a new medicine is said to help improve sleep a sample of subjects are picked at random and given

a) We should use the t-distribution to construct a confidence interval on the population mean be

Question

A new medicine is said to help improve sleep. A sample of subjects is picked at random and given the medicine. After the medication, the hours of sleep for each person were recorded: 8.5; 6.9; 7; 7.8; 7.1; 9.2; 7.4; 8.3; 6.9; 6.6; 8.1; 8.2; 7.9; 7.6; 8.2; 8. Assume that the number of hours of sleep is normally distributed with a standard deviation of 0.8. a) Which distribution should you use to construct a confidence interval on the population mean? Why? b) Calculate the necessary sample quantities to construct a confidence interval on the population mean. Show all your calculations. c) Construct a 95% confidence interval for the mean number of hours of sleep. d) Suppose that the population standard deviation is more than 0.8, how does this change affect the length of the 95% confidence interval? Discuss. (All the other quantities remain the same). e) Define the random variable X in words. f) Define the random variable X̄ in words. g) Solve part c) by using Minitab. Compare with your result. Are they different? Why? / Why not?

          A new medicine is said to help improve sleep. A sample of subjects is picked at random and given the medicine. After the medication, the hours of sleep for each person were recorded: 8.5; 6.9; 7; 7.8; 7.1; 9.2; 7.4; 8.3; 6.9; 6.6; 8.1; 8.2; 7.9; 7.6; 8.2; 8.
Assume that the number of hours of sleep is normally distributed with a standard deviation of 0.8.
a) Which distribution should you use to construct a confidence interval on the population mean? Why?
b) Calculate the necessary sample quantities to construct a confidence interval on the population mean. Show all your calculations.
c) Construct a 95% confidence interval for the mean number of hours of sleep.
d) Suppose that the population standard deviation is more than 0.8, how does this change affect the length of the 95% confidence interval? Discuss. (All the other quantities remain the same).
e) Define the random variable X in words.
f) Define the random variable X̄ in words.
g) Solve part c) by using Minitab. Compare with your result. Are they different? Why? / Why not?

Added by Jaime G.

Question

Please give Ace some feedback