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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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The diagram below shows a rectangle with a shaded region. What is the area, in square meters, of the shaded region in the diagra
Mila [183]

Answer:

Step-by-step explanation:

Area of shaded region= area of rectangle- area of triangle

Area of rectangle= l×b

                            =9×3

                            = 27m²

Area of triangle= \frac{1}{2} b×h

                        =\frac{1}{2} ×3×3

                        =\frac{9}{2} ⇒4.5

Area of shaded region= area of rectangle- area of triangle

                                     =27-4.5

                                     =22.5m²

5 0
2 years ago
Given segments AB and CD intersect at E.
nata0808 [166]

The length of a segment is the distance between its endpoints.

  • \mathbf{AB = 3\sqrt{2}}
  • AB and CD are not congruent
  • AB does not bisect CD
  • CD does not bisect AB

<u>(a) Length of AB</u>

We have:

\mathbf{A = (1,2)}

\mathbf{B = (4,5)}

The length of AB is calculated using the following distance formula

\mathbf{AB = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}

So, we have:

\mathbf{AB = \sqrt{(1 - 4)^2 + (2 - 5)^2}}

\mathbf{AB = \sqrt{18}}

Simplify

\mathbf{AB = 3\sqrt{2}}

<u>(b) Are AB and CD congruent</u>

First, we calculate the length of CD using:

\mathbf{CD = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2}}

Where:

\mathbf{C = (2, 4)}

\mathbf{D = (2, 1)}

So, we have:

\mathbf{CD = \sqrt{(2 -2)^2 + (4 - 1)^2}}

\mathbf{CD = \sqrt{9}}

\mathbf{CD = 3}

By comparison

\mathbf{CD \ne AB}

Hence, AB and CD are not congruent

<u>(c) AB bisects CD or not?</u>

If AB bisects CD, then:

\mathbf{AB = \frac 12 \times CD}

The above equation is not true, because:

\mathbf{3\sqrt 2 \ne \frac 12 \times 3}

Hence, AB does not bisect CD

<u>(d) CD bisects AB or not?</u>

If CD bisects AB, then:

\mathbf{CD = \frac 12 \times AB}

The above equation is not true, because:

\mathbf{3 \ne \frac 12 \times 3\sqrt 2}

Hence, CD does not bisect AB

Read more about lengths and bisections at:

brainly.com/question/20837270

7 0
3 years ago
Hello! Please answer this ASAP! Its a math question..
dedylja [7]

Answer:

  1. The hikers carried 17.5 litres of water
  2. The Koshy family travled 34.5 km while visiting Delhi

Step-by-step explanation:

1-

Multiply 1.75 liters by 10 (the number of days there were hiking) : 17.5 litres

2-

Multiply 11.5 km by 3 (the number of days visiting Delhi) : 34.5 km

7 0
3 years ago
Read 2 more answers
What is the range of y-log,(6)?
Morgarella [4.7K]
ALL REAL NUMBERS IS 0
6 0
3 years ago
If P = (-1,-1), find the image
yawa3891 [41]
<h3>Answer:     (-1, 1)</h3>

=========================================================

Explanation:

The rotation rule we use is (x,y) \to (y, -x)

The x and y coordinates step places, then the second coordinate (after the swap) changes in sign from positive to negative, or vice versa.

For example, the point (5,7) rotates to (7, -5). As another example, (2,-1) becomes (-1, -2). As another example, (-9,4) becomes (4,9).

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

In our case, the point (-1,-1) will rotate to (-1, 1)

Note: A 270 degree counterclockwise rotation about the origin is the same as a 90 degree clockwise rotation about the origin. Refer to the diagram below.

6 0
3 years ago
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