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.
Chat with our AI personalities
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.