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प्रश्न
The mean I.Q of a sample of 1600 children was 99. Is it likely that this was a random sample from a population with a mean I.Q 100 and standard deviation of 15? (Test at 5% level of significance)
उत्तर
Sample size n = 1600
`bar(x)` = 99
Sample mean
Population mean µ = 100
Population S.D σ = 15
Under the Null hypothesis H0: µ = 100
Alternative hypothesis H1: µ = 100 ......(two tails)
Level of significance µ = 0.05
Test statistic z =`(bar(x) - mu)/sigma` N ∼ (0.1)
= `sigma/sqrt("n")`
z = `(99 - 100)/((15/sqrt(1600))`
= `(-1)/((15/40))`
= `(-1)/0.375`
z = – 2.666
z = – 2.67
Calculated value |z| = 2.67
Critical value at 5% level of significance is
`"Z"_(alpha/2)` = 1.96
Inference: Since the calculated value is greater than table value i.e z
⇒ `"Z"_(alpha/2)` at 5% level of significance, the null hypothesis is rejected.
Therefore we conclude that the sample mean differs, significantly from the population mean.
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