Answer:
a. The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57
b. Yes
c. The power of the test is 0.03836
d. The sample size can be considered adequate
Step-by-step explanation:
a. The given data in the study
Catalyst 1: 57.9, 66.2, 65.4, 65.4, 65.2, 62.6, 67.6, 63.7, 67.2, 71.0
Catalyst 2: 66.4 , 71.7, 70.3, 69.3, 64.8, 69.6, 68.6, 69.4, 65.3, 68.8
Using the Average, Standard Deviation function from Microsoft Excel, we have;
The mean for Catalyst 1, [tex]\overline x_1[/tex] = 65.22
The standard deviation for catalyst 1, σ₁ = 3.444416
The mean for Catalyst 2, [tex]\overline x_2[/tex] = 68.42
The standard deviation for catalyst 2, σ₂ = 2.22401
The 95% confidence interval on the difference in mean is given as follows;
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]
The critical-z for a 95% confidence interval = 1.96
Therefore, we have;
[tex]\left (65.22-68.42 \right ) \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}}[/tex]
Therefore, we have;
The 95% C.I. is approximately -5.83 < μ₁ - μ₂ < -0.57
The test statistics is given as follows;
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
Therefore we have;
[tex]z=\dfrac{(65.22-68.42)}{\sqrt{\dfrac{3^{2} }{10}+\dfrac{3^{2}}{10}}} = -2.385[/tex]
The p-value = P(Z<-2.39 or Z > 2.39) = 2P(Z<-2.39) = 2 × 0.00842 = 0.01684
b. From the confidence interval which range from approximately -5.83 to -0.57 and does not include 0, therefore, there is a difference in mean active concentration which depends on the choice of catalyst
c. The power of the test
The sample mean difference is given as follows;
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm z_{c}\sqrt{\dfrac{\sigma _{1}^{2}}{n_{1}} + \dfrac{\sigma_{2}^{2}}{n_{2}}}[/tex]
Therefore, we have;
[tex]\left (\bar{x}_1-\bar{x}_{2} \right ) = \pm 1.96 \times \sqrt{\dfrac{3^{2}}{10} + \dfrac{3^{2}}{10}} = \pm 2.6296[/tex]
The z-value is given as follows;
[tex]z=\dfrac{(\bar{x}_{1}-\bar{x}_{2})-(\mu_{1}-\mu _{2} )}{\sqrt{\dfrac{\sigma_{1}^{2} }{n_{1}}-\dfrac{\sigma _{2}^{2}}{n_{2}}}}[/tex]
μ₁ - μ₂ = 5
When [tex]\bar{x}_1-\bar{x}_{2} = 2.6296[/tex]
[tex]z=\dfrac{2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -1.7667918[/tex]
When [tex]\bar{x}_1-\bar{x}_{2} = -2.6296[/tex]
[tex]z=\dfrac{-2.6296-5}{\sqrt{\dfrac{3^{2} }{10}-\dfrac{3^{2}}{10}}} \approx -5.686768[/tex]
The power of the test is given by P = P(Z<-5.69) + P(Z>-1.77) = 0 + 0.03836 = 0.03836
The power of the test = 0.03836
d. The sample size is statistically adequate because the confidence interval of -5.83 < μ₁ - μ₂ < -0.57 has a value of -5 as a possible population difference in mean
The assumption of normality seems adequate because the confidence interval obtained by using the sample standard deviation is given as follows;
(-5.74, -0.66) which also contains -5 which is the difference in the population mean
which fraction is the least 2/4, 5/10, 2/5, 3/4
Answer:
2/5 or the third one
Step-by-step explanation:
The first two are 1/2 after they are simplified and the second two are just below or just above one half, the last one is above and the third one is below.
Answer:
2/5
Step-by-step explanation:
Convert all fractions to have a common denominator
4, 10, and 5 can all be multiplied to equal 20
As a result, we will use 20 for the common denominator
What multiplied by 4 equals 20? 5 × 4 = 20
What multiplied by 10 equals 20? 2 × 10 = 20
What multiplied by 5 equals 20? 4 × 5 = 20
If we multiply this to the denominator, we must also multiply the same number to the numerator
Starting from left to right:
2 × 5 / 4 × 5 = 10/20
5 × 2 / 10 × 2 = 10/20
2 × 4 / 5 × 4 = 8/20
3 × 5 / 4 × 5 = 15/20
Compare: 10/20, 10/20, 8/20, 15/20
Which fraction has the smallest numerator?
8/20 as 8 is less than 15 and 10
Which fraction was 8/20? Check back to our work.
8/20 = 2/5
2/5 is the least
2.45 divided by 0.17 =
Its not 14.41176470588235
Answer:
0.06938775
Step-by-step explanation:
This is the correct answer.
A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy analyst would like to determine whether the law has decreased the proportion of drivers under the age of 18 who use a cell phone.
complete question
study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving ( The Wall Street Journal , May 5, 2010). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age of 18. A policy analyst would like to determine whether the law has decreased the proportion of drivers under the age of 18 who use a cell phone.a. State the null and the alternative hypotheses to test the policy analyst’s objective.
b. Suppose a sample of 200 drivers under the age of 18 results in 150 who still use a cell phone while driving. What is the value of the test statistic? What is the p-value?c. At α = 0.05 has the law been effective?
d. Repeat this exercise using the critical value approach with α = 0.05
Answer:
1. H0: p>=0.82
H1: p<0.82
2. z test statistic = -2.5767
3. the law has been effective
4. the null is rejected, the law has been effective
Step-by-step explanation:
1. hypothesis formulation
H0: p>= 0.82
H1: p< 0.82
2. p = 82% = 0.82
estimated p^ = x/n = 150/200 = 0.75
standard error calculation:
= √0.82(1-0.82)/200
= √0.82x0.18/200
= √0.02716615
Z test statistic calculation:
= 0.75-0.82/0.02716615
= -2.5767
3. this test is 1 tailed
the p-value using a p value calculator is = 0.004983
0.004983 < 0.05 so we Reject null and conclude that the law has been effective.
4. we Reject null at 0.05 if z is less than -1.645.
-2.5767<-1.645 so we Reject H0 and conclude law has been effective and there is a decrease in drivers under this age who use cell phones
The length of a rectangle is 3m less than twice the width, and the area of the rectangle is 65m^2 . Find the dimensions of the rectangle.
W
L=2w-3
Area=(L×w)
65=[(2w-3)×w]
65 =(2w²-3w)
65=2w²-3w
2w²-3w-65=0
by using the quadratic equation
you'll get 2 values in which one will be negative
Obviously a length can't be negative so you take the positive.
w=6.5m
L=2(6.5)-3
=10m
Mr Soto bought some dvds each DVD cost 13.55 if Mr Soto did not spend more Thales 75$ which inequality could be used to find d the number of DVDs Mr. Soto bought
Answer:
c
Step-by-step explanation:
C is the only equality that no matter what, the value would be $75 or less
The owner of a pizza restaurant in France knows that the time customers spend in the restaurant on Saturday evening has mean 90 minutes and standard deviation 15 minutes. He has read that pleasant odors can influence customers, so he spreads a lavender odor throughout the restaurant. Presented are the times, in minutes, for customers on the next Saturday evening.
Answer:
hello your question is incomplete attached below is the missing part
Question : What is the value of the test statistic
answer : = 5.73
Step-by-step explanation:
Mean value = 90 minutes
std = 15 minutes
Calculate the test statistic
mean value of given data = ∑ x / n = 105.7
since the value of standard deviation is given we will assume a normal distribution
Hence we will apply z test statistics
z = mean value of given data - Mean value / 15 √30
= ( 105.7 - 90 ) / 15 √30
= 5.73
Zachary's rectangle measures 4 1 /4 units by 4 1 /4 units. What is its area?
Answer:
169/12 square units.
Step-by-step explanation:
Which of the following cannot be the side lengths of a triangle?
10, 12, 18
9, 9, 10
3, 11, 15
10, 15, 20
Answer:
3, 11, 15
Step-by-step explanation:
The two shorter sides add up to 14, which is smaller than 15, therefore making the triangle impossible as the sum of the two smaller sides have to be larger than the longest side
how do we pass maths
Answer:
1- Create a Distraction Free Study Environment. Mathematics is a subject that requires more concentration than any other.
2- Master the Key Concepts.
3- Understand your Doubts.
4- Apply Maths to Real World Problems.
5- Practice, Practice and Practice even more.
3 Select the correct answer. 52 + 51 + 6 For the rational equation, 1 + 3 = 1 what is a valid value of x? ОА. B. -1 O C. 2 O D. 3 Reset Next
9514 1404 393
Answer:
B. -1
Step-by-step explanation:
[tex]\dfrac{x^2 +5x +6}{x+3}=1\qquad\text{given}\\\\\dfrac{(x+2)(x+3)}{x+3}=1\qquad\text{factor}\\\\x+2=1\qquad x\ne-3\qquad\text{cancel factors}\\\\x=-1\qquad\text{add $-2$}[/tex]
The only valid value of x is -1.
Can someone help me
Answer:
x is 10
Step-by-step explanation:
draw a line AD to make triangle ABD (which will be a right triangle)
use Pythagorean theorem to find the length of AD
[tex]a^{2} +b^{2} =c^{2} \\6^{2} +8^{2} =c^{2} \\36+64=c^{2} \\100=c^{2} \\10=c[/tex]
Side AD is a radius of the circle, x is also a radius, so they are equal so x is 10
A report summarized a survey of 2305 working adults (representative sample of all working adults). The report indicates that 484 of the working adults surveyed said they were very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next five years. Obtain a point estimate for the population proportion of all working adults who very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next five years. Select the correct answer, including appropriate notation.
Answer:
The point estimate for the population proportion of all working adults who very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next five years is 0.21.
Step-by-step explanation:
Point estimate of a proportion:
The point estimate of a proportion, from a sample, is the sample proportion.
In this question:
2305 working adults, 484 said they were very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next five years. This means that:
[tex]p = \frac{484}{2305} = 0.21[/tex]
The point estimate for the population proportion of all working adults who very concerned that their job will be automated, outsourced, or otherwise made obsolete in the next five years is 0.21.
Diego needs rug with an area of 540sq feet what are all the ways to get 540 square feet
Answer:
260*2
540*1
180*3
135*4
108*5
Step-by-step explanation:
Benny went to 36 baseball games this year he went to 40 games last year how many baseball games did Benny go to in total
Answer:
76
Step-by-step explanation:
36+40=76
Hope this helps!!
Answer:
76 games in total
Step-by-step explanation:
Can anyone help? The question is at the bottom
Answer:
Step-by-step explanation:
Answer:
24 is awnser
Step-by-step explanation:
Pls mark me as brainliest
Solve - x/6 >_ 3
A
B
C
C
Answer:
C
Step-by-step explanation:
-×/6>_3
-x>_3×6
-x>_18
x<_-18
Solve the triangle. A = 46°, a = 31, b = 27
Answer:
A=46 degrees, B=33.4 degrees, C=100.6 degrees
a=34, b=27, c=48.2
Step-by-step explanation:
(a/sin(A)) = (b/sin(B)) = (c/sin(C))
we are given
(34/sin(46)) = (27/sin(B))
34sin(B) = 26sin(46)
34sin(B) = 18.702834809
sin(B) = 0.550083377
note use inverse sin function to find angle B
B = 33.372733167 approx 33.4 degrees then
C = 180 - (46 + 33.4) = 100.6
Then, (b/sin(B)) = (c/sin(C))
27/0.550083377 = c/0.982935349
0.550083377 * c = 27 * 0.982935349
0.550083377 * c = 26.539254427
c = 48.245876056 approx 48.2 .
Lastly, you get: A=46 degrees, B=33.4 degrees, C=100.6 degrees
a=34, b=27, c=48.2
Centerville Middle School spends $13 for every workbook it buys. At most how many
workbooks can Centerville Middle School buy if it has $26 to spend?
Answer:
2
Step-by-step explanation:
13*2=26
he response times for a random sample of 40 medical emergencies were tabulated. The sample mean is 13.25 minutes. The population standard deviation is believed to be 3.2 minutes. The EMS director wants to perform a hypothesis test, with a .05 level of significance, to determine whether the service goal of 12 minutes or less is being achieved.
Answer:
The calculated value Z = 2.5 > 1.96 at 0.05 level of significance
The null hypothesis is rejected
The Alternative hypothesis is rejected
The EMS director wants to service goal of 12 minutes or less is being achieved
Step-by-step explanation:
Step(i):-
Given that the size of the random sample = 40
Given that the mean of the sample (x ⁻) = 13.25
Given that the standard deviation of the Population = 3.2 minutes
Level of significance = 0.05
The mean of the Population (μ) = 12
Step(ii):-
Null hypothesis:-H₀: (μ) = 12
Alternative Hypothesis: H₁ : μ < 12
Test statistic
[tex]Z = \frac{x^{-}-mean }{\frac{S.D}{\sqrt{n} } }[/tex]
[tex]Z = \frac{13.25-12 }{\frac{3.2}{\sqrt{40} } }[/tex]
Z = 2.5
The tabulated value Z₀.₀₅ = 1.96
The calculated value Z = 2.5 > 1.96 at 0.05 level of significance
The null hypothesis is rejected
The Alternative hypothesis is rejected
Final answer:-
The EMS director wants to service goal of 12 minutes or less is being achieved
Which confidence level will produce the widest confidence interval, given a
sample proportion of 0.6?
A. 95%
B. 80%
C0. 68%
D. 90%
Answer:
95%
Step-by-step explanation:
Just answer it
Solve and graph and plot this on the line
Daria rolls a number cube. What is the probability that it will land on a 1?
Answer:
1 out of 6 or 16.7%
Step-by-step explanation:
what is
14+6×(9−6)
PLEASE HELP MEE
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[tex]174[/tex]
[tex]\large\purple{ChaEunWoo2009}[/tex]
#CarryOnLearning
During the flight of a projectile the x component of the velocity is
A.same during its whole journey
B.maximum when it hits the ground
C. Zero at the highest point
D. Maximum when it leaves the ground
Answer:
D. Maximum when it leaves the ground
A door is 8 feet tall and 4 feet wide. What is the area?
Answer:
32
Step-by-step explanation:
a door is rectangular in shape
area = length × breadth
8 × 4
32
answer:
The area of the door is 32 square ft
14. Enzo needs to buy some sand for his sandbox. He can either buy a
10-pound bag of sand for $18 or a 6-kilogram bag of sand for $20.
a. Which is a better value? Explain.
b. If Enzo needs 18 pounds of sand, what should he buy so that
he spends the least amount of money overall? Explain.
Answer:
A: 6 kilo bag B: He should buy two 10 pound bags.
Step-by-step explanation:
Brainliest?
The 6-kilogram pack of sand for $20 is a better value. Then the amount of money for 18 pounds of sand will be $27.18.
What is the rate?The rate is the ratio of the amount of something to the unit.
For example - If the speed of the car is 20 km/h which means the car travels 20 km in one hour.
Enzo requirements to get some sand for his sandbox. He can either purchase a 10-pound sack of sand for $18 or a 6-kilogram pack of sand for $20.
The rate in the first case is written as,
⇒ 18/10
⇒ $1.8 per pound
The rate in the second case is written as,
⇒ 20/6
⇒ $3.33 per kilogram
⇒ $1.51 per pound
The 6-kilogram pack of sand for $20 is a better value.
Then the amount of money for 18 pounds of sand will be given as,
⇒ $1.51 x 18
⇒ $27.18
Thus, the amount of money for 18 pounds of sand will be $27.18.
More about the rate link is given below.
https://brainly.com/question/14731228
#SPJ2
Select all the expressions that are equivalent to 16x + 36
16(x + 20)
x(16 + 36)
4(4x + 9)
2(8x + 18)
2(8x + 36)
Answer:
2(8x+18)
multiply the values in the bracket with 2
2×8x=16x
2×18=36
16x + 36
Answer: 2(8x+18) ,4(4x+9)
Step-by-step explanation:
16 x+36 =4(4x+9)=2(8x+18)
Please please help please
Answer:
I have to know what you need help with, maybe post a picture or type the question next time?
The measure of an angle is 47º. What is the measure of its complementary angle?
Answer:
137 degrees since it says 47
Step-by-step explanation:
PLZ HELP ASAP!!! 9 equals x over 2 + 2