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loris [4]
3 years ago
5

A doctor is measuring the average height of male students at a large college. The doctor measures the heights, in inches, of a s

ample of 40 male students from the baseball team. Using this data, the doctor calculate the 95% confidence interval (63.5, 74.4).
Mathematics
1 answer:
RoseWind [281]3 years ago
4 0

Answer:

There is a 95% confidence that the true mean height of all male student at the large college is between the interval (63.5, 74.4).

Step-by-step explanation:

The (1 - <em>α</em>)% confidence interval for population mean is:

CI=\bar x\pm z_{\alpha/2}\times\frac{\sigma}{\sqrt{n}}

The (1 - α)% confidence interval for population parameter implies that there is a (1 - α) probability that the true value of the parameter is included in the interval.

Or, the (1 - α)% confidence interval for the parameter implies that there is (1 - α)% confidence or certainty that the true parameter value is contained in the interval.

The 95% confidence interval for the average height of male students at a large college is, (63.5 inches, 74.4 inches).

The 95% confidence interval for the average height of male students (63.5, 74.4) implies that, there is a 0.95 probability that the true mean height of all male student at the large college is between the interval (63.5, 74.4).

Or, there is a 95% confidence that the true mean height of all male student at the large college is between the interval (63.5, 74.4).

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The 2008 Workplace Productivity Survey, commissioned by LexisNexis and prepared by World One Research, included the question, "H
LenaWriter [7]

Answer:

A 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

Step-by-step explanation:

We are given that x is normally distributed with a known standard deviation of 12.6.

A sample of 250 legal professionals was surveyed, and the sample's mean response was 9 hours.

Firstly, the pivotal quantity for finding the confidence interval for the population mean is given by;

                               P.Q.  =  \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }  ~ N(0,1)

where, \bar X = sample average mean response = 9 hours

            \sigma  = population standard deviation = 12.6

            n = sample of legal professionals = 250

            \mu = mean number of hours a legal professional works

<em>Here for constructing a 95% confidence interval we have used One-sample z-test statistics as we know about population standard deviation.</em>

<u>So, 95% confidence interval for the population mean, </u>\mu<u> is ;</u>

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level

                                                   of significance are -1.96 & 1.96}  

P(-1.96 < \frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } } < 1.96) = 0.95

P( -1.96 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X-\mu} < -1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

P( \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.95

<u>95% confidence interval for</u> \mu = [ \bar X-1.96 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+1.96 \times {\frac{\sigma}{\sqrt{n} } } ]

                                       = [ 9-1.96 \times {\frac{12.6}{\sqrt{250} } } , 9+1.96 \times {\frac{12.6}{\sqrt{250} } } ]

                                       = [7.44 hours, 10.56 hours]

Therefore, a 95% confidence interval estimate of the mean number of hours a legal professional works on a typical workday is [7.44 hours, 10.56 hours].

5 0
2 years ago
6) A cube has a volume of 125 mm3, what is its surface area?<br> Volume = s3<br> Area = 6x s2
Elena L [17]
<h3>~Geometry</h3>

Step-by-step explanation:

r³ = 125

r = 5 mm

...

V = 5³

V = 125 mm³

...

A = 6 . s²

A = 6 . 5²

A = 6 . 25

A = 150 mm²

#mathisfun

3 0
2 years ago
Read 2 more answers
If p: All birds fly. What is ~ p?
Vika [28.1K]
C. not all birds fly.
When using _:_, you are contrasting two things so, you are putting a argument to go against the other side.
Not all birds can fly is going against All birds can fly.

Hope this helps. :)
3 0
3 years ago
Which of the equation of the line with slope 3 that contains point (-1,5)
SpyIntel [72]

The point-slope form:

y-y_1=m(x-x_1)

We have the slope m = 3 and the point (-1, 5). Substitute:

y-5=3(x-(-1))

\boxed{y-5=3(x+1)}      <em>use distributive property</em>

y-5=3x+3           <em>add 5 to both sides</em>

\boxed{y=3x+8} - slope-intercept form

3 0
3 years ago
536-248 answer and show your work
Anni [7]

Answer:

288

Step-by-step explanation:

288+248=536

8 0
2 years ago
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