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butalik [34]
3 years ago
13

Company A is trying to sell its website to Company B. As part of the sale, Company A claims that the average user of their site

stays on the site for 10 minutes. To test this claim Company B collects the times (in minutes) below for a sample of 12 users. Assume normality. Assignment 6q3 data Construct a 94% confidence interval for the true mean time spent on the web site. a) What is the lower limit of the 94% interval
Mathematics
1 answer:
Ymorist [56]3 years ago
5 0

Answer:

L = 3.975

Step-by-step explanation:

Given

See comment for data

Required

The lower limit 94% confidence interval

First, calculate the mean

\bar x =\frac{\sum x}{n}

\bar x =\frac{0.9+10+0.9+8.7+4.8+2.6+1+13.3+9.5+8.9+8.9+4.6}{12}

\bar x =\frac{74.1}{12}

\bar x =6.175

Next, calculate the standard deviation using:

\sigma = \sqrt{\frac{\sum(x - \bar x)^2}{n}}

So, we have:

\sigma = \sqrt{\frac{(0.9 - 6.175)^2 +(10- 6.175)^2 +.................+(8.9- 6.175)^2 +(4.6- 6.175)^2}{12}}

\sigma = \sqrt{\frac{197.2625}{12}}

\sigma = \sqrt{16.4385416667}

\sigma = 4.054

For 94% interval, the z score is

z = 1.88

So, the margin of error (E) is:

E = z * \frac{\sigma}{\sqrt n}

E = 1.88 * \frac{4.054}{\sqrt {12}}

E = 1.88 * \frac{4.054}{3.464}

E = 2.200

The confidence interval of the true mean is:

CI = (\bar x \± E)

The lower limit (L) is:

L = \bar x -E

L = 6.175 -2.200

L = 3.975

and the upper limit (U) is

U = \bar x + E

U = 6.175 + 2.200

U = 8.375

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