A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.) part a Construct a 95% confidence interval for the population mean length of time. (i) State the confidence interval. (Round your answers to two decimal places.) (ii) part b Sketch the graph. a/2 = CL= a/2 = part c iii) Calculate the error bound. (Round your answer to two decimal places.) Part (d What does it mean to be "95% confident" in this problem? This means that the chances of a tranquilizer being effective is 95%. This means that we are 95% confident that the average length of effectiveness of tranquilizers in the sample of 9 people is between the interval values. We are 95% confident that the effectiveness of a tranquilizer lies between the interval values. This means that if intervals are created from repeated samples, 95% of them will contain the true population average length of effectiveness of tranquilizers.

A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.6; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.
NOTE: If you are using a Student's t-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)
part a Construct a 95% confidence interval for the population mean length of time.
(i) State the confidence interval. (Round your answers to two decimal places.)

(ii) part b Sketch the graph.

a/2 =

CL=

a/2 =

part c iii) Calculate the error bound. (Round your answer to two decimal places.)
Part (d
What does it mean to be "95% confident" in this problem?
This means that the chances of a tranquilizer being effective is 95%.
This means that we are 95% confident that the average length of effectiveness of tranquilizers in the sample of 9 people is between the interval values.
We are 95% confident that the effectiveness of a tranquilizer lies between the interval values.
This means that if intervals are created from repeated samples, 95% of them will contain the true population average length of effectiveness of tranquilizers.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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