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Yakvenalex [24]
3 years ago
15

Joe heard from a reliable source that only 22% of people actually sleep 8 hours or more per night. You do a survey and find 58 o

ut of 148 sleep for 8 hours or longer. Build a 95% confidence interval. Round to the nearest hundredth.
Mathematics
1 answer:
Juliette [100K]3 years ago
8 0

Answer:

95% Confidence interval:  (31.32%,47.04%)

Step-by-step explanation:

We are given the following in the question:

Sample size, n = 148

Number of people who sleep for 8 hours or longer, x = 58

\hat{p} = \dfrac{x}{n} = \dfrac{58}{148} = 0.3918

95% Confidence interval:

\hat{p}\pm z_{stat}\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}

z_{critical}\text{ at}~\alpha_{0.05} = 1.96

Putting the values, we get:

0.3918\pm 1.96(\sqrt{\dfrac{0.3918(1-0.3918)}{148}})\\\\ = 0.3918\pm 0.0786\\\\=(0.3132,0.4704)=(31.32\%,47.04\%)

(31.32%,47.04%)  is the required 95% confidence interval.

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Step-by-step explanation:

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3 years ago
Write an equation of the line that passes through (0 0) and (2 6)
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Answer:

y = 3x

Step-by-step explanation:

Slope equation:

y2 - y1

--------

x2 - x1

----------------------------------------------------------------------------------------------------------------

         6 - 0          6

m = ----------- =   ----- = 3

         2 - 0           2

Your slope is 3.

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Equation:

y = mx + b

Plug in the slope and you get:

y = 3x + b

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Now to find b, you can use either coordinate point. So I will show you both ways :)

<u>(0,0)</u>                                                                     <u>(2,6)</u>

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Multiply 0 and 3                                           Multiply 2 and 3

0 = 0 + b                                                         6 = 6 + b

Subtract 0 to 0                                            Subtract 6 from 6

0 = b                                                                    0 = b

There is no y-intercept

----------------------------------------------------------------------------------------------------------------

Your answer: y = 3x

Hope this helped :)

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