Use the singer ranges dataset. Calculate the mean lowkey and mean highkey for the men and women singers.

a) If we randomly selected a man with an average lowkey value, could we statistically distinguish him from women? Assume that both the men and women singers come from a normally distributed population of professional men and women singers with the means and sigmas of the samples. Interpret your findings.

b) Now do the same thing for highkey. Interpret your findings.

c) Now assume you select 4 men with average highkey values. Can you statistically distinguish them from women? Interpret your findings.

d) Suppose the dataset included the three BeeGee brothers (famous for their ability to sing very high noteslisten to Stayin' Alive and Tragedy to see what I mean). Twins Robin and Maurice Gibb and their older brother Barry Gibb formed the trio. What problem would this introduce into your analysis, especially for b and c? Is there any way to use any of the BeeGees data in a statistically legitimate way?

e) Which

singerranges singerranges_2 name [1] Luke Bryan Low high Lowkey highkey birthyear female monhas susanhas kenknows band name Luke Bryan 25 49 1976 Male Variables Elvis Presley 81 61 1935 Male Name Label John Lennon 1940 Male Beatles Joe Cocker 1944 Male Singer Bruno Mars B72 1985 Male low LowestNote Joni Mitchell C#3 1943 Female Led Zeppelin high HighestNo.. Robert Plant E2 1948 Male lowkey Mick Jagger E2 1943 Male Rolling Stones LowestKey E2 61 1933 Female highkey HighestKey Nina Simone F#2 1949 Journey Steve Perry 61 Male birthyear Year Of Bi... Bob Marley 1945 Male female Female Paul Mccartney 1942 Male Beatles momhas My Mom.. Janis Joplin 1943 Female susanhas Susan Ow. Lady Gaga B72 1986 Female Adele 1988 kenknows Ken Heard.. C3 Female E72 1949 Male band Band 16 Bruce Springsteen 17 Justin Timberlake F#2 1981 Male 18 Aretha Franklin 1942 Female Eurythmics 19 Annie Lennox 1954 Female Prince 1958 Male 21 Dusty Springfield 875 1939 Female Katy Perry 875 1984 Female Jim Morrison 875 1943 Male Doors Ray Charles G#2 B75 1930 Male Axl Rose 876 1962 Male Guns n Roses Sam Cooke 1931 Male 27 David Ruffin 1941 Male Temptations 28 Van Morrison 1945 Male Chuck Berry 1926 Male Jerry Lee Lewis G#2 1935 Male Jackie Wilson A2 1934 Male Whitney Houston 1963 Female Rod Stewart 1945 Male Properties Justin Bieber 1994 Male Rihanna C#6 1988 Female > Variables 36 Lana Del Rey CA6 1985 Female Michael Jackson G#2 1956 Male Data 37 38 Christina Aguilera 1980 Female Traffic Frame defa Steve Winwood 1948 Filename singerranges_20 Elton John 1947 Male Label Bjork 1965 Female > Notes RNBSOONKO Dolly Parton 1946 Female Variables 11 1947 Male Stooges Iggy Pop Observations 77 Stevie Nicks 1948 Female Fleetwood Mac Size 4.44K 45 Roy Orbison 1936 Male Memory 64M FR Beyonce 1981 Female