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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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If the pattern continues how many cups of milk does George need to make 6 batches of muffins
alexdok [17]

Answer:

see explanation

Step-by-step explanation:

If we consider the differences between consecutive terms, that is

\frac{3}{4} - \frac{3}{8} = \frac{3}{8}

1 \frac{1}{8} - \frac{3}{4} = \frac{3}{8}

1 \frac{1}{2} - 1 \frac{1}{8} = \frac{3}{8}

To obtain the next term in the pattern add \frac{3}{8} to the previous term.

batches = 5 ⇒ milk = 1 \frac{1}{2} + \frac{3}{8} = 1 \frac{7}{8}

batches = 6 ⇒ milk = 1 \frac{7}{8} + \frac{3}{8} = 2 \frac{1}{4}


6 0
3 years ago
I really need help with this its past due
zloy xaker [14]
Sorry but grade math is this so I can have a better understanding
7 0
2 years ago
An equation with an exponent is called an exponential equation. True False
lyudmila [28]

Answer:

true

Step-by-step explanation:

7 0
3 years ago
A ball is thrown into the air with a initial velocity of 25 meters per second.The function h(t)+-4.9t^2+25t+6 represents the hei
Rainbow [258]

Answer:

36.9 m

Step-by-step explanation:

h(t) = -4.9t² + 25t + 6

At t = 3:

h(3) = -4.9(3)² + 25(3) + 6

h(3) = -44.1 + 75 + 6

h(3) = 36.9

After 3 seconds, the ball will have a height of 36.9 meters.

6 0
3 years ago
A school P is 16km due west of a school Q. what is the bearing of Q from P​
Irina-Kira [14]

Answer:

16Km due east of school P

Step-by-step explanation:

Given

A school P is 16km due west of a school Q

Thus, we can say that distance PQ = 16 km.

________________________________

now we have to find  the bearing of Q from P​

As distance is same

distance PQ = distance QP

Thus,

Distance will remain same of 16 km.

For direction,

If Q is west of P, then P will be east of QP------------------>Q

as shown in figure P is west of Q,

now from point P , Q is west P.

Thus,

Bearing of  School Q from P is 16Km due east of school P

7 0
3 years ago
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