That is with a confidence interval of approximately 95% the "true mean" is within the interval of [336.10, 353.90] and that the sample mean (which is an estimate of the "true mean") is $350.00.
SMALL-SAMPLE CONFIDENCE INTERVAL FOR A POPLATION MEAN, t-DISTRIBUTION
95% Confidence Interval = x-bar +/- (t-critical value) * s/SQRT(n)
x-bar = SAMPLE MEAN [350]
s = STANDARD DEVIATION [100]
n = NUMBER OF SAMPLES [200]
n - 1 = 199 df (DEGREES OF FREEDOM)
t-critical value = (approx) 1.972 from "look-up Table for "two-sided interval" df = 200 [CLOSED df IN TABLE]
95% Confidence Interval: 350+/- 1.972 *100 / SQRT(200) = [336.10, 353.90]
That is with a confidence interval of approximately 95% the "true mean" is within the interval of [336.10, 353.90] and that the sample mean (which is an estimate of the "true mean") is $350.00.
c. ANSWER: A random selection of 1537 customers will provide 95% confidence for estimating the mean extended warranty price paid.
Why???
CHOOSING THE SAMPLE SIZE
n = [(z-critical value * s)/B]^2
z-critical value = 1.96 (associated with 95% confidence level)
s = STANDARD DEVIATION [100.00]
B = BOUND ON THE ERROR OF ESTIMATION [5.00]
n = [(1.96 * 100.00)/5.00]^2 = 1537 (ROUNDED - UP)
CONCLUSION: A random selection of 1537 customers will provide 95% confidence for estimating the mean extended warranty price paid.
The confidence interval becomes wider.
confidence level
Confidence intervals represent an interval that is likely, at some confidence level, to contain the true population parameter of interest. Confidence interval is always qualified by a particular confidence level, expressed as a percentage. The end points of the confidence interval can also be referred to as confidence limits.
The width of the confidence interval willdecrease if you decrease the confidence level,increase if you decrease the sample sizeincrease if you decrease the margin of error.
, the desired probabilistic level at which the obtained interval will contain the population parameter.
Confidence level is a statistical measure that indicates the likelihood that a conclusion is true. It is expressed as a percentage, where a higher confidence level indicates a greater probability that the conclusion is accurate. A confidence level of 95%, for example, suggests that there is a 95% chance that the conclusion is true.
Confidence level 99%, and alpha = 1%.
95% confidence level is most popular
A z-value by itself, has nothing to do with level of confidence.A z-value can be used to calculate probabilities of observing a result that is at least as far from the mean. That probability measure can be used to calculate the level of confidence but you need to be careful about using the one-tailed or two-tailed measures - as appropriate.A z-value by itself, has nothing to do with level of confidence.A z-value can be used to calculate probabilities of observing a result that is at least as far from the mean. That probability measure can be used to calculate the level of confidence but you need to be careful about using the one-tailed or two-tailed measures - as appropriate.A z-value by itself, has nothing to do with level of confidence.A z-value can be used to calculate probabilities of observing a result that is at least as far from the mean. That probability measure can be used to calculate the level of confidence but you need to be careful about using the one-tailed or two-tailed measures - as appropriate.A z-value by itself, has nothing to do with level of confidence.A z-value can be used to calculate probabilities of observing a result that is at least as far from the mean. That probability measure can be used to calculate the level of confidence but you need to be careful about using the one-tailed or two-tailed measures - as appropriate.
The confidence interval becomes wider.
confidence level
confidence level
True.
The width reduces.
Confidence intervals represent an interval that is likely, at some confidence level, to contain the true population parameter of interest. Confidence interval is always qualified by a particular confidence level, expressed as a percentage. The end points of the confidence interval can also be referred to as confidence limits.
The width of the confidence interval willdecrease if you decrease the confidence level,increase if you decrease the sample sizeincrease if you decrease the margin of error.
No, in science, ideas with the lowest level of confidence are typically referred to as hypotheses. Theories are well-established explanations supported by a large body of evidence and are considered to have a high level of confidence.