Question

Sara sa hip-hop music fan. Her friend Matt is a big rap music fan. They each have a huge library of songs in their digtal music libraries. They each randomly sample 50 songs from their braries and record the length of the songs selected. The average of the selected hip-hop songs was x, = 230 seconds with a sample standard deviation of 5 seconds. The average of the selected rap songs was x2 - 250 seconds with a sample standard deviation of 8 seconds. They would like to know if the average length of hip-hop songs is different than the average length of songs. (a) What are the appropriate null and alternative hypotheses for this test? Ho: M-4₂0 MO: Ni - My > 0 HOH - M - 0 HH - H - HoiH, H2 - 0 HH - H2> Hi Hi - M - 0 Mi-20 (1) Calculate the test statistic (Round your answer to two decimal places.) . At a significance level what is the critical value for the test? (Round your answer to two decimal places. Just give the value (c) Assume for purposes of this study, the degrees of freedom are of the critical value, no negative or positive sign)

Answer 1

Ansi- Given that, no M = 230 and X z 250 se 5 =8 n = 50 M₂ 280 Here claim e that to know if the average length of hip-hop Songs (a) is different than the average length of rap songs (X2) Here Hoi ly lz=0 - Ha :- l, -lz to s options ® is correct Here consider test statuti formula as below in Heel t , m-D) 5* + (1 +1) 520 ) Chittoo nith -2

230 - 250 1901) (59 +(504)(8)" (ots) 50 € 50-2 -14.99 an t = -14.991 = t=-14.99 Givern degrees of freedom, df = so and significance level, a=54.20.05 from 2 Tailed t- tert, we get for L=0.05 and df=80 j Critical t-Value, tc=1.99