(i) Compute the means and variances of neck length in males and females; (ii) Co

Question

 (i) Compute the means and variances of neck length in males and females;   (ii) Compute the t test on the data. (iii) Compute the corresponding p-value. You are computing a  two-sided p-value.  show all work please.  Number of individuals simulated: 50  Gender  Neck Length Male    222.58 Female  255.074 Male    205.634 Female  239.78 Male    179.484 Male    162.88 Female  187.842 Female  99.4519 Male    168.868 Male    255.441 Male    121.258 Female  244.515 Male    177.807 Male    220.274 Male    174.69 Male    154.233 Female  146.868 Male    138.277 Female  220.873 Female  110.822 Male    245.068 Male    150.724 Female  169.461 Male    221.622 Female  198.191 Female  227.222 Male    240.023 Male    202.763 Male    203.316 Female  156.516 Male    136.157 Female  254.225 Female  176.369 Male    180.342 Male    196.139 Female  200.554 Male    150.133 Male    178.406 Male    238.956 Female  252.685 Male    137.868 Female  217.195 Female  210.95 Male    177.182 Male    208.601 Female  62.3559 Male    181.198 Female  216.385 Female  297.236 Male    131.826 

Explanation / Answer

Part i

Solution:

The mean and variances of neck length in males and females is given as below:

Variable

Gender

N

Mean

Variance

Std. Deviation

Neck Length

Male

29

184.8879

1370.02065

37.01379

Female

21

197.3605

3342.36956

57.81323

Part ii

We have to compute two sample t test for population means assuming equal population variances the given data.

H0: µmale = µfemale Vs Ha: µmale µfemale

This is a two tailed test.

Level of significance or alpha value is given as 0.05 or 5%.

= 0.05

DF = n1+n2 – 2 =29 + 21 – 2 = 50 – 2 = 48

Pooled variance = Sp2 =[ (n1 – 1)*S1^2 + (n2 – 1)*S2^2 ]/[ (n1 + n2 – 2)]

Sp2 = [ (29 – 1)* 37.01379^2 + (21 – 1)* 57.81323^2] / (29 + 21 – 2)

Sp2 = 2191.8327

Test statistic formula is given as below:

t = (X1bar – X2bar) / sqrt[Sp2((1/n1)+(1/n2))]

t = (184.8879 - 197.3605) / sqrt(2191.8327*((1/29)+(1/21)))

t = -0.9298

Part iii

P-value = 0.3571 (by using t-table or excel)

P-value > = 0.05

So, we do not reject the null hypothesis that average neck length for male and females are same.

There is sufficient evidence to conclude that average neck length for male and females are same.

Variable

Gender

N

Mean

Variance

Std. Deviation

Neck Length

Male

29

184.8879

1370.02065

37.01379

Female

21

197.3605

3342.36956

57.81323

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