A random sample of 10 HMOs was selected. For each HMO, the co-payment(in dollars) for a doctor's office visit was recorded. The results are as follows. 8,5,11,12,9,11,10,7,12,5. Under the assumption that co-payment amounts are normally distributed, find a 99% confidence interval for the mean co-payment amount in dollars. Then find to lower limit and upper limit of the 99% confidence interval. Carry intermediate computations to at least 3 decimal places. Round answer to 1 decimal place.
A random sample of 10 HMOs was selected. For each HMO, the co-payment(in dollars) for a doctor's office visit was recorded. The results are as follows. 8,5,11,12,9,11,10,7,12,5. Under the assumption that co-payment amounts are
Given Information:
Sample size (n) = 10
Confidence level = 99% = 0.99
To construct 99% confidence interval for the mean co-payment amount:
Since, population standard deviation is not known and sample size is less than 30, we use t-distribution.
Confidence Interval for mean is obtained using the formula:
where, is the sample mean
is the sample standard deviation
is the t-critical value at degrees of freedom and 99% confidence level or significance level.
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