IMathAS-libretexts

Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 12 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows:

2.3
2.2
3
2.7
2.9
2.1
3
2.3
2.7
2.6
2.8
2

What is a point estimate for the population mean length of time. (Round answer to 4 decimal places) (2 points)

Which distribution should you use for this problem? (1 point)

t-distribution
normal distribution

What must be true in order to construct a confidence interval in this situation? (1 point)

The population must be approximately normal
The sample size must be greater than 30
The population mean must be known
The population standard deviation must be known

Construct a 99% confidence interval for the population mean length of time. Enter your answer as an open-interval (i.e., parentheses) Round upper and lower bounds to two decimal places (4 points)

What does it mean to be "99% confident" in this problem? (2 points)

There is a 99% chance that the confidence interval contains the population mean
99% of all simple random samples of size 12 from this population will result in confidence intervals that contain the population mean
The confidence interval contains 99% of all samples

Suppose that the company releases a statement that the mean time for all patients is 2 hours.

Is this possible? (1 point)

Is it likely? (1 point)

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