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Sampling Distribution Sample Assignment

Question: A random sample of 16 items from a normal population showed a mean of 53 and sum of squares of deviation from this mean equals to 150. Can this sample be regarded as taken from the population having 56 as mean? Obtain 95% and 99% confidence limits of mean of the population.
You may use the following information from statistical table:



Sol:
1. Null Hypothesis, μ = 56.
2. We are given n-16, χ = 53, ∑(X – χ)² = 150







3. Decision. The value of t for (16-1) degress of freedom at the 0.05 level of significance is + 2131 as found from table. The calculate value of t(-3.79) is smaller than -2.131, or falls in the rejection region. Thus we reject the hypothesis that the sample is taken from population with 56 as mean.

4. (i) 95% confidence limits of the population mean:

χ + t_0.05 x (s/√n)
 
or 53 + 2.131 x (3.162/4)
or 53 + 1.684

or 51.316 and 54.684

Thus 51.316 < μ < 54.684

(ii) 09% confidence limits of the population means:
χ + t_0.05 x (s/√n) or 53+ 2.33

or 53 + 2.33 x (3.162/4) or 50.67 and 55.33
Thus 50.67 < μ < 55.33.

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Statistical Inference About 2 Population	Time Series Forcasting Index Number
Statistical Quality Control	Correlation
Index Number	Larger Sample Mean Proportions
Non Parametric Test	Probability Theory
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Unvariate Analysis

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