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MAXImum [283]
3 years ago
15

A college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of

hours they watch per week. The results are provided below. Calculate the 80% confidence interval of the true average number of hours of TV watched per week.
P.S: excel formola needed only. For lower and Upper Bound
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Mathematics
1 answer:
Alla [95]3 years ago
7 0

Answer:

80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

Step-by-step explanation:

We are given that a college student is interested in investigating the TV-watching habits of her classmates and surveys 20 people on the number of hours they watch per week. The results are provided below;

<u>Hours of TV per week (X)</u>: 6, 14, 13, 6, 16, 10, 19, 4, 5, 5, 18, 8, 7, 14, 8, 8, 9, 12, 6, 5.

Firstly, the Pivotal quantity for 80% confidence interval for the true average is given by;

                                P.Q. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean number of hours of TV watched per week = \frac{\sum X}{n} = 9.65

            s = sample standard deviation = \sqrt{\frac{\sum (X -\bar X)^{2} }{n-1} }  = 4.61

            n = sample of people = 20

           \mu = true average number of hours of TV watched per week

<em>Here for constructing 80% confidence interval we have used One-sample t-test statistics as we don't know about population standard deviation.</em>

<u>So, 80% confidence interval for the true average, </u>\mu<u> is ;</u>

P(-1.33 < t_1_9 < 1.33) = 0.80  {As the critical value of t at 19 degrees of

                                               freedom are -1.33 & 1.33 with P = 10%}  

P(-1.33 < \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } } < 1.33) = 0.80

P( -1.33 \times {\frac{s}{\sqrt{n} } } < {\bar X-\mu} < 1.33 \times {\frac{s}{\sqrt{n} } } ) = 0.80

P( \bar X-1.33 \times {\frac{s}{\sqrt{n} } } < \mu < \bar X+1.33 \times {\frac{s}{\sqrt{n} } } ) = 0.80

<u>80% confidence interval for</u> \mu = [ \bar X-1.33 \times {\frac{s}{\sqrt{n} } } , \bar X+1.33 \times {\frac{s}{\sqrt{n} } } ]

                                         = [ 9.65-1.33 \times {\frac{4.61}{\sqrt{20} } } , 9.65+1.33 \times {\frac{4.61}{\sqrt{20} } } ]

                                         = [8.28 hours, 11.02 hours]

Therefore, 80% confidence interval of the true average number of hours of TV watched per week is [8.28 hours, 11.02 hours].

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