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One tailed test for difference between means (small sample)

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The mean high temperature for 12 days in July in Detroit, Michigan was 88 degrees with a standard deviation of 4 degrees. The mean high temperature in Hilton Head, South Carolina for 8 July days was 91 degrees with a standard deviation of 3 degrees. At the .05 significance level, can we conclude that it is warmer in Hilton Head?

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The solution tests hypothesis for difference between means of two independent samples.

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One tailed test for difference between means (small sample size)

At significance level= 0.05

1 2
Detroit Hilton Head
Mean =μ=88.00 91.00 Difference of means= 3.00 = 91 - 88
Standard deviation =s= 4 3
Sample size=n= 12 8

pooled estimate of σ^2=sp^2={ (n1-1)s1^2+(n2-1)s2^2}/(n1+n2-2)=
=(11 * 4 ^2 + 7 * 3 ^2 )/ 18 = 13.2778
pooled estimate of σ=sp= = square root of 13.2778 ...

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