Sara is a big hip-hop music fan. Her friend Matt is a big rapmusic fan. They each have a huge library of songs in their digitalmusic libraries. They each randomly sample 50 songs from theirlibraries and record the lengths of the songs selected. The averageof the selected hip-hop songs was
x1 = 240
seconds with a sample standard deviation of 5 seconds. Theaverage of the selected rap songs was
x2 = 265
seconds with a sample standard deviation of 8 seconds. Theywould like to know if the average length of hip-hop songs isdifferent than the average length of rap songs.
(a)
What are the appropriate null and alternative hypotheses forthis test?
H0: μ1 −μ2 = 0
Ha:μ1 − μ2 > 0
H0: μ1 −μ2 = 0
Ha:μ1 − μ2 ≠0
   Â
H0: μ1 −μ2 = 0
Ha:μ1 − μ2 < 0
H0: μ1 −μ2 < 0
Ha:μ1 − μ2 > 0
(b)
Calculate the test statistic. (Round your answer to two decimalplaces.)
(c)
Assume for purposes of this study, the degrees of freedom are80. At a 5% significance level, what is the critical value for thetest? (Round your answer to two decimal places. Just give the valueof the critical value, no negative or positive sign)
