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? O normal distribution Ot distribution c. Why?

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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:
2.8
2.6
3
2.2
2.1
2.6
2.7
3
2.3
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?
O normal distribution
Ot-distribution
c. Why?
d. What must be true in order to construct a confidence interval in this situation?
O The population mean must be known
O The population standard deviation must be known
O The population must be approximately normal
O The sample size must be greater than 30
e. Construct a 99% confidence interval for the population mean length of time. Enter your answer as
an open-interval (l.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 "99% confident" in this problem? Use the definition of confidence level.
O There is a 99% chance that the confidence interval contains the population mean
O The confidence interval contains 99% of all samples
O 99% 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?
O Yes
O No
Is it likely?
O No
O Yes
Transcribed Image Text: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: 2.8 2.6 3 2.2 2.1 2.6 2.7 3 2.3 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? O normal distribution Ot-distribution c. Why? d. What must be true in order to construct a confidence interval in this situation? O The population mean must be known O The population standard deviation must be known O The population must be approximately normal O The sample size must be greater than 30 e. Construct a 99% confidence interval for the population mean length of time. Enter your answer as an open-interval (l.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 "99% confident" in this problem? Use the definition of confidence level. O There is a 99% chance that the confidence interval contains the population mean O The confidence interval contains 99% of all samples O 99% 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? O Yes O No Is it likely? O No O Yes
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