Question

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: 2.4 2.2 2.2 2.6 2.2 2 2.5 2.8 2 2.4

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

Which distribution should you use for this problem?

normal distribution

t-distribution

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

The population must be approximately normal and/or the sample size must be at greater than 30

The population mean must be known The population standard deviation must be known

The sample size must be greater than 30

The margin of error is 0.18485820181011. 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

What does it mean to be "95% confident" in this problem?

There is a 95% chance that the confidence interval contains the population mean

95% of all simple random samples of size 10 from this population will result in confidence intervals that contain the population mean

The confidence interval contains 95% of all samples

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

Answer 1

The data is provided as:

	Data
	2.4
	2.2
	2.2
	2.6
	2.2
	2
	2.5
	2.8
	2
	2.4
Count	10
Mean	2.33
St. Dev	0.2584

Point estimate for the population mean length of time:

2.3300

Which distribution should you use for this problem?

t-distribution

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

The population must be approximately normal and/or the sample size must be at greater than 30

The margin of error is 0.18485820181011. Construct a 95% confidence interval for the population mean length of time.

C.I = (2.33-0.18485820181011, 2.33+0.18485820181011)

= (2.15,2.51)

What does it mean to be "95% confident" in this problem?

95% of all simple random samples of size 10 from this population will result in confidence intervals that contain the population mean

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

Is this possible?

Yes

Is it likely?

No

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