Question

Confidence intervals for the mean

Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 10 patients. The period of effectiveness of the tranquilizer 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 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 95% 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 "95% confident" in this problem? Use the definition of confidence level.

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

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

Is this possible?

• No
• Yes

Is it likely?

• No
• Yes

Answer 1

Result:

Confidence intervals for the mean

Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 10 patients. The period of effectiveness of the tranquilizer 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)

point estimate = 2.5100

b. Which distribution should you use for this problem?

• t-distribution

c. Why?

population standard deviation is not known and sample size is small( <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 95% 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

95% CI = (2.28, 2.74)

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

we are 95% confident that population mean length of time falls in the interval (2.28, 2.74).

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

• 95% of all simple random samples of size 10 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

Is it likely?

• Yes

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	0.3213
Sample Mean	2.51
Sample Size	10
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	0.1016
Degrees of Freedom	9
t Value	2.2622
Interval Half Width	0.2298
Confidence Interval
Interval Lower Limit	2.2802
Interval Upper Limit	2.7398