean, the narrower the confidence interval.

4. The term 1 – alpha refers to the probability that a confidence interval does not contain the population parameter.

5. In the formula , Xbar plus or minus z alpha / 2 times the stand dev. / sq root of n. the subscript alpha over 2 refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

6. When constructing confidence interval for a parameter, we generally set the confidence level 1 - alpha close to 1 (usually between 0.90 and 0.99) because it is the probability that the interval includes the actual value of the population parameter.

7. Suppose that a 90% confidence interval for Mu is given by Xbar plus or minus .75. This notation means that we are 90% confident that Mu falls between xbar minus .75 and xbar plus .75

8. When a sample standard deviation is used to estimate a population standard deviation, the margin of error is computed by using the standard normal distribution.

9. The width of a confidence interval is independent of the sample size.

10. Suppose a sample size of 5 has mean 9.60. If the population variance is 5 and the population is normally distributed, the lower limit for a 92% confidence interval is 7.85.

Expert Solution

Answer true or false with a sentence or two explanation.

1. In order to construct a confidence interval estimate of the population mean, the value of the population mean is needed.

False: To construct a confidence interval estimate of the population mean, we need sample mean.

2. A confidence interval is an interval estimate for which there is a specified degree of certainty that the actual value of the population parameter will fall within the interval.

True. There is a specified degree of certainty or confidence like 90%, 95%, 99% that actual value of the population parameter will fall within the interval

3. The larger the confidence level used in constructing a confidence interval estimate of the population mean, the narrower the confidence interval.

False. Larger the confidence level, the broader the confidence interval.

4. The term 1 – alpha refers to the probability that a confidence interval does not contain the population parameter.

False. 1 – alpha refers to the probability that a confidence interval contains the population parameter.

5. In the formula , Xbar plus or minus z alpha / 2 times the stand dev. / sq root of n. the subscript alpha over 2 refers to the area in the lower tail or upper tail of the sampling distribution of the sample mean.

False: z alpha / 2 times refers to the critical value in the lower tail or upper tail side of the standard normal distribution.

6. When constructing confidence interval for a parameter, we generally set the confidence level 1 - alpha close to 1 (usually between 0.90 and 0.99) because it is the probability that the interval includes the actual value of the population parameter.

False: Between 0.90 and 0.99 are the commonly used confidence levels.

7. Suppose that a 90% confidence interval for Mu is given by Xbar plus or minus .75. This notation means that we are 90% confident that Mu falls between xbar minus .75 and xbar plus .75

True: 90% confident that Mu falls between (xbar - 0.75, xbar+ 0.75).

8. When a sample standard deviation is used to estimate a population standard deviation, the margin of error is computed by using the standard normal distribution.

False: When a sample standard deviation is used, we are using t distribution.

9. The width of a confidence interval is independent of the sample size.

False: when sample size increases, standard error decreases, so width of a confidence interval decreases.

10. Suppose a sample size of 5 has mean 9.60. If the population variance is 5 and the population is normally distributed, the lower limit for a 92% confidence interval is 7.85.

True:

Z value for 92% level = 1.751

Lower limit = 9.60- 1.751*sqrt(5/5) =7.849

= 7.85( two decimals)

milcah answered 1 year ago

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