Construct a Confidence Interval For $\mu _ { \mathrm { d } }$

Multiple Choice

Construct a confidence interval for $\mu _ { \mathrm { d } }$ , the mean of the differences d for the population of paired data. Assume that the
population of paired differences is normally distributed.
-A manager at a bank is interested in the standard deviation of the waiting times when a single waiting line is used and when individual lines are used. He wishes to test the claim that the population standard deviation for waiting times when multiple lines are used is greater than the population standard deviation for waiting times when a single line is used. Find the P-value for a test of this claim given the following sample data. You won't be able to find the exact P-value, but will be able to give a range of possible values.
Sample 1: multiple waiting lines: $\mathrm { n } _ { 1 } = 13 , \mathrm {~s} 1 = 2.1$ minutes
Sample 2: single waiting line: $n _ { 2 } = 16 , s _ { 2 } = 1.1$ minutes

A) $0.005 < \mathrm { P }$ -value $< 0.01$
B) $0.02 < \mathrm { P }$ -value $< 0.05$
C) $0.025 < \mathrm { P }$ -value $< 0.05$
D) $0.01 < \mathrm { P }$ -value $< 0.025$