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Sagot :
For the given data
(a) sample mean is 17 and sample standard deviation = 8.91 .
(b) the 95% confidence interval is (9.551 , 24.449) .
(c) the 90% confidence interval is (11.032 , 22.968) . .
In the question ,
the data is given as 25, 11, 12, 27,26, 22, 8,5.
So , the number of terms (n) = 8
Part(a)
the sample mean(μ) is = (25+11+12+27+26+22+8+5)/8 = 17
the standard deviation is calculated as :
= √[(25 - 17)² + (11 - 17)² + (12 - 17)² + (27 - 17)² + (26 - 17)² + (22 - 17)² + (8 - 17)² + (5 - 17)²)]/7
Simplifying the above data further ,
we get
= 8.91
Part(b)
we know that at 95% confidence interval , the critical value is t₀.₀₂₅,₇ = 2.3646
So , the 95% confidence interval is :
= μ ± t₀.₀₂₅,₇*s/√n
= 17 ± 2.3646*8.91/√8
= 17 ± 7.449
So , the interval is ⇒ (9.551 , 24.449) .
Part(c)
we know that at 90% confidence interval , the critical value is t₀.₀₅,₇=1.8946
So , the 90% confidence interval is :
= μ ± t₀.₂₅,₇*s/√n
= 17 ± 1.8946*8.91/√8
= 17 ± 5.968
So , the interval is ⇒ (11.032 , 22.968) .
Therefore ,(a) the sample mean and standard deviation are 17 and 8.91
(b) the 95% interval is (9.551 , 24.449) .
(c) the 90% interval is (11.032 , 22.968) .
The given question is incomplete , the complete question is
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 25, 11, 12, 27,26, 22, 8,5.
(a) Calculate the sample mean and the sample standard deviation.
(b) Construct the 95% confidence interval for the population mean.
(c) Construct the 90% confidence interval for the population mean.
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