The popular sport of mounting biking involves riding bikes off-road, often over very rough terrain. Trek is a leading manufacturer of mountain bikes, specially designed for durability and performance. A random sample of 10 Trek mountain bikes was obtained and each was carefully weighed. The resulting data yielded a sample mean of 10.67 kg and a sample standard deviation of 2.27 kg. Assume the underlying distribution of weights is normal. Find a 98% confidence interval for the true mean weight of Trek mountain bikes. (Round your answers to 2 decimal places.)

(8.64, 12.7)

Step-by-step explanation:

When population standard deviation is unknown then, confidence interval for population mean is given by :-

, where n= sample size , s= sample standard deviation, = sample mean, = two tailed t value for confidence level of 1- and degree of freedom = 1-n.

Given: n= 10 , s= 2.27 kg , kg

df = 10-1=9

For 98% confidence, significance level =

T-critical value:

Now, 98% confidence interval for the true mean weight of Trek mountain bikes will be :

Hence, a 98% confidence interval for the true mean weight of Trek mountain bikes=  (8.64, 12.7)

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hope this .