Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 11 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows: 2.5 2.5 2.2 2.5 2.1 2.4 2.8 2 2.9 2 2.7 a. What is a point estimate for the population mean length of time. (Round answer to 4 decimal places) b. Which distribution should you use for this problem? normal distribution t-distribution c. Why?
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 11 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows:
| 2.5 |
| 2.5 |
| 2.2 |
| 2.5 |
| 2.1 |
| 2.4 |
| 2.8 |
| 2 |
| 2.9 |
| 2 |
| 2.7 |
a. What is a point estimate for the population mean length of time. (Round answer to 4 decimal places)
b. Which distribution should you use for this problem?
normal distribution - t-distribution
c. Why?
d. What must be true in order to construct a confidence interval in this situation?
- The population mean must be known
- The
sample size must be greater than 30 - The population standard deviation must be known
- The population must be approximately normal
e. Construct a 98% 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
f. Interpret the confidence interval in a complete sentence. Make sure you include units
g. What does it mean to be "98% confident" in this problem? Use the definition of confidence level.
- There is a 98% chance that the confidence interval contains the population mean
- 98% of all simple random samples of size 11 from this population will result in confidence intervals that contain the population mean
- The confidence interval contains 98% of all samples
h. Suppose that the company releases a statement that the mean time for all patients is 2 hours.
Is this possible?
- Yes
- No
Is it likely?
- Yes
- No
i. Use the results above and make an argument in favor or against the company's statement. Structure your essay as follows:
- Describe the population and parameter for this situation.
- Describe the sample and statistic for this situation.
- Give a brief explanation of what a confidence interval is.
- Explain what type of confidence interval you can make in this situation and why.
- Interpret the confidence interval for this situation.
- Restate the company's claim and whether you agree with it or not.
- Use the confidence
interval to estimate the likelihood of the company's claim being true. - Suggest what the company should do.
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