Question

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:

2.4
2
2
2
2
2.9
2.2
2.5
2.3
2.8
2.3

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

e. Construct a 90% 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 "90% confident" in this problem? Use the definition of confidence level.

• The confidence interval contains 90% of all samples
• There is a 90% chance that the confidence interval contains the population mean
• 90% of all simple random samples of size 11 from this population will result in confidence intervals that contain the population mean

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:

1. Describe the population and parameter for this situation.
2. Describe the sample and statistic for this situation.
3. Give a brief explanation of what a confidence interval is.
4. Explain what type of confidence interval you can make in this situation and why.
5. Interpret the confidence interval for this situation.
6. Restate the company's claim and whether you agree with it or not.
7. Use the confidence interval to estimate the likelihood of the company's claim being true.
8. Suggest what the company should do.

Answer 1

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

2.3091

b. Which distribution should you use for this problem?

• t-distribution

c. Why?

σ is unknown and the sample size is less than 30.

d. What must be true in order to construct a confidence interval in this situation?

• The population must be approximately normal

e. Construct a 90% 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  

2.13	confidence interval 90.% lower
2.48	confidence interval 90.% upper

f. Interpret the confidence interval in a complete sentence. Make sure you include units  
We are 90% confident that the true population mean length of time is between 2.13 and 2.48.
g. What does it mean to be "90% confident" in this problem? Use the definition of confidence level.

• 90% of all simple random samples of size 11 from this population will result in confidence intervals that contain the population mean

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

Is this possible?

• No

Is it likely?

• No