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Ten individuals are chosen at random, from a normal population and their weights (in kg) are

found to be 63, 63, 66, 67, 68, 69, 70, 70, 71 and 71. In the light of this data set, test the claim that the mean weight in population is 66 kg at 5% level of significance

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Mean weight of the given weights = μ = 67.8 kg We assume that the mean weight of the population is 67.8 kg.

Standard deviation = σ = 8.16 kg

Normal
distribution variable is Z. Ztable (z) gives area under the normal
distribution curve between Z=0 and z. The area gives the probability.

Z = (X - μ ) / σ = (66 - 67.9) / 8.16 kg = - 0.2328

ZTable(-0.2328) = Ztable (0.2328) = 0.091

The
weight 66 kg is far from estimated mean of 67.9 kg by probability of
0.091 or 9.1 %. The error margin should be at least 9.1% to say that
66kg can be considered to be the mean weight of the population.

0.091 is 9.1 % significance level.

So the claim that the mean weight in the population is 66 kg at 5% level of significance is WRONG.