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Sonja [21]
3 years ago
5

Question 17 options:

Mathematics
1 answer:
tatiyna3 years ago
7 0

Answer:

We have 92 % confidence that the true mean time a student sleeps per night is between (-0.25, 1.61).

Step-by-step explanation:

Compute the sample mean and sample standard deviation as follows:

\bar x=\frac{1}{n}\sum X=\frac{54.3 }{8}=6.788\\\\s=\sqrt{\frac{1}{n-1}\sum (x-\bar x)^{2}}=\sqrt{\frac{1}{8-1}\times 11.8288}=1.299

Since, the sample standard deviation is computed the <em>t</em>-statistics will be used for the confidence interval.

The critical value of <em>t</em> for (<em>n</em> - 1) degrees of freedom and 92% confidence level is:

t_{\alpha/2, (n-1)}=t_{0.04, 7}=2.046

*Use a <em>t</em>-table.

Compute the 92% confidence interval for the true mean time a student sleeps per night as follows:

CI=\bar x\pm t_{\alpha/2, (n-1)}\cdot\frac{s}{\sqrt{n}}

     =6.788\pm 2.046\times\frac{1.299}{\sqrt{8}}\\\\=6.788\pm 0.9392\\\\=(-0.2504, 1.6080)\\\\\approx (-0.25, 1.61)

We have 92 % confidence that the true mean time a student sleeps per night is between (-0.25, 1.61).

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