SOLUTION: Please� i do really need help� Exercise 2: Several drugs are used to treat diabetes. A sales specialist for a leading pharmaceutical company randomly sampled the records of 10 sa

Question 380538: Please� i do really need help�
Exercise 2:
Several drugs are used to treat diabetes. A sales specialist for a leading pharmaceutical company randomly sampled the records of 10 sales districts to estimate the number of new prescriptions that had been written during a particular month for her company�s new diabetes drug. The numbers of new prescriptions were as follows:
210, 240, 190, 275, 290, 265, 312, 284, 261, 243.
a)Find a 90% confidence interval for the average number of new prescriptions written for this new drug among all sales district. What are the assumptions?
b)Calculate the widths of the 95% and 98% confidence intervals
c)Assuming that the confidence level remains constant, what sample size is needed to reduce by half the margin of error of the confidence interval in part (a)?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
210, 240, 190, 275, 290, 265, 312, 284, 261, 243.
----
sample mean = 257
sample std = 37.16
-----
a)Find a 90% confidence interval for the average number of new prescriptions written for this new drug among all sales district. What are the assumptions?
E = 1.645*37.16/sqrt(10) = 19.33
---
90% CI: 257-19.33 < u < 257+19.33
-----------------------------------------
b)Calculate the widths of the confidence intervals
for 95% CI:::Use a z-value of 1.96 in place of 1.645
------
for 98% CI::: Usa a z-value of 2.3263
------------------------------------------------

c)Assuming that the confidence level remains constant, what sample size is needed to reduce by half the margin of error of the confidence interval
in part (a)?
From part (a): E = 1.645*37.16/sqrt(10) = 19.33
----
E/2 = [1.645*37.16/sqrt(10)*(1/2)
E/2 = [1.645*37.16/sqrt(10*4)
Sample size needed = 10*4 = 40
===================================
Cheers,
Stan H.

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