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Helga [31]
2 years ago
7

A clinical trial was conducted to test the effectiveness of the drug zopiclone for treating insomnia in older subjects. Before t

reatment with zopiclone, 16 subjects had a mean wake time of 102.8 minutes. After treatment with zopiclone, the 16 subjects had a mean wake time of 98.9 minutes and s standard deviation of 42.3 minutes. Assume that the 16 sample values appear to be from a normally distributed population and construct a 98% confidence interval estimate of the mean wake time for a population with zopiclone treatments. What does the result suggest about the mean wake time of 102.8 minutes before the treatment? Does zopiclone appear to be effective?
Mathematics
1 answer:
aleksklad [387]2 years ago
7 0

Answer:

We cannot say that the mean wake time are different before and after the treatment, with 98% certainty. So the zopiclone doesn't appear to be effective.

Step-by-step explanation:

The goal of this analysis is to determine if the mean wake time before the treatment is statistically significant. The question informed us the mean wake time before and after the treatment, the number of subjects and the standard deviation of the sample after treatment. So using the formula, we can calculate the confidence interval as following:

IC[\mu ; 98\%] = \overline{y} \pm t_{0.99,n-1}\sqrt{\frac{Var(y)}{n}}

Knowing that t_{0.99,15} = 2.602:

IC[\mu ; 98\%] = 98.9 \pm 2.602\frac{42.3}{4} \Rightarrow 98.9 \pm 27.516

IC[\mu ; 98\%] = [71.387 ; 126,416]

Note that 102.8 \in [71.384 ; 126.416] so we cannot say, with 98% confidence, that the mean wake time before treatment is different than the mean wake time after treatment. So the zopiclone doesn't appear to be effective.

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Find the volume of a right circular cone that has a height of 12.5 cm and a base with a circumference of 5.8 cm. Round your answ
BaLLatris [955]

Answer:

V = 11.2 cm^3

Step-by-step explanation:

Given

Shape: Right Circular cone

Height, h = 12.5 cm

Base circumference, C = 5.8cm

Required:

Calculate Volume

The volume of a cone is calculated as thus;

Volume, V = \frac{1}{3}\pi r^2h

Where V, r and h represent the volume, the radius and the height of the cone respectively

But first we need to calculate the radius of the cone.

Using formula of circumference.

C = 2\pi r

We have C to be 5.8cm

By substituting this value;

5.8 = 2\pi r

Divide through by 2\pi

\frac{5.8}{2\pi} = \frac{2\pi r}{2\pi}

r = \frac{5.8}{2\pi}

r = \frac{2.9}{\pi}

Now, we can calculate the volume of the cone

By substituting r = \frac{2.9}{\pi} and h = 12.5 cm;

V = \frac{1}{3}\pi r^2h becomes

V = \frac{1}{3}\pi * (\frac{2.9}{\pi})^2 * 12.5

V = \frac{1}{3}\pi * \frac{8.41}{\pi^2} * 12.5

V = \frac{1}{3} * \frac{8.41}{\pi} * 12.5

Take \pi as 3.14

V = \frac{1}{3} * \frac{8.41}{3.14} * 12.5

V = 11.15976

V = 11.2 cm^3 ---- Approximated

Hence, the volume of the cone is; V = 11.2 cm^3

4 0
2 years ago
A student wants to know how far above the ground the top of a leaning flagpole is. At high​ noon, when the sun is almost directl
MariettaO [177]

Answer:

15.43 ft

Step-by-step explanation:

To solve this question, one should use the concept of similar triangles.

The pole's shadow and the distance to the ground (x) form a similar triangle to the distance of the plumb bob from the base and the length of the plumb bob, respectively. Note that we do not need to know the measurements of the third side of the triangles to solve the problem.  Therefore, the distance of the top of the pole to the ground is:

14 in = 1.1667 ft

1.1667x=6*3\\x = 15.43

The distance of the top of the pole to the ground is 15.43 ft.

4 0
2 years ago
Derek has 12 shirt in his closet. If 2 out of every 3 of these shirts are striped,how many striped shirts does Derek have in his
SOVA2 [1]
12 divided by 3 is 4
if 2 of each of these is stripped that means 8/12 are striped
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2 years ago
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What is the total amount of sap trees produced that day? Please tell me ASAP(as soon as possible) because this lesson is due for
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Answer: 5 gallons


Step-by-step explanation:

There are 3 x's on the graph for 1/4, so 1/4 times 3=3/4

There are 2 x's on the graph for 3/8, so 3/8 times 2=3/4

There are 4 x's on the graph for 5/8, so 5/8 times 4=5/2

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Hope this helped!


3 0
2 years ago
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The purpose of an equation is to show the equivalence between two mathematical expressions. This implies in the equation "–2 + 4x = y" the value of y should always be the same that -2 + 4x. Additionally, if a table is created with different values of x and y the equivalence should always be true. This occurs only in the third option.

   x                 y

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   0                -2

   3                 10

First row:

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Third row:

-2 + 4 (3) = y

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2 years ago
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