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lawyer [7]
3 years ago
7

A university claims that the mean time professors are in their offices for students is at least 6.5 hours each week. A random sa

mple of eight professors finds that the mean time in their offices is 6.2 hours each week. With a sample standard deviation of 0.49 hours from a normally distributed data set, can the university’s claim be supported at α=0.05?
Mathematics
1 answer:
kolezko [41]3 years ago
3 0
<h2>Answer with explanation:</h2>

Let \mu be the population mean.

Null hypothesis : H_0: \mu\geq 6.5

Alternative hypothesis : H_a: \mu

Since alternative hypothesis is left-tailed , so the test is a left-tailed test.

Since n= 8 <30 , so we use t-test.

Test statistic for population mean : t=\dfrac{\overline{x}-\mu}{\dfrac{\sigma}{\sqrt{n}}}

t=\dfrac{6.2-6.5}{\dfrac{0.49}{\sqrt{8}}}\approx-1.73

Critical value for t=t_{n-1, \alpha}=t_{7,0.05}=1.895

Since the absolute t-value (1.73) is less than the critical t-value(1.895), it means we are fail to reject the null hypothesis.

Thus , we conclude that we have enough evidence to support the university’s claim.

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Compute the amount of interest earned in the following simple interest problem. A deposit of $8,000 at 9.5% for 120 days.
elena-14-01-66 [18.8K]
Hi there

I=prt
P principle 8000
R interest rate 0.095
T time 120/360
I interest earned?

I=8,000×0.095×(120÷360)
I=253.33

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6 0
3 years ago
Read 2 more answers
The ball followed a path modelled by the equation h = −0.001! + 0.5 + 2.5 where h is the height of the ball in feet and is the h
Mama L [17]

The heights the balls hit a fence at 350 ft distance are 65 feet, 38 feet and 30 feet, respectively

<h3>Represent the distance-height relationship for each player’s ball as an equation, in a table and on a graph. </h3>

<u>Juan</u>

Juan's equation is given as:

h = -0.001d^2 + 0.5d + 2.5

h =

Set d to multiples of 50 from 0 to 400.

So, the table of values of Juan's function is:

d (ft)                   h(ft)

0                          2.5

50                        25

100                      42.5

150                        55

200                      62.5

250                        65

300                      62.5

350                        65

400                      42.5

See attachment for the graph of Juan's function

<u>Mark</u>

A quadratic function is represented as:

h = ad^2 + bd + c

Using the values on the table of values, we have:

c = 3 -- the constant value

So, the equation becomes

h = ad^2 + bd + 3

Using the two other values on the table of values, we have:

23 = a(50)^2 + b(50) + 3

38 = a(100)^2 + b(100) + 3

Using a graphing tool, we have:

a = -0.001

b = 0.45

So, Mark's equation is h(d) = -0.001d^2 + 0.45d + 3

See attachment for Mark's graph.

<u>Barry</u>

From the graph, we have the table of values of Barry's function to be:

d (ft)                   h(ft)

0                          2.5

50                        21

100                      35

150                       44

200                      48

250                       46

300                      41

350                       30

400                      14

450                      0

Using a graphing tool, we have the quadratic function to be:

y = -0.001x^2 +0.4x +2.5

<h3><u>The shortest and the greatest distance before hitting the ground</u></h3>

From the graphs, equations and tables, the distance travelled by the balls are:

Juan = 505 feet

Mark = 457 feet

Barry = 450 feet

This means that Juan's ball would travel the greatest distance while Barry's ball would travel the shortest.

<h3>The height the balls hit a fence at 350 ft distance</h3>

To do this, we set d = 350

From the graphs, equations and tables, the height at 350 ft by the balls are:

Juan = 65 feet

Mark = 38 feet

Barry = 30 feet

The above represents the height the balls hit the fence

Read more about quadratic functions at:

brainly.com/question/12446886

#SPJ1

4 0
2 years ago
Total world consumption of iron was approximately 900 million tons in 1993. If consumption had increased by 2.5% each year and t
Lilit [14]

Step-by-step explanation:

We can model the annual consumption of iron by the equation

c = 900 million tons x 1.025^n, where

n is the number of years after 1993 and

c is the consumption for that year.

An estimate for the total consumption of iron can now be obtained by integrating this equation with respect to a dummy variable, x from 0 to n.

C = 900*10^6* \int\limits^n_0 {1.025^x} \, dx

This equation simplifies to

C = 900 million tons x (1.025^n - 1) / ln(1.025), where

x is a dummy variable and

C is the total consumption of iron n years after 1993.

Let R be the amount of iron remaining at n years after 1993, so

R = 480 billion tons - C

R = 480 billion tons - 900 million tons x (1.025^n - 1) / ln(1.025)

We need to find the value of n when R is 0, so

0 = 480 billion tons - 900 million tons x (1.025^n - 1) / ln(1.025)

Simplify this equation to obtain

n = 107.4

So the iron will run out in the year 1993 + 107 = 2100

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Kaja completed construction of her rases flowerbed project and is ready to begin fing with sol. The rased flower bed is in the s
Alja [10]

Answer: She would need 32

Step-by-step explanation:

6 0
3 years ago
A local maximum of the function f(x) occurs for which x-value?<br> -4<br> -3<br> -2<br> -1
Naddika [18.5K]
My guess is -1 because when a x value don’t got a number replace it with a 1
8 0
3 years ago
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