A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows:2.6;2.8;3.1;2.3;2.3;2.2;2.8;2.1; and2.4.

NOTE: If you are using a Student'st-distribution, you may assume that the underlying population is normally distributed. (In general, you must first prove that assumption, though.)

• Part (a)
• (i) Round your answer to two decimal places.
• x=
• (ii) Round your answer to two decimal places.
• s_x=
• (iii) Enter an exact number as an integer, fraction, or decimal.
• n=
• (iv) Enter an exact number as an integer, fraction, or decimal.
• n1 =
• Part (b) multiple choice
• In words, define the random variableX.

a) the number of tranquilizers the hospital used for each patient

b) the number of patients that were given a tranquilizer

c) time, in hours, of the effectiveness of a tranquilizer

d) time, in minutes, of the effectiveness of a tranquilizer

• Part (c) multiple choice
• In words, define the random variablex.

a) the average length, in hours, of the effectiveness period of tranquilizers

b) the average number of tranquilizers the pharmaceutical company dispenses to hospitals

c) the average length, in minutes, of the effectiveness period of tranquilizers

d) the average number of tranquilizers used for each patient

• Part (d)
• Which distribution should you use for this problem? (Enter your answer in the formzort_dfwheredfis the degrees of freedom.)
• _____________
• Explain your choice.

a) The standard normal distribution should be used because the population standard deviation is known.

b) The Student'st-distribution should be used because the sample size is small.

c) The Student'st-distribution should be used because the sample standard deviation is known and the sample size is small.

d) The standard normal distribution should be used because the sample standard deviation is known.

• Part (e)
• Construct a 95% confidence interval for the population mean length of time.
• (i) State the confidence interval. (Round your answers to two decimal places.)
• (_____,_____)
• (ii) Sketch the graph.
• a/2=____ c.l.=_______a/2=_____
• (iii) Calculate the error bound. (Round your answer to two decimal places.)
• Part (f) multiple choice
• What does it mean to be "95% confident" in this problem?

a) We are 95% confident that the effectiveness of a tranquilizer lies between the interval values.

b) This means that if intervals are created from repeated samples, 95% of them will contain the true population average length of effectiveness of tranquilizers.

c) This means that we are 95% confident that the average length of effectiveness of tranquilizers in the sample of 9 people is between the interval values.

d) This means that the chances of a tranquilizer being effective is 95%.