Do male bears have longer feet than female bears? Are you sure? B) Give a range

Question

Do male bears have longer feet than female bears? Are you sure?

B) Give a range of values in which you would expect to find 95% of all bears’ feet lengths. Explain why you picked this range.

C)What is the shape of the distribution of bears’ feet lengths? Explain.

FEMALES MALES Mean 12.77 in Mean 9.4 in Standard Error 0.162 Standard Emor 0.104 Median 9.115 Std Dev 1 44 Std Derr 1.81 Sample V 3.26 Sample v ariance 2.07 Range 7.67 Range 9.78 Min 9.26 Min 4,57 Max 1693 Mac 14.35 Sum 1145.77 Suan 2439 Count 191 Count 124

Explanation / Answer

We will do t-test for comparing the two sample means. We will test the hypothesis whether male bears have longer feet than female bears.

H0: µm µf

H1: µm < µf

µm = 9.4, m = 1.81, nm = 124

µf = 12.77, f = 1.44, nf = 191

SE = sqrt[ (sm2/nm) + (sf2/nf) ]

= 0.193

DF = (sm2/nm + sf2/nf)2 / { [ (sm2 / nm)2 / (nm - 1) ] + [ (sf2 / nf)2 / (nf - 1) ] } = 68

t = (µm - µf) / SE = -17.54

p-value is almost zero. Hence, we have to reject the null hypothisis and we can say that female bears have longer feet than male bears.

b) z value for 95% CI = 1.96

Margin of Error(E) = z*/n = 1.96*1.81/124 = 0.3185

Interval = [µ ± E] = [9.08, 9.71]

c.) The distribution will be mostly normally distributed because we have large enough sample size.

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