In a large financial firm, five programmers that are familiar with both Python and Java

are randomly selected. The time $($in minutes$),$ it takes to correctly write the code to

complete the same task is recorded.

Python $2114131423$

Java $1913151124$

a$.$ Provide and interpret a $90\%$ confidence interval.

Based on the confidence interval, does this indicate the mean time to complete the

tasks differs?

b$.$ In a larger study, how many programmers should be used to be $90\%$ confident the

sample estimate is within $30$ seconds of the true difference in means?