Minitab data: ProgRockSample: 4.883, 4.967, 4.667, 5.700, 5.117, 5.500, 5.867, 4
ID: 3363329 • Letter: M
Question
Minitab data: ProgRockSample: 4.883, 4.967, 4.667, 5.700, 5.117, 5.500, 5.867, 4.600, 5.100, 3.883, 3.517, 6.150, 4.767, 4.317, 3.867, 4.183, 4.983, 6.867, 6.250, 4.400, 4.117, 5.400, 4.067, 5.238, 4.267, 5.033, 3.983
HeavyRockSample: 3.817, 4.433, 3.883, 4.183, 4.267, 3.700, 5.133, 4.500, 4.200, 6.283, 4.150, 3.800, 4.050, 4.200, 4.033, 3.933, 2.933, 4.250, 4.017, 3.383, 3.883, 4.550, 5.583, 5.700, 4.450, 5.283, 3.500, 4.350, 5.717, 3.883
(1 point) Conventional wisdom suggests that Progressive Rock, or "Prog-Rock -bands that do not regularly get their songs played on the radio- write and record songs that are longer than other." Hard Rock" bands that receive regular radio airplay. The reason being that . prog-rock" bands songs are payed less often than . hardrock' bands songs. since song-length is not limited to fit in radio-station format and allow for commercials between air-play To test this claim, a statistics professor randomly selected songs from two of his playlists on his iPod, the "ProgRock" playlist and the 'HardRock" playlist, and recorded the length of each song in minutes. The data is found in the accompanying MINITAB data file. Minitab File Assume that the length of both types of songs are normally distributed. Let PR represent the mean length of songs in the professor's ProgRock playlist, and 11R be the mean length of songs in his HardRock" playlist. (a) Construct the most appropriate statistical hypotheses that will test this professor's claim. B. H D. H E. Ho (o) Using technology available to you, does there appear to be a difference in the variation in song-length between progressive rock bands and heavy rock bands? 0 A. There appears to be unequal variation in the song-length when comparing progressive rock bands to heavy rock bands. B. There appears to be more variation in the song-length of progressive rock bands when compared to heavy rock bands. C. There appears to be equal variation in the song-length when comparing progressive rock bands and heavy rock bands. D. There appears to be less variation in the song-length of progressive rock bands when compared to heavy rock bands. (c) Report the p-value of the test you ran in (b) use three decimals in your answer. P-value = (d) Test the statistical hypotheses in (a) by carrying out the appropriate statistical test. Find the value of the test statistic for this test, use two decimals in your answer. Test Statistic = (e) Determine the P-value of your statistical test in part (d), and report it to three decimal places. (f) Determine the appropriate degrees of freedom for the test in part (d). As an integer. DF= (g) using an of 5%, this data suggest that the null hypothesis should length of heavy rock songs. ? Progressive rock songs are? when compared to theExplanation / Answer
Given that,
mean(x)=5.1667
standard deviation , s.d1=1.6021
number(n1)=6
y(mean)=4.3333
standard deviation, s.d2 =0.5164
number(n2)=6
null, Ho: uPR < uHR
alternate, H1: uPR > uHR
level of significance, = 0.05
from standard normal table,right tailed t /2 =2.015
since our test is right-tailed
reject Ho, if to > 2.015
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =5.1667-4.3333/sqrt((2.56672/6)+(0.26667/6))
to =1.2128
| to | =1.2128
critical value
the value of |t | with min (n1-1, n2-1) i.e 5 d.f is 2.015
we got |to| = 1.21276 & | t | = 2.015
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:right tail - Ha : ( p > 1.2128 ) = 0.13969
hence value of p0.05 < 0.13969,here we do not reject Ho
ANSWERS
---------------
null, Ho: uPR - uHR = 0
alternate, H1: uPR - uHR >0
test statistic: 1.2128
critical value: 2.015
decision: do not reject Ho
p-value: 0.13969
we don't have evidence that progrock is play less than Hard rock music