The mean height of 10yearold girls is N54527 and for boys it

The mean height of 10-year-old girls is N(54.5,2.7) and for boys it is N(54.1,2.4)

Solution

z for 90% CI= 1.64
declare p larger than alpha=0.1 not significant.

mean1 eq: 54.5 (variance= 6.25) (se= 0.3536)
mean2 eq: 54.1 (variance= 6.25) (se= 0.3536)

Probability that var1 p=0.5 (left: 0.5; double: 1)

Difference between means:
M1-M2=54.5-54.1=0.4
sd=4.9497; se=0.5
90% CI of difference:
-0.4224 <0.4< 1.2224 (Wald)
t-difference: 0.8
df-t: 97.5; p= 0.78718
(left p: 0.2128; two sided: 0.4256)

Difference not significant at 10%

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Let us assume sample size = 70

t-difference: 0.947
df-t: 137.5; p= 0.82724
(left p: 0.1728; two sided: 0.3456)

Difference not significant at 10%

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Analysis with continuity correction

z for 1-power=0.84
z for alpha double sided=1.64
z for alpha single sided=1.28

TWO SAMPLE ANALYSIS

RESULTS for double sided

The sample size required for
group1=n1=484
The sample size required for
group2=n1*allocation ratio=484*1=484
The total sample size required
N=n1+n2=484+484=968

RESULTS for single sided

The sample size required for
group1=n1=353
The sample size required for
group2=n1*allocation ratio=353*1=353
The total sample size required
N=n1+n2=353+353=706

Optimum allocation ratio= 1

Thus sample size should be atleast 353 for each sex.