Some measurements in mm were made on a species of spider named Sosippus Floridan
ID: 3158001 • Letter: S
Question
Some measurements in mm were made on a species of spider named Sosippus Floridanus that are native to Florida. There are 10 female spiders and 10 male spiders. The total body lengths are as follows Female 11.06 13.87 12.93 15.08 17.82 14.14 12.26 17.82 20.17 16.88 Male 12.26 11.66 12.53 13.00 11.79 12.46 10.65 10.39 12.26 14.07 Assuming the population variances are equal, a. Compute a confidence interval for the difference of the mean body sizes in female and male spiders. b. Test the null hypothesis that the lengths of female and male spiders are equal against the alternative that they are different, including the p-value. c. Now retest it against the alternative that female spiders are longer, and update the p-valueExplanation / Answer
a) From information given, x1bar=15.203, x2bar=12.107, s1=2.889, and s2=1.074, where 1 and 2 represent females and male spider respectively.
The 95% c.i=(x1bar-x2bar)+-t11,0.05*SE(x1bar-x2bar), whereSE(x1bar-x2bar)=sqrt[s1^2/n1+s2^2/n2]=sqrt[2.889^2/10+1.074^2/10]=0.975
=(15.203-12.107)+-2.201*0.975
=0.951 to 5.241
b) H0:mu1-mu2=0 (length of female and male spiders are equal)
H1:mu1-mu2 not equal to 0 (length of females and male spiders are not equal).
t=(x1bar-x2bar)/SE(x1bar-x2bar)
=(15.20-12.11)/0.975
=3.18
The corresponding p value is 0.009.
The p value is less than 0.05. Rejecy H0 to cocnclude that length of female and male spiders are different.
c) H0:mu1-mu2<=0 (length of female spider is atmost the length of male spiders)
H1:mu1-mu2>=0 (length of female spider sis higher)
t=3.18, p value is 0.004.
The p value is less than alpha=0.05. Reject H0, to cocnclude that length of female spiders are larger.
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.