The percentage of change in productivity from April to May is found to be 6.66%.
Productivity ChangeWhat is meant by change in productivity?A change in labour productivity reflects an output change that cannot be accounted for by a change in the number of hours worked. The development of technology over time might lead to an increase in output per hour enhanced employee skills.
Step by step solutionStep 1: Productivity for month of AprilWe must first determine the number of man hours worked in April in order to compute the percentage change in productivity:
8 employs worked for 40 hours along with 7 employs worked for 10 hours in a week( total 4 weeks in April).
Input of April is,
= 8×40 + 7×10×4
= 1560 hours
To determine the productivity in April, divide the total sales by the number of man hours:
= 45000/1560
= 28.846
Step 2: Productivity for month of May8 employs worked for 40 hours along with 9 employs worked for 15 hours in a week( total 4 weeks in April).
Input of May is,
= 8×40 + 9×15×4
= 1820 hours
To determine the productivity in April, divide the total sales by the number of man hours:
= 56000/1820
= 30.769
Step 3: Calculate the total productivityFinding the difference between productivity in each month and dividing by April's productivity percentage yields the percent change in productivity:
= [tex]\frac{30769-28.846}{28.846}[/tex]×[tex]100[/tex]
= 6.66 %
Therefore, the productivity from April to May increased by 6.66%.
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ssume that the readings at freezing on a batch of thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A single thermometer is randomly selected and tested. Find the probability of obtaining a reading between -1.94°C and -1.5°C.
Answer:
[tex]P(-1.94<X<-1.5)=P(\frac{-1.94-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{-1.5-\mu}{\sigma})=P(\frac{-1.94-0}{1}<Z<\frac{-1.5-0}{1})=P(-1.94<z<-1.5)[/tex]
And we can find this probability with this difference:
[tex]P(-1.94<z<-1.5)=P(z<-1.5)-P(z<-1.94)=0.0668-0.026= 0.0408[/tex]
Step-by-step explanation:
Let X the random variable that represent the temperatures of a population, and for this case we know the distribution for X is given by:
[tex]X \sim N(0,1)[/tex]
Where [tex]\mu=0[/tex] and [tex]\sigma=1[/tex]
We are interested on this probability
[tex]P(-1.94<X<-1.5)[/tex]
And using the z score formula given by:
[tex]z=\frac{x-\mu}{\sigma}[/tex]
And using this formula we got:
[tex]P(-1.94<X<-1.5)=P(\frac{-1.94-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{-1.5-\mu}{\sigma})=P(\frac{-1.94-0}{1}<Z<\frac{-1.5-0}{1})=P(-1.94<z<-1.5)[/tex]
And we can find this probability with this difference:
[tex]P(-1.94<z<-1.5)=P(z<-1.5)-P(z<-1.94)=0.0668-0.026= 0.0408[/tex]
In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls (1 through 41) and matching the number on the gold ball (1 through 31). If one ticket is purchased what is the probability of winning the jackpot?
(Type answer as an integer or a simplified fraction)
Answer:
1 / 2,787,760,560
Step-by-step explanation:
The number of permutations is:
41 × 40 × 39 × 38 × 37 × 31 = 2,787,760,560
So the probability of winning the jackpot is 1 / 2,787,760,560.
I WILL MARK BRAINLIEST!!! I NEED HELP!! MY PARENTS ARE IN THE HOSPITAL I HAVE NO ONE TO ASK FOR HELP!!! I HAVE TWO MINUTES LEFT!!! I AM FINISHING THIS COURSE TO MAKE THEM PROUD!!! SOMEONE HELP!!!
Answer:
D
Step-by-step explanation:
Educators are testing a new program designed to help children improve their reading skills. The null hypothesis of the test is that the program does not help children improve their reading skills. For the educators, the more consequential error would be that the program does not help children improve their reading skills but the test indicated that it does help.
Which of the following should the researchers do to avoid the more consequential error?
a. Increase the significance level to increase the probability of Type I error.
b. Increase the significance level to decrease the probability of Type I error.
c. Decrease the significance level to increase the probability of Type I error.
d. Decrease the significance level to decrease the probability of Type I error.
e. Decrease the significance level to decrease the standard error.
Answer:
a
Step-by-step explanation:
increase the significance level to increase the probability of type 1 error
You can use the definition of type I and type II error to find the correct option.
To avoid the more consequential error, the researchers should do:
Option D: Decrease the significance level to decrease the probability of Type I error.
Firstly the whole story starts from hypotheses. The null hypothesis is tried to reject and we try to accept the alternate hypothesis.
The type 1 error occurs if we get false positive conclusion (false positive means we accuse null hypothesis being wrong when it was actually correct).The type 2 error occurs if we get false negative conclusion (false negative means we accept null hypothesis when it was actually false).The negative is just like the doctor's test getting negative means no disease. Similarly, if we conclude null hypothesis negative means it is accepted. If it is accepted wrongly means the negative test result was false, thus called false negative. This error is called type II error.
How are the type I error and the level of significance of the hypothesis test related?The probability of committing the type I error is called the significance level of the hypothesis test.
How to find what does researchers should do to avoid more consequential error?Since in the given context, by using the definitions of the type I error and the type II error, we have
Type I error : False positive : Accepting that the new program does help the children in improving the reading skills when it actually don't.Type II error: False negative: Failing to reject that the program doesn't help the children in improving the reading skills when it actually improves the skill.More consequential error for educators : For the educators, the more consequential error would be that the program does not help children improve their reading skills but the test indicated that it does help.
Thus, the more consequential error for the educators is committing the type I error.
To prevent committing this error, they need to decrease type I error's probability which is denoted by level of significance, need to decrease the level of significance of the hypothesis test.
Thus,
Option D: Decrease the significance level to decrease the probability of Type I error.
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The Interplanet Space Centre is planning to launch a probe which will travel from Earth to Mars, on to Jupiter and then to Saturn. Distance from Earth to Mars 78 300 000 km Distance from Mars to Jupiter 550 400 000 km Distance from Jupiter to Saturn 648 700 000 km million km
Estimate to the nearest million how far it will travel on its journey.
Answer:
1,300,000,000
Step-by-step explanation:
78 300 000
550 400 000
648 700 000
1 277 400 000
To the nearest million
1,2 | 77 400 000 more than 4, so +1
1,300,000,000
Would you rather 36 spherical bottles with radi = 4.57 or three 12-packs of cans if each box is 15inx5inx4.4in
Answer:
36 bottles
Step-by-step explanation:
Each spherical bottle will have a volume of ...
V = (4/3)πr³ = (4/3)π(4.57³) = 399.8 . . . . cubic inches
Each box (12-pack?) will have a volume of ...
V = LWH = (15 in)(5 in)(4.4 in) = 330 in³
This is a smaller volume than even one spherical bottle, so 36 bottles will have the larger volume.
solve system by substitutition or elimination.
9x-8x=9
-18x+16y=-18
Answer:
1. 9x-8y=9
2. -18x+16y= -18 ⇒ -9x+8y= -9 ⇒ 9x-8y=9
as we see both equations are same, it means the lines overlap and there is infinite number of solutions
Explain what is meant by the equation lim x → 8 f(x) = 9. If |x1 − 8| < |x2 − 8|, then |f(x1) − 9| < |f(x2) − 9|. The values of f(x) can be made as close to 8 as we like by taking x sufficiently close to 9. f(x) = 9 for all values of x. If |x1 − 8| < |x2 − 8|, then |f(x1) − 9|≤ |f(x2) − 9|. The values of f(x) can be made as close to 9 as we like by taking x sufficiently close to 8. Is it possible for this statement to be true and yet f(8) = 6?
Explain. Yes, the graph could have a hole at (8, 9) and be defined such that f(8) = 6. Yes, the graph could have a vertical asymptote at x = 8 and be defined such that f(8) = 6. No, if f(8) = 6, then lim x→8 f(x) = 6. No, if lim x→8 f(x) = 9, then f(8) = 9.
Complete Question
1 Explain what is meant by the equation lim x → 8 f(x) = 9.
A If |x1 − 8| < |x2 − 8|, then |f(x1) − 9| < |f(x2) − 9|.
B The values of f(x) can be made as close to 8 as we like by taking x sufficiently close to 9.
C f(x) = 9 for all values of x.
D If |x1 − 8| < |x2 − 8|, then |f(x1) − 9|≤ |f(x2) − 9|.
E The values of f(x) can be made as close to 9 as we like by taking x sufficiently close to 8.
2 Is it possible for this statement to be true and yet f(8) = 6? Explain.
A Yes, the graph could have a hole at (8, 9) and be defined such that f(8) =6.
B Yes, the graph could have a vertical asymptote at x = 8 and be defined such that f(8) = 6.
C No, if f(8) = 6, then lim x→8 f(x) = 6.
D No, if lim x→8 f(x) = 9, then f(8) = 9.
Answer:
1
The correct option is D
2
The correct option is A
Step-by-step explanation:
Generally a a limit function [tex]\lim_{n \to x } f(x) = L[/tex]
Tell us that as n tends toward x the values of f(x) tends towards L hence for the first question E is the correct option
Now looking at the second question
Yes it is possible for lim x → 8 f(x) = 9. to be true and f(8) = 6 this is because the graph defined by this limit equation can have a hole the point
(8, 9) and created in such a way that f(8) = 6
Calculus's basic idea of limits in mathematics describes how a function behaves when its input approaches a specific value. No, if f(8) = 6, then lim x → 8 f(x) = 6. The correct option is C.
The statement "lim x → 8 f(x) = 9" means that as x approaches 8, the limit of f(x) is equal to 9. This implies that the function f(x) gets arbitrarily close to 9 as x gets arbitrarily close to 8.
If f(8) = 6, it means that the function f(x) has a specific value of 6 at x = 8. This contradicts the idea that f(x) gets arbitrarily close to 9 as x approaches 8.
Therefore, if f(8) = 6, it is not possible for the statement "lim x → 8 f(x) = 9" to be true.
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What is the radius of the circle whose equation is x2 + y2 = 9?
81
3
9
Answer:
3
Step-by-step explanation:
x^2 + y^2 = 9
The equation of a circle is
(x-h)^2 + (y-k)^2 = r^2
( h,k) is the center and r is the radius
x^2 + y^2 = 3^2
The radius is 3
What errors are shown here? Check all that apply.
-the arrows should be a length of 2
-the arrows should be a length of 6
-the arrows should be pointing in the positive direction
-the arrows should start at zero
-the arrows should point in the negative direction
Answer:
-The arrows should be a length of 6
-The arrows should point in the negative direction
-The arrows should start at zero
Step-by-step explanation:
Hope this helps!
Answer:
B
D
E
Step-by-step explanation:
What’s the correct answer for this question?
Answer:
The answer is drawing the 6 of clubs or the 6 of spades because those are the only black 6's.
When you add two rational numbers, each number
can be written as a ?
You take a train away from Bangkok at 1:50 a.m. on Wednesday. You ride the train for 16 hours and 40 minutes, at which point you arrive in Vladivostok at 9:30 p.m. on Wednesday, local time. How does Vladivostok’s time zone relate to Bangkok’s time zone?
a.
Vladivostok is three hours ahead of Bangkok.
b.
Vladivostok is nine hours behind Bangkok.
c.
Vladivostok is fifteen hours behind Bangkok.
d.
Vladivostok is twenty-one hours ahead of Bangkok.
Answer:
a.
Vladivostok is three hours ahead of Bangkok.
Step-by-step explanation:
Time the train left Bangkok is 1:50am
It traveled for 16 hours 40 minutes.
If the train was to be in Bangkok.
The Time Will be 1+16 hours then 50+40 minutes
Which is 17 hours + 1 hour 30 minutes
Which is 18 hours and 30 minutes
And 18 hours = 6:00 pm
So if it was in Bangkok the time with be 6:30 pm
But in Vladivostok, it was 9:30 pm
It's clear that Vladivostok time is faster by 3 hours
Which is the graph of the equation ? y-1=2/3(x-3)?
A function assigns values. The graph of the equation y-1=2/3(x-3) is the second graph.
What is a Function?A function assigns the value of each element of one set to the other specific element of another set.
As the function is given to us that y-1=2/3(x-3), now substitute the value of x as 0 and y as 0 to get the intercept of the function. Therefore,
x-intercept
[tex]y-1=\dfrac23(x-3)\\0-1= \dfrac23x-\dfrac23(3)\\\\-1 = \dfrac23x - 2\\\\-1+2 = \dfrac23x\\\\x = \dfrac32[/tex]
y-intercept
[tex]y-1=\dfrac23(x-3)\\\\y-1=\dfrac23(0-3)\\\\y-1=\dfrac23(-3)\\\\y= -2+1\\\\y=-1[/tex]
Thus, we need to look for the graph which intersects the x-axis at 3/2 while the y-axis at -1. Therefore, as shown the below graph.
Hence, the graph of the equation y-1=2/3(x-3) is the second graph.
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A circle has a diameter of 10 feet. What is the area of the circle? Leave answers in terms of π.
Answer:
25pi
Step-by-step explanation:
If the circle has a diameter of 10, it has an radius of 5. The area of a circle is pi*r^2. If r=5, then it is 25pi.
Answer:
25π feet^2
Step-by-step explanation:
The area of a circle can be found using the following formula.
a=πr^2
We are given the diameter, but we need to find the radius. The radius is half of the diameter, or
r=d/2
We know the diameter is 10 feet. Therefore, we can substitute 10 in for d.
r=10/2
Divide 10 by 2
r=5
The radius is 5 feet.
Now we know the radius, and can substitute it into the area formula.
a=πr^2
r=5
a=π*5^2
Evaluate the exponent.
5^2 is equal to 5*5, which is 25.
a=π*25
a=25π
Add appropriate units. Area always uses units^2, and the units in this problem are feet.
a=25π feet^2
The area of the circle is 25π square feet
Which of the following measurements is the most precise?
A.A 15.5 foot tall tree
B.An 84-year-old man
C.A gas price of $2.359 per gallon
Answer:
C.)
Step-by-step explanation:
C.) Because it states the exact decimals rather than just stating about $2.36. Also, the other options were not specific. Hope this helps!
why should i have different units for volume and base area Ex: volume = [tex]in^{3}[/tex] Base Area = [tex]in^{2}[/tex] pyramid ^^^
Answer:
Step-by-step explanation:
Volume has three parameters and is three dimensional, thus needing a unit in the third power
In difference,
Area is two-dimensional and has only 2 parameters, thus needing a unit only in the second power
Answer:
see below
Step-by-step explanation:
Area is found by multiplying two dimensions together ( l*w)
Volume is found by multiplying three dimensions together ( l*w*n)
Suppose that you had consumer group wanted to test to see if weight of participants in a weight loss program changed (up or down). They computed a 95% confidence interval of the result (-4.977, 2.177). What do we know about the p-value for the test?
Answer:
What we know about the p-value for the test is that it will be less than 0.05
Step-by-step explanation:
The complete question is as follows;
Suppose that you had consumer group wanted to test to see if weight of participants in a weight loss program changed (up or down). They computed a 95% confidence interval of the result (-4.977, -2.177). Suppose that we had a significance test with the following hypothesis:
H0: population mean weight loss = 0
Ha: population mean weight loss does not equal 0
What do we know about the p-value for the test?
solution;
Given the information in the question, we are concerned with saying what we know about the p-value for the test
To answer this question, we shall be looking at it from the angle of the confidence interval
The confidence interval given is 95%.
Now what does this indicate?
It indicates that 95% confidence interval contains only values which are less than 0.
What does this mean for the p-value?
This means that the p-value will be less than 0.05
What is the quotient of 3/4 divided by 1/5
Answer:
15/4
Step-by-step explanation:
3/4:1/5= 3/4*5= 15/4
Consider the following equation. f(x, y) = sin(4x + 3y), P(−6, 8), u = 1 2 3 i − j (a) Find the gradient of f. ∇f(x, y) = (b) Evaluate the gradient at the point P. ∇f(−6, 8) = (c) Find the rate of change of f at P in the direction of the vector u. Duf(−6, 8) =
Answer:
Step-by-step explanation:
a) Find the gradient
[tex]\nabla f(x,y) =f_x(x,y)\bold{i} +f_y (x,y)\bold{j}[/tex]
[tex]Also, sin(4x+3y)= sin(4x)cos(3y)+sin(3y)cos (4x)[/tex]
[tex]f_x(x,y) = 4cos(4x)cos(3y)-4sin(3y)sin(4x) = 4 cos(4x-3y)[/tex]
[tex]f_y(x,y) = -3sin(4x)sin(3y)+3cos(3y)cos(4x)=3cos(4x-3y)[/tex]
Hence
[tex]\nabla f(x,y) = 4cos(4x-3y)\bold{i}+3cos(4x-3y)\bold{j}[/tex]
b) At point (-6, 8) just replace the values in gradient to find it out. You can do it.
c) directional derivative in the direction u.
[tex]D_uf(x,y)=\nabla f(x,y). u[/tex]
I stuck with your 1 2 3 i -j . What does 1 2 3 mean? is it not 123 or 1 2/3 or else?
rewrite the following equation in logarithmic form and exponential form
Answer:The answer for the first one is log2(.25)=-2
The answer for the second one is 8^3=512
Step-by-step explanation:
When Easton goes bowling, his scores are normally distributed with a mean of 130
and a standard deviation of 11. What percentage of the games that Easton bowls does
he score higher than 112, to the nearest tenth?
Answer:
P(X≥112) = 0.9495
The percentage of the games that Easton bowls does he score higher than 112 = 94.95%
Step-by-step explanation:
Given mean of the Population = 130
Given standard deviation of the Population = 11
Let X= 112
[tex]Z =\frac{x-mean}{S.D} =\frac{112-130}{11}=-1.636[/tex]
P(X≥112) = P(Z≥ z)
= 1-P(Z≤z)
= 1- ( P(Z≤-1.636)
= 1- (0.5-A(-1.636)
= 0.5 +A(1.636)
= 0.5 + 0.4495
P(X≥112) = 0.9495
The percentage of the games that Easton bowls does
he score higher than 112 = 94.95%
What is the equation of the horizontal line through (-5,-2)
Answer:
y = -2
Step-by-step explanation:
A horizontal line has an equation of the form ...
y = constant
In order for the line to go through a point with a y-coordinate of -2, the constant must be -2.
y = -2 . . . . horizontal line through (-5, -2)
The sugar company will choose from two companies to transport its sugar to market. the first company charges $6500 to rent trucks plus an additional fee of $150.50 for each Ton of sugar. The second company charges $4995 to Trang trucks plus an additional fee of $225.75 for each Ton of sugar. For what amount of sugar do the two companies charge the same?
Answer:
20 ton
Step-by-step explanation:
We created a system of two separate equations to answer these questions.
"y" will be the total cost to transport the sugar
"x" will be the amount of sugar transported
Therefore, we have to:
y = 3995 + 225.50 * x
y = 6500 + 100.25 * x
We must establish these equations equal to each other because it asks how much of x is necessary to make the same amount of y, therefore:
3995 + 225.50 * x = 6500 + 100.25 * x
solved we have:
225.50 * x - 100.25 * x = 6500 - 3995
125.25 * x = 2505
x = 2505 / 125.25
x = 20
which means that when the amount of sugar transported is 20 tons, the price is the same
Please answer this correctly
Answer:
11 5/8
Step-by-step explanation:
Simply the 5/8 to 16th
5/8 equals to 10/16
Then add the 16ths together
The divide it by 16
Then add the whole numbers
Then add of them together to get your answer
Answer:
Exact Form:
93 /8
Decimal Form:
11.625
Mixed Number Form:
11 5 /8
Step-by-step explanation:
If you add every side together:
3 3/16 + 2 5/8 + 3 3/16 + 2 5/8 = 93/8
It's quite easy, just add everything together ;)
What’s the correct answer for this?
Answer:
6
Explanation:
According to secant-secant theorem,
(PB)(PA)=(PD)(PC)
(7)(12)=(PD)(14)
NOW
84/14 = PD
PD = 6
Find the critical value needed to construct a confidence interval of the given level with the given sample size. Round the answers to three decimal places.
Part 1 of 4
(a) For level 95% and sample size 7.
Part 2 of 4
(b) For level 98% and sample size 12.
Part 3 of 4
(c) For level 99% and sample size 27.
Part 4 of 4
(d) For level 98% and sample size 14.
Answer:
a) [tex] t_{\alpha/2}=\pm 2.447[/tex]
b) [tex] t_{\alpha/2}=\pm 2.718[/tex]
c) [tex] t_{\alpha/2}=\pm 2.779[/tex]
d) [tex] t_{\alpha/2}=\pm 2.650[/tex]
Step-by-step explanation:
Part a
The degrees of freedom are given by:
[tex] df=n-1= 7-1=6[/tex]
The confidence is 95% or 0.95 the significance would be [tex]\alpha=0.05[/tex] and the critical values would be:
[tex] t_{\alpha/2}=\pm 2.447[/tex]
Part b
The degrees of freedom are given by:
[tex] df=n-1=12-1=11[/tex]
The confidence is 98% or 0.98 the significance would be [tex]\alpha=0.02[/tex] and the critical values would be:
[tex] t_{\alpha/2}=\pm 2.718[/tex]
Part c
The degrees of freedom are given by:
[tex] df=n-1=27-1=26[/tex]
The confidence is 99% or 0.99 the significance would be [tex]\alpha=0.01[/tex] and the critical values would be:
[tex] t_{\alpha/2}=\pm 2.779[/tex]
Part d
The degrees of freedom are given by:
[tex] df=n-1=14-1=13[/tex]
The confidence is 98% or 0.98 the significance would be [tex]\alpha=0.02[/tex] and the critical values would be:
[tex] t_{\alpha/2}=\pm 2.650[/tex]
A value of a test statistic defines the upper bounds of a confidence interval, statistical significance in a test statistic is known as the crucial value.
critical value:For part a )
n = 7
Calculating the degrees of freedom [tex]= df = n - 1 = 7 - 1 = 6[/tex]
At [tex]95\%[/tex] the confidence level, the t:
[tex]\alpha = 1 - 95\% = 1 - 0.95 = 0.05\\\\\frac{\alpha}{ 2} = \frac{0.05}{ 2} = 0.025\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.025,6} = 2.447\\\\[/tex]
The critical value = 2.447
For part b )
n =12
Calculating the degrees of freedom[tex]= df = n - 1 = 12 - 1 = 11[/tex]
At [tex]98\%[/tex] the confidence level , the t:
[tex]\alpha = 1 - 98\% = 1 - 0.98 = 0.02\\\\\frac{\alpha}{ 2}= \frac{0.02}{ 2} = 0.01\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.01,11} =2.718\\\\[/tex]
The critical value =2.718
For part c )
n = 27
Calculating the degrees of freedom [tex]= df = n - 1 = 27 - 1 = 26[/tex]
At [tex]99\%[/tex] the confidence level, the t:
[tex]\alpha = 1 - 99\% = 1 - 0.99 = 0.01\\\\\frac{\alpha}{ 2} = \frac{0.01}{ 2} = 0.005\\\\t_{\frac{\alpha}{ 2}}\\\\df = t_{0.005,26}=2.779\\\\[/tex]
The critical value =2.779
For part d )
n = 14
Calculating the degrees of freedom [tex]= df = n - 1 = 14 - 1 = 13[/tex]
At [tex]98\%[/tex] the confidence level, the t:
[tex]\alpha = 1 - 98\% = 1 - 0.98 = 0.02\\\\\frac{\alpha}{ 2} = \frac{0.02}{ 2} = 0.01\\\\t_{\frac{\alpha}{ 2}} \\\\df = t_{0.01,13} =2.650[/tex]
The critical value =2.650
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What is the minimum and maximum whole number side length for △ABC with given side lengths of 9 cm and 11 cm? Please explain why
Answer:
Step-by-step explanation:
We would assume that triangle ABC is a right angled triangle. This means that we can apply Pythagoras theorem in determining the unknown side length.
For the case of the minimum side length, we would assume that the unknown length, L is one of the shorter legs of the triangle. By applying Pythagoras theorem, it becomes
11² = 9² + L²
L² = 121 - 81 = 40
L = √40 = 6.32
For the case of the maximum side length, we would assume that the unknown length, L is one of the hypotenuse of the triangle. By applying Pythagoras theorem, it becomes
L² = 9² + 11²
L² = 81 + 121 = 202
L = √202 = 14.21
The minimum side length is 6.32 and the maximum side length is 14.21
what does a shape need to be a prallelogram?
Answer: Needs to be flat with opposite sides that are parallel and are the same in length
A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before treatment, 17 subjects had a mean wake time of 100.0 min. After treatment, the 17 subjects had a mean wake time of 90.3 min and a standard deviation of 21.8 min. Assume that the 17 sample values appear to be from a normally distributed population and construct a 99% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 100.0 min before the treatment? Does the drug appear to be effective?
Answer:
Step-by-step explanation:
Confidence interval is written in the form,
(Sample mean - margin of error, sample mean + margin of error)
The sample mean, x is the point estimate for the population mean.
Margin of error = z × s/√n
Where
s = sample standard deviation = 21.8
n = number of samples = 17
From the information given, the population standard deviation is unknown and the sample size is small, hence, we would use the t distribution to find the z score
In order to use the t distribution, we would determine the degree of freedom, df for the sample.
df = n - 1 = 17 - 1 = 16
Since confidence level = 99% = 0.99, α = 1 - CL = 1 – 0.99 = 0.01
α/2 = 0.01/2 = 0.005
the area to the right of z0.005 is 0.005 and the area to the left of z0.005 is 1 - 0.005 = 0.995
Looking at the t distribution table,
z = 2.921
Margin of error = 2.921 × 21.8/√17
= 15.44
The confidence interval for the mean wake time for a population with drug treatments is
90.3 ± 15.44
The upper limit is 90.3 + 15.44 = 105.74 mins
The lower limit is 90.3 - 15.44 = 74.86 mins
The result suggests that the mean wake time might have really reduced since the values barely fall above 100 minutes as in before treatment with a high degree of confidence. Therefore, the drug is effective.