2. Many types of error will cause a computer program to terminate or give incorrect results. One type of error is punctuation. For instance, if a comma is inserted in the wrong place, the program might not run. A study of programs written by students in an introductory programming course showed that 75 out of 300 errois selected at random were punctuation emors. (a) Find a 99% confidence interval for the proportion of errors made by beginning programming students that are punctuation errors. Interpret the results in a clear sentence. The z value at 99% confidence level allows the confidence interval to be 0.2128 to 0.2872. It is 99% confident that the true population proportion lie between 0.2128 to 0.2872. (b) Find a 95% confidence interval. Is this interval longer or shorter? Thus, the confidence interval is 0.2217 to 0.2783. This interval is shorter than 99% confidence interval. (c) Find the margin of error for each confidence interval. (Hint: you do have enough information from the calculator output!) (d) Compare the margin of error from part (b) with the quick method we leamed early in the semester. Is it the same? Why or why not?

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2. Many types of error will cause a computer program to terminate or give incorrect results. One type of error
is punctuation. For instance, if a comma is inserted in the wrong place, the program might not run. A
study of programs written by students in an introductory programming course showed that 75 out of 300
errois selected at random were punctuation emors.
(a) Find a 99% confidence interval for the proportion of errors made by beginning programming
students that are punctuation errors. Interpret the results in a clear sentence.
The z value at 99% confidence level allows the confidence interval to be 0.2128 to 0.2872.
It is 99% confident that the true population proportion lie between 0.2128 to 0.2872.
(b) Find a 95% confidence interval. Is this interval longer or shorter?
Thus, the confidence interval is 0.2217 to 0.2783.
This interval is shorter than 99% confidence interval.
(c) Find the margin of error for each confidence interval. (Hint: you do have enough information
from the calculator output!)
(d) Compare the margin of error from part (b) with the quick method we leamed early in the
seme ster. Is it the same? Why or why not?
Transcribed Image Text:2. Many types of error will cause a computer program to terminate or give incorrect results. One type of error is punctuation. For instance, if a comma is inserted in the wrong place, the program might not run. A study of programs written by students in an introductory programming course showed that 75 out of 300 errois selected at random were punctuation emors. (a) Find a 99% confidence interval for the proportion of errors made by beginning programming students that are punctuation errors. Interpret the results in a clear sentence. The z value at 99% confidence level allows the confidence interval to be 0.2128 to 0.2872. It is 99% confident that the true population proportion lie between 0.2128 to 0.2872. (b) Find a 95% confidence interval. Is this interval longer or shorter? Thus, the confidence interval is 0.2217 to 0.2783. This interval is shorter than 99% confidence interval. (c) Find the margin of error for each confidence interval. (Hint: you do have enough information from the calculator output!) (d) Compare the margin of error from part (b) with the quick method we leamed early in the seme ster. Is it the same? Why or why not?
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