Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution.
6) The football coach randomly selected ten players and timed how long each player took to perform a certain drill.
The times (in minutes) were:
7.8 | 10.6 | 9.9 | 8.1 | 11.5 |
7.2 | 6.2 | 11.1 | 10.6 | 12.9 |
Determine a 95% confidence interval for the mean time for all players.
Confidence interval for Population mean is given as below:
Confidence interval = Xbar ± t*S/sqrt(n)
From given data, we have
Xbar = 9.59
S = 2.151201215
n = 10
df = n – 1 = 9
Confidence level = 95%
Critical t value = 2.2622
(by using t-table)
Confidence interval = Xbar ± t*S/sqrt(n)
Confidence interval = 9.59 ± 2.2622*2.151201215/sqrt(10)
Confidence interval = 9.59 ± 1.5389
Lower limit = 9.59 - 1.5389 = 8.05
Upper limit = 9.59 + 1.5389 =11.13
Confidence interval = (8.05, 11.13)
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