Question

Suppose you are a researcher in a hospital. You are experimenting with a new tranquilizer. You collect data from a random sample of 13 patients. The period of effectiveness of the tranquilizer for each patient (in hours) is as follows:

Hours

2.8

2.9

2.1

2.3

2.4

2.4

2.2

2.8

3

2.7

2

2.9

3

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

  

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

  Select an answer The population standard deviation must be known The population mean must be known The population must be approximately normal The sample size must be greater than 30

c) Construct a 99% confidence interval for the population mean length of time. Enter your answer as an open-interval (i.e., parentheses example (5.2314,8.1245)) Round upper and lower bounds to 4 decimal places.

d) What does it mean to be "99% confident" in this problem?

• 99% of all times will fall within this interval.
• There is a 99% chance that the confidence interval contains the sample mean time.
• The confidence interval contains 99% of all sample times.
• 99% of all confidence intervals found using this same sampling technique will contain the population mean time.

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

Is this possible?  Select an answer Yes No

Is it likely? Select an answer No Yes

Answer 1

From the given sample data : Sample size=n=13

Sample mean=

Sample standard deviation=s=

a) The point estimate for the population mean length of time =

b) The population must be approximately normal.

c) The 99% confidence interval for the population mean length of time is ,

: From t-table

d) The 99% of all confidence intervals found using this same sampling technique will contain the population mean time.

e) Hypothesis : VS

Here , The value does not lies in the 99% confidence interval

Therefore , reject Ho

Hence , it is not poosible that the mean time for all patients is 2 hours