Help with part C and part F

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;2.9;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=
• (rounded to two decimal places)
• (ii) Round your answer to two decimal places.
• s_x=
• (rounded to two decimal places)
• (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)
• In words, define the random variableX.
• the number of tranquilizers the hospital used for each patient
• the number of patients that were given a tranquilizer
• time, in hours, of the effectiveness of a tranquilizer
• time, in minutes, of the effectiveness of a tranquilizer
• Correct! The pharmaceutical company is interested in how many hours a tranquilizer is effective.
• Part (c)
• In words, define the random variableX.
• the average length, in minutes, of the effectiveness period of tranquilizers
• the average number of tranquilizers the pharmaceutical company dispenses to hospitals
• the average number of tranquilizers used for each patient
• the average length, in hours, of the effectiveness period of tranquilizers
• Incorrect. The pharmaceutical company is not interested in the average number of minutes a tranquilizer is effective.
• Part (d)
• Which distribution should you use for this problem? (Enter your answer in the formzort_dfwheredfis the degrees of freedom.)
• t8
• Explain your choice.
• The Student'st-distribution should be used because the sample size is small.
• The Student'st-distribution should be used because the sample standard deviation is known and the sample size is small.
• The standard normal distribution should be used because the population standard deviation is known.
• The standard normal distribution should be used because the sample standard deviation is known.
• Correct! Only sample data is given for nine samples; therefore, the calculated standard deviation is a sample standard deviation.
• 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.
• (iii) Calculate the error bound. (Round your answer to two decimal places.)
• Part (f)
• What does it mean to be "95% confident" in this problem?
• This means that if intervals are created from repeated samples, 95% of them will contain the true population average length of effectiveness of tranquilizers.
• 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.
• This means that the chances of a tranquilizer being effective is 95%.
• We are 95% confident that the effectiveness of a tranquilizer lies between the interval values.
• Incorrect. A confidence interval is based on a claim about a population parameter and not one object in the population.

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A sample of 20 heads of lettuce was selected. Assume that the population distribution of head weight is normal. The weight of each head of lettuce was then recorded. The mean weight was2.2 poundswith a standard deviation of0.1 pounds.The population standard deviation is known to be0.2 pounds.

What would happen if 40 heads of lettuce were sampled instead of 20, and the confidence level remained the same?

The confidence interval would become wider.

The confidence interval would become narrower.

There would be no change.