Question

# Use the given degree of confidence and sample data to construct a confidence interval for the...

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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