Answer :
Therefore, the 95% confidence interval for the population mean is approximately 49.969 seconds to 53.431 seconds.
To estimate the population mean, the margin of error can be approximated as the critical value (Z*) multiplied by the standard error (s/√(n)). For a 95% confidence level, Z* is approximately 1.96.
Using the given sample results:
n = 49
x = 51.7 seconds (sample mean)
s = 6.2 seconds (sample standard deviation)
The standard error (SE) is calculated as s/√(n):
SE = 6.2 / √(49)
≈ 0.883 seconds
The margin of error (ME) is then calculated as Z * SE:
ME = 1.96 * 0.883
≈ 1.731 seconds
The 95% confidence interval is calculated by subtracting and adding the margin of error to the sample mean:
95% Confidence Interval = (x - ME, x + ME)
= (51.7 - 1.731, 51.7 + 1.731)
= (49.969, 53.431)
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