Confidence intervals for the mean

Suppose you are a researcher in a hospital. You areexperimenting with a new tranquilizer. You collect data from arandom sample of 10 patients. The period of effectiveness of thetranquilizer for each patient (in hours) is as follows:

3
2.7
2
2.3
2.4
2.6
2.7
2.2
2.3
2.9

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 inthis 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 95% confidence interval for the population meanlength of time. Enter your answer as anopen-interval (i.e., parentheses) Roundupper and lower bounds to two decimal places

f. Interpret the confidence interval in a complete sentence. Makesure you include units

g. What does it mean to be \"95% confident\" in this problem? Use thedefinition of confidence level.

• 95% of all simple random samples of size 10 from thispopulation will result in confidence intervals that contain thepopulation mean
• There is a 95% chance that the confidence interval contains thepopulation mean
• The confidence interval contains 95% of all samples

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

Is this possible?

• No
• Yes

Is it likely?

• No
• Yes