Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 9 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows: Hours 2.2 2.1 2.2 2.6 2.3 3 2.8 2.3 2.2 1)What is a point estimate for the population mean length of time. (Round answer to 2 decimal places) 2)What must be true in order to construct a confidence interval in this situation? Select an answer: a)The population mean must be known b)The sample size must be greater than 30 c)The population must be approximately normal d)The population standard deviation must be known 3)Construct a 98% confidence interval for the population mean length of time. (Round upper and lower bounds to 2 decimal places.) ( , )
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 9 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows:
| Hours |
|---|
| 2.2 |
| 2.1 |
| 2.2 |
| 2.6 |
| 2.3 |
| 3 |
| 2.8 |
| 2.3 |
| 2.2 |
1)What is a point estimate for the population mean length of time. (Round answer to 2 decimal places)
2)What must be true in order to construct a confidence interval in this situation?
Select an answer:
a)The population mean must be known
b)The sample size must be greater than 30
c)The population must be approximately normal
d)The population standard deviation must be known
3)Construct a 98% confidence interval for the population mean length of time. (Round upper and lower bounds to 2 decimal places.)
( , )
4) What does it mean to be "98% confident" in this problem?
a)The confidence interval contains 98% of all sample times.
b)98% of all times will fall within this interval.
c)98% of all confidence intervals found using this same sampling technique will contain the population mean time.
d)There is a 98% chance that the confidence interval contains the sample mean time.
5) Suppose that the company releases a statement that the mean time for all patients is 2 hours.
Is this possible?
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