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: 2.7; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.Part 1) Find the values sample mean, sx, n, and n − 1 Part 2) Which distribution should you use for this problem? (Enter your answer in the form z or tdf where df is the degrees of freedom.)Part 3) Construct a 95% confidence interval for the population mean length of time (State the confidence interval, sketch the graph, and calculate the error bound) The image shows a bell-shaped curve, commonly representing a normal distribution in statistics. There are three distinct parts marked on the curve:1. **Left Tail**: Labeled as $ \frac{\alpha}{2} $.2. **Center**: Labeled as C.L., which stands for Confidence Level. 3. **Right Tail**: Also labeled as $ \frac{\alpha}{2} $.Descriptions:- The curve is symmetric, indicative of a normal distribution, with two tails representing the tails in a hypothesis test.- The arrows pointing towards $ \frac{\alpha}{2} $ on both sides highlight the significance level split evenly between the two tails.- The arrow pointing downwards labeled C.L. represents the area under the curve that comprises the confidence interval.- P′ is likely a point of interest or parameter related to the distribution on the horizontal axis.This setup is typically used in confidence interval estimation where:- $ \alpha $ is the significance level.- The confidence level (C.L.) is the probability that the interval will contain the true parameter.

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Description: 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 tranquil

Part (1): From the given information, Sample size n =9 Mean of the sample data: x̅…

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MATLAB: An Introduction with Applications

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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: 2.7; 2.8; 3.1; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4.

Part 1) Find the values sample mean, s_x,n, and n − 1

Part 2) Which distribution should you use for this problem? (Enter your answer in the form z or t_df where df is the degrees of freedom.)

Part 3) Construct a 95% confidence interval for the population mean length of time (State the confidence interval, sketch the graph, and calculate the error bound)

The image shows a bell-shaped curve, commonly representing a normal distribution in statistics. There are three distinct parts marked on the curve:

1. **Left Tail**: Labeled as $ \frac{\alpha}{2} $.
2. **Center**: Labeled as C.L., which stands for Confidence Level.
3. **Right Tail**: Also labeled as $ \frac{\alpha}{2} $.

Descriptions:
- The curve is symmetric, indicative of a normal distribution, with two tails representing the tails in a hypothesis test.
- The arrows pointing towards $ \frac{\alpha}{2} $ on both sides highlight the significance level split evenly between the two tails.
- The arrow pointing downwards labeled C.L. represents the area under the curve that comprises the confidence interval.
- P′ is likely a point of interest or parameter related to the distribution on the horizontal axis.

This setup is typically used in confidence interval estimation where:
- $ \alpha $ is the significance level.
- The confidence level (C.L.) is the probability that the interval will contain the true parameter.

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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