Solution to The following data shows heights in centimeters of 10 persons selected at random from a … - Sikademy
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Archangel Macsika

The following data shows heights in centimeters of 10 persons selected at random from a village. Find out whether, it would be reasonable or justifiable to suppose the height of that village population as 182 cm. The heights are 185, 181, 173, 177, 176, 174, 189, 185, 183, 177. [At 5% level of significance]

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n=10\\\bar x={\sum x\over n}={1800\over10}=180

s^2={\sum x^2-{(\sum x)^2\over n}\over n-1}={324260-324000\over9}=28.8888889

The null and alternative hypothesis tested are,


We shall apply the t distribution to perform this hypothesis test because the sample size n=10\lt30 and the population variance is unknown.

The test statistic is given as,

t_c={\bar x-\mu\over{s\sqrt{n}} }={180-182\over {5.375\over\sqrt{10}}}={-2\over1.6997}=-1.1766968

The critical value is the t distribution table value at \alpha=0.05 with n-1=10-1=9 degrees of freedom given as,


The null hypothesis is rejected if, |t_c|\gt t_{0.025,9}.

Since |t_c|=1.1766968\lt t_{0.025,9}=2.262, we fail to reject the null hypothesis and conclude that there is sufficient evidence to show that the  height of this village population is 182 cm at 5% significance level. 

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