Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Identify the null and alternative hypotheses, test statistic, P-value, critical value(s), and state the final conclusion that addresses the original claim. A simple random sample of 25 filtered 100mm cigarettes is obtained, and the tar content of each cigarette is measure. The sample has a mean of 19.4 mg and a standard deviation of 3.52 mg. Use a 0.05 significance level to test the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg, which is the mean for unfiltered king size cigarettes. What do the results suggest about the effectiveness of the filters? What are the hypotheses? Identify the test statistic. Identify the P-value Identify the critical value(s). State the final conclusion that addresses the original claim. A. Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. B. Reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. C. Fail to reject H0. There is sufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. D. Reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg. What do the results suggest, if anything, about the effectiveness of the filters? A. The results are inconclusive because the sample size is less than 30. B. The results suggest that the filtered cigarettes have the same tar content as unfiltered king size cigarettes. C. The results do not suggest that the filters are effective. D. The results suggest that the filters are effective. E. The results suggest that the filters increase the tar content.
Answers
Answer:
1) Option A: Fail to reject H0. There is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.
2)Option D: The results suggest that the filters are effective
Step-by-step explanation:
We are given;
Sample size; n = 25
Sample mean; x' = 19.4 mg
Standard deviation; s = 3.52 mg
Population mean; μ = 21.1 mg
Let's state the hypotheses;
Null Hypothesis;H0: μ = 21.1 mg
Alternative Hypothesis; Ha; μ < 21.1 mg
Now, since sample size is less than 30,we will use a t-test.
Thus;
t = (x' – μ)/[s/√(n)]
t = (19.4 - 21.1)/(3.52/√25)
t = -2.415
Using an online p-value from t-score calculator as attached with the parameters t = -2.415, DF = 25 - 1 = 24, significance level = 0.05, one tailed, we have;
The p-value is 0.011885.
The calculated p-value is less than the significance level of 0.05. Thus, we will fail to reject the null hypothesis and conclude that there is insufficient evidence to support the claim that the mean tar content of filtered 100 mm cigarettes is less than 21.1 mg.
Related Questions
Value of the expression when n=3
-2n(5+n-8-3n)
Answers
Answer:
54
Step-by-step explanation:
Substitute n into the equation:
-2(3)[5+3-8-3(3)]
-6[-9]
+54
An arhitect wants to draw a rectangle with a diagonal of 20 inches. The length of the rectangle is to be 8 inches more than twice the width.what dimensions should she make the rectangle
Answers
The diagonal of a rectangle = sqrt(w^2 + l^2)
w = width
l = length
In this problem,
The diagonal = 20 in
w = x
l = 2x + 8
Let's plug our numbers into the formula above.
20in = sqrt((x)^2 + (2x + 8)^2)
Let's simplify the inside of the sqrt
20 in = sqrt(5x^2 + 32x + 64)
Now, let's square both sides.
400 = 5x^2 + 32x + 64
Subtract 400 from both sides.
0 = 5x^2 + 32x - 336
Factor
0 = (5x - 28)(x + 12)
Set both terms equal to zero and solve.
x + 12 = 0
Subtract 12 from both sides.
x = -12
5x - 28 = 0
Add 28 to both sides.
5x = 28
Divide both sides by 5
x = 28/5
The width cant be a negative number so now we know that the only real solution is 28/5
Let's plug 28/5 into our length equation.
Length = 2(28/5) + 8 = 56/5 + 8 = 96/5
In conclusion,
Length = 96/5 inches
Width = 28/5
Graph the solution of 5 ≤ 9 - 4a
A) A
B) B
C) C
D) D
Answers
Answer:
D
Step-by-step explanation:
♡ The Question ♡
Graph the solution of 5 ≤ 9 - 4a
A) A
B) B
C) C
D) D
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Answer ♡
-I believe the answer should be the first choice, A!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ The Explanation/Step-By-Step ♡
-No Explanation/Step-By-Step provided!
*୨୧ ┈┈┈┈┈┈┈┈┈┈┈┈ ୨୧*
♡ Tips ♡
-No Tips provided!
what is the least common multiple of 6, 12 , and 15
Answers
Answer:
It's 3.
Step-by-step explanation:
3x2=6
3x4=12
3x5=15
The baker fits 26 rolls onto a pan that measures 1 5/ 8 ft.² how many square feet does the Baker use for each roll? Show your work.
Answers
Answer:
1/16ft²
Step-by-step explanation:
If 26 rolls fits into 1 5/8 ft² pan, then for us to get the number of square feet for each roll, we will fillw the steps;
26rolls = 1 5/8ft²
1 roll = xft²
26 rolls = 13/8 ft²
1roll = xft²
Cross multiply
26×x = 1×13/8
26x = 13/8
Ceoaa multiply
26x×8 = 13
208x = 13
x =13/208
x = 1/16 ft²
Hence the baker uses 1/16ft² for each roll
solve each inequality -3x<12
Answers
Answer:
-3x<12
/-3 /-3
x<-4
Step-by-step explanation:
integral of x+2/
[tex] \sqrt{x { + 2x + 3}^{2} } [/tex]
Answers
Looks like the integral should be
[tex]\displaystyle\int\frac{x+2}{\sqrt{x+(2x+3)^2}}\,\mathrm dx[/tex]
Expand the denominator:
[tex]\displaystyle\int\frac{x+2}{\sqrt{4x^2+13x+9}}\,\mathrm dx[/tex]
Notice that
[tex]u=4x^2+13x+9\implies \mathrm du=(8x+13)\,\mathrm dx[/tex]
In order to use this substitution, expand the integral as
[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx+\frac38\int\frac{\mathrm dx}{\sqrt{4x^2+13x+9}}[/tex]
In the first integral, use the previously mentioned substitution:
[tex]\displaystyle\frac18\int\frac{8x+13}{\sqrt{4x^2+13x+9}}\,\mathrm dx=\frac18\int\frac{\mathrm du}{\sqrt u}=\frac14\sqrt u[/tex]
[tex]=\dfrac14\sqrt{4x^2+13x+9}[/tex]
In the second integral, complete the square in the denominator:
[tex]4x^2+13x+9=4\left(x+\dfrac{13}8\right)^2-\dfrac{25}{16}[/tex]
Now substitute
[tex]x=\dfrac58\sec t-\dfrac{13}8\implies\mathrm dx=\dfrac58\sec t\tan t\,\mathrm dt[/tex]
so that
[tex]\sec t=\dfrac{8x+13}5[/tex]
Then
[tex]4x^2+13x+9=\dfrac{25}{16}(\sec^2t-1)=\dfrac{25}{16}\tan^2t[/tex]
and the integral becomes
[tex]\displaystyle\frac{\frac{15}{64}}{\frac54}\int\frac{\sec t\tan t}{\sqrt{\tan^2t}}\,\mathrm dt=\frac3{16}\int\sec t\,\mathrm dt[/tex]
[tex]=\dfrac3{16}\ln|\sec t+\tan t|[/tex]
[tex]=\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|[/tex]
So, the integral is
[tex]\dfrac14\sqrt{4x^2+13x+9}+\dfrac3{16}\ln\left|\dfrac{8x+13}5+\dfrac{\sqrt{(8x+13)^2-25}}5\right|+C[/tex]
Suppose 7 quarters, 4 dimes, 4 nickels, and 3 pennies are in a box. One coin is selected at random. What is the expected value of the money drawn from the box?
Answers
First, let's get the total amount of coins inside the box.
7 quarters + 4 dimes + 4 nickels + 3 pennies = 18 total coins.
(7 quarters / 18 coins) * 100 = 38.89% chance of picking a quarter
(4 dimes / 18 coins) * 100 = 22.22% chance of picking a dime
(4 nickels / 18 coins) * 100 = 22.22% chance of picking a nickel
(3 pennies / 18 coins) * 100 = 16.67% chance of picking a dime
Since the quarters have a higher percentage of being picked, we can expect to draw $0.25 from the box
Please help I’d appreciate it so so so so much because I suck at math thank you! Ily
Answers
Answer:
the order of operations tells us how to solve a problem.
first is P for parentheses. this means you solve all the expressions within the parentheses. this ensures a simplified expression before moving on.
second is E for exponents. this means you solve all the expressions with exponents. by doing this before MDAS, you do not raise the wrong values.
third and fourth is M/D for multiplication/division. the / is between these two because these steps are interchangeable. you can multiply or divide first. the results will be the same.
this also applies to the fifth and sixth, which are A/S for addition/subtraction.
357,335 rounded to the nearest ten357,335 rounded to the nearest ten
Answers
Answer:
357,340
Step-by-step explanation:
Locate the tens place:
357,335
Check the number to the right:
357,335
If the number is greater than or equal to 5, then we round up. If the number is less than or equal to 4, we round down.
The number next to the tens place is a '5'. We round up.
357,335 ≈ 357,340
Hope this helps.
Answer:
357340
Step-by-step explanation:
A grid that represents 1 whole , what would you shade for 0.4 and 0.04? 100 squares in rows of 10.
Answers
Answer:
40/4 shaded in squares
Step-by-step explanation:
for 0.4, since 100 is a whole, multiply by 100.
0.4*100=40
shade in 40 squares
for 0.04, multiply by 100
0.04*100=4
shade in 4 squares
Which unit should be used to measure mass of pencil?
Answers
Answer:
Grams
Step-by-step explanation:
Pencils are pretty light, so they should be measured in grams.
Answer:
grams :)
Step-by-step explanation:
I looked it up
Find an equation of a line with slope m=−2/5 that contains the point (10,−5). Type your answer is slope-intercept form.
Answers
The equation of a line in slope intercept form with slope (-2/3) and point (10,-5) is y = (-2/3) - 1.
What is the slope?The slope is the rate of change of y-axis with respect to x-axis.
We know that equation of a line in slope intercept form is y = mx + b.
To find the y-intercept b we will substitute the value of m and point (x,y).
∴ The equation of the line in slope intercept form with slope -2/5 and points (10,-5) is,
-5 = -(2/5)×10 + b.
-5 = -4 + b.
b = -1.
So the given equation of the line is y = (-2/3)x - 1.
learn more about slope here :
https://brainly.com/question/3605446
#SPJ5
Why did I get this question wrong?
Answers
Step-by-step explanation:
∫ 9 arctan(1/x) dx
If u = 9 arctan(1/x), then:
du = 9 / (1 + (1/x)²) (-1/x²) dx
du = -9 dx (1/x²) / (1 + (1/x²))
du = -9 dx / (x² + 1)
If dv = dx, then v = x.
∫ u dv = uv − ∫ v du
= 9x arctan(1/x) − ∫ -9x dx / (x² + 1)
= 9x arctan(1/x) + 9/2 ∫ 2x dx / (x² + 1)
= 9x arctan(1/x) + 9/2 ln(x² + 1)
Evaluate from x=1 to x=√3.
[9√3 arctan(1/√3) + 9/2 ln(3 + 1)] − [9 arctan(1) + 9/2 ln(1 + 1)]
[9√3 (π/6) + 9/2 ln(4)] − [9 (π/4) + 9/2 ln(2)]
(3π√3)/2 + 9/2 ln(4) − (9π/4) − 9/2 ln(2)
(6π√3)/4 + 9 ln(2) − (9π/4) − 9/2 ln(2)
(6π√3 − 9π)/4 + 9/2 ln(2)
Answer:
[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]
Step-by-step explanation:
We are given the integral 9 arctan(1/x)dx on the interval x[ from 1 to √3 ].
Now let's say that u = arctan(1/x). The value of 'du' would be as follows:
du = - x / (1 + x²) * dx
If we apply integration by parts, v = 1, and of course u = arctan(1/x):
=> 9x arctan(1/x) − ∫ -9x dx / (x² + 1)
=> 9[x arctan(1/x) - ∫ - x / (1 + x²) * dx] on the interval x[ from 1 to √3 ]
Let's now simplify the expression ' ∫ - x / (1 + x²) * dx':
=> (Take the constant out, in this case constant = - 1), - ∫ x / (1 + x²) * dx
=> (Apply u-substitution, where u = 1 + x²), - ∫ 1/2u * du
=> (Take constant out again, in this case 1/2), - 1/2 ∫ 1/u * du
=> (Remember that 1/u * du = In( |u| )), - 1/2In( |u| )
=> (Substitute back 'u = 1 + x²), - 1/2In| 1 + x² |
So now we have the expression '9[x arctan(1/x) + 1/2In| 1 + x² |]' on the interval x[ from 1 to √3 ]. Let's further simplify this expression;
[tex]9\left[x\arctan \left(\frac{1}{x}\right)+\frac{1}{2}\ln \left|1+x^2\right|\right]^{\sqrt{3}}_1\\\\=> 9\left[\frac{1}{2}\left(2x\arctan \left(\frac{1}{x}\right)+\ln \left|1+x^2\right|\right)\right]^{\sqrt{3}}_1[/tex]
Now computing the boundaries we have the following answer:
[tex]9\left(\frac{1}{2}\ln \left(2\right)-\frac{\pi }{4}+\frac{\pi }{2\sqrt{3}}\right)[/tex]
A store offers customers a 40% discount on the price of x of selected items. Then, the store takes off an additional 16% at the cash register. Write a price function P(x) that computes the final price of the item in terms of the original price x.
P(x) = ?
Answers
Answer:
x-40%-16%
Step-by-step explanation:
Tom has cases of soda. If there are 12 cans in a case, how many cans does tom have?
Answers
Answer:54
4 1/2times 12
Convert 4 1/2 to an improper fraction.
9/2 times 12
Cancel the common factor of 2
9 times 6
Multiply
9 by 6 the you'll get 54
I really need help with this answer can someone help?
Answers
Answer:
$7075 or 7718
Step-by-step explanation:
91100-6200=84900
84900/11= 7718.18181818 or rounded= 7718
(This is if the december month doesnt count.)
84900/12=7075
(If december is included.)
Answer:
her monthly salary = 84900/12= 7075 dollars
Step-by-step explanation:
total earns= 91100 dollars
actual salary does not include bonus
her actually salary : 91100-6200= 84900
her monthly salary = 84900/12= 7075 dollars
Which one of these shapes is not like the other and why?
Answers
A and B is not, because if you were to make the A bigger it'll be the same as B, so I think is C
A carton has a length of fraction 2 and 1 over 6 feet, width of fraction 1 and 1 over 5 feet, and height of fraction 2 and 1 over 2 feet. What is the volume of the carton?
Answers
Answer:
6 1/2 cubic feet
Step-by-step explanation:
A carton has a length of 2 1/6 feet
The width is 1 1/5 feet
The height is 2 1/2 feet
Therefore the volume of the carton can be calculated as follows
= length × width × height
= 2 1/6 × 1 1/5 × 2 1/2
= 13/6 × 6/5 × 5/2
= 390/60
= 13/2
= 6 1/2 cubic feet
Hence the volume of the carton is 6 1/2 cubic feet
Factor by grouping.
8y2 + y + 40y + 5
Answers
Step by step:
8y2 + y +40y + 5
y(8y+1) + 5(8y+1)
(8y+1)(y+5)
A gallon of gas cost $2.16. Rob buys 13.5 gallons of gas. How much did he pay?
Answers
Answer:
$29.16
Step-by-step explanation:
Each gallon of gas is $2.16.
13.5 gallons of gas is 2.16 (13.5) = $29.16.
Evaluate 4-0.25g+0.5h when g=10 and h=5
Answers
Add -0.25 and 0.25
4-0=4
Tim biked 40 miles in 2 hours. His Rate is
every hour.
This means Tim biked
miles for every hour ?
Answers
Answer:
20 miles/hour
Step-by-step explanation:
40 miles in 2 hours,
thus,
40/2 miles in 2/2 hours = 20 miles in 1 hour.
Therefore, Tim bikes 20 miles per hour.
Evaluate –32 + (2 – 6)(10)
Answers
Answer:
-72
Step-by-step explanation:
-32 + (2-6)(10)
-32 + (-4)(10)
-32 + -40
-72
Answer:
-72
Step-by-step explanation:
Use PEMDAS and solve from left to right.
2 - 6 = -4
Parenthesis means multiplication.
-4 x 10 = -40
Then you add the negatives.
-32 + -40 or
-32 - 40 = -72
A footballer scores in one out of five matches. What percentage of the matches does the footballer score in?
Answers
Answer:
20%
Step-by-step explanation:
100 divided by 5 =20 20x1=20
True or false 16.-84.-184-284 is an arithmetic sequence?
O True
O False
Answers
Answer:
false
plz tell me if im wrong i hope i helped
simplify. can you please help? I don’t know how to do negative exponents. And I forgot how to do exponents.
Answers
1/5832
Decimal Form:
0.00017146
What is the density of Basalt? Mass = 20g ; Volume = 6.47 cubic cm. Round
to TWO decimal places.
Answers
Answer:
3.09g/cm cubedStep-by-step explanation:
Density = mass/volume = 20/6.47
could you help me answer this for a friend
Answers
Answer:
The correct option is option C(SAS) as there are 2 angles and 1 common side(BC) used to prove the triangles congruent..HHEELLPP ME PLEASE
1/2x + 1/3y = 3
Which of the following equations is equivalent to the given equation?
A. 3x + 2y = 3
B. 2x + 3y = 18
C. 3x + 2y = 18
Answers
1/2x•6= 3x
1/3y•6= 2y