Set environment
env <- c("dplyr")
lapply(env, library, character.only = 1)Part A
A publishing company has just published a new textbook. Before the company decides the price at which to sell this textbook, it want to know the average price of all such textbooks in the market. The research department at the company took a sample of 25 comparable textbooks and collected information on their prices. This information produced a mean price of $145 for this sample. It is known that the standard deviation of the prices of all such textbooks is $35 and the population of such prices is normal.
Construct a 90% confidence interval for the mean price of all such textbooks.
In trying to find the CI given the normal distribution assumptions, we have the population standard deviation (35) and sample mean (145) and sample size (25).
For CI using: \(\Large \bar{x} \ \pm z \ \frac{alpha}{2} \cdot \frac{\sigma}{sqrt(n)}\)
\(\bar{x} = 145 \ ->\) xbar
\(alpha = 0.10 \ ->\) alpha
\(\sigma = 35 \ ->\) sd
\(n = 25 \ ->\) n
In R: xbar +- qnorm( alpha/2 ) * ( sd/sqrt(n) )
Price 1 = 133.4860246
Price 2 = 156.5139754
The 90% CI is ($133 , $157 ).
Part B
According to Mobes Services Inc. an individual checking his/her account at major U.S banks via cellphones cost the banks between $350 and $650. A recent random sample of 600 such checking account produced a mean annual cost of $500 to major U.S banks. Assume that the standard deviation of annual costs to major US banks of all such checking account is $40.
Make a 99% confidence interval for the current mean annual cost to major banks all such checking account.
Assuming a normal distribution, we have the population standard deviation (40) and sample mean (500) and sample size (600).
For CI using: \(\Large \bar{x} \ \pm z \ \frac{alpha}{2} \cdot \frac{\sigma}{sqrt(n)}\)
\(\bar{x} = 500 \ ->\) xbar
\(alpha = 0.01 \ ->\) alpha
\(\sigma = 40 \ ->\) sd
\(n = 600 \ ->\) n
In R: xbar +- qnorm( alpha/2 ) * ( sd/sqrt(n) )
Price 1 = 495.7936884
Price 2 = 504.2063116
The 99% CI is ($495 , $505 ).
GitHub
Related file(s) can be found at Git Me
No comments:
Post a Comment