1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bumek [7]
3 years ago
8

An article includes the accompanying data on compression strength (lb) for a sample of 12-oz aluminum cans filled with strawberr

y drink and another sample filled with cola. Beverage Sample Size Sample Mean Sample SD Strawberry Drink 10 530 23 Cola 10 553 16 Does the data suggest that the extra carbonation of cola results in a higher average compression strength? Base your answer on a P-value. (Use α = 0.05.)
Mathematics
1 answer:
seraphim [82]3 years ago
4 0

Answer:

Step-by-step explanation:

This is a test of 2 independent groups. The population standard deviations are not known. Let μ1 be the mean compression strength from the extra carbonation of strawberry drink and μ2 be the mean compression strength from the extra carbonation of cola.

The random variable is μ1 - μ2 = difference in the mean compression strength from the extra carbonation of strawberry drink and the mean compression strength from the extra carbonation of cola.

We would set up the hypothesis.

The null hypothesis is

H0 : μ1 = μ2 H0 : μ1 - μ2 = 0

The alternative hypothesis is

H1 : μ1 < μ2 H1 : μ1 - μ2 < 0

This is a left tailed test.

Since sample standard deviation is known, we would determine the test statistic by using the t test. The formula is

(x1 - x2)/√(s1²/n1 + s2²/n2)

From the information given,

x1 = 530

x2 = 553

s1 = 23

s2 = 16

n1 = 10

n2 = 10

t = (530 - 533)/√(23²/10 + 16²/10)

t = - 2.6

The formula for determining the degree of freedom is

df = [s1²/n1 + s2²/n2]²/(1/n1 - 1)(s1²/n1)² + (1/n2 - 1)(s2²/n2)²

df = [23²/10 + 16²/10]²/[(1/10 - 1)(23²/10)² + (1/10 - 1)(16²/10)²] = 6162.25/383.752

df = 16

We would determine the probability value from the t test calculator. It becomes

p value = 0.0097

Since alpha, 0.05 > than the p value, 0.0097, then we would reject the null hypothesis. Therefore, at 5% significance level, the data suggests that the extra carbonation of cola results in a higher average compression strength.

You might be interested in
What is the rate of change between (-8,- 8) and (0,8)
iren [92.7K]

{ \qquad\qquad\huge\underline{{\sf Answer}}}

We need to find thr rate of change (slope) of the line joining these two points ~

\qquad \sf  \dashrightarrow \: m =   \dfrac{rise}{run}

\qquad \sf  \dashrightarrow \: m =  \cfrac{8 - ( - 8)}{0 - ( - 8)}

\qquad \sf  \dashrightarrow \: m =  \cfrac{8  +  8}{0  + 8}

\qquad \sf  \dashrightarrow \: m =  \cfrac{16}{8}

\qquad \sf  \dashrightarrow \: m = 2

Slope of the line (m) joining the two points is 2 ~

7 0
2 years ago
PLZ HELP ASAP A candy machine contains spherical candies. Each candy is solid and has a diameter of 0.25 in.
NikAS [45]
Each candy has a volume of about 8.18 * 10^-3 which is simplified to .00818
5 0
3 years ago
Two siblings' ages have a sum of 64 years. The older sibling was born 6 years before their young sibling.
Elina [12.6K]

Hi!

So we have to make a system of equations here.

Let sibling 1 be O and sibling 2 be Y (for older and younger)

So:

O + Y = 64

O = 64 - Y

(Either one works)

The older sibling is 6 years older.

O = Y + 6

Make everything in terms of Y.

64 - Y = Y + 6

Same to both:

58 = 2y

2y = 58

Divide by 2 on both sides:

y = 29

Since the older sibling is 6 years older:

29 + 6 = 35

Y = 29

O = 35

Let me know if you have any questions.

4 0
2 years ago
Find the surface area of a sphere that has a volume of 288 pi cu. in.​
icang [17]

Answer:

144

Step-by-step explanation:

The surface area of a sphere that has a volume of 288π cu in is 144 pi.

6 0
2 years ago
Read 2 more answers
The Food and Drug Administration (FDA) produces a quarterly report called Total Diet Study. The FDA’s report covers more than 20
pav-90 [236]

Using the normal approximation to the binomial, it is found that:

  • The mean of X is of 52 samples.
  • The standard deviation of X is of 4.2661 samples.
  • 0.0017 = 0.17% probability that less than half without any traces of pesticide.

--------------------------------

Binomial probability distribution

Probability of exactly x successes on n repeated trials, with p probability.

Can be approximated to a normal distribution, with mean given by:  

E(X) = np

And standard deviation of:

\sqrt{V(X)} = \sqrt{np(1-p)}

Normal probability distribution  

Z-score formula is used, which, in a set with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • Each z-score has an associated p-value, which measures the percentile of measure X.

--------------------------------

  • 65% of samples had no pesticide, thus p = 0.65
  • 80 samples, thus n = 80

The mean of X is of:

E(X) = np = 0.65(80) = 52

The standard deviation of X is of:

\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{80(0.65)(0.35)} = 4.2661

Using the approximation and continuity correction, the probability is P(X < 40 - 0.5) = P(X < 39.5), which is the p-value of Z when X = 39.5. Thus:

Z = \frac{X - \mu}{\sigma}

Z = \frac{39.5 - 52}{4.2661}

Z = -2.93

Z = -2.93 has a p-value of 0.0017, thus:

0.0017 = 0.17% probability that less than half without any traces of pesticide.

A similar problem is given at brainly.com/question/24261244

8 0
1 year ago
Other questions:
  • a.Karim is ordering video games. Each game costs $39.99, and there is a $4.85 shipping charge per order. How much will it cost h
    8·2 answers
  • Your sister is considering two different shapes of her garden. One is a square with side lengths of 3.5 meters, and the other is
    14·2 answers
  • What are the solutions to the equation and check for extraneous solutions:<br><br> 16=(x-2)^2/3
    5·1 answer
  • The seventh-grade class is building target areas for a PE activity. The bases for the game will be in a circular shape. The diam
    6·2 answers
  • Can someone help me on this
    12·1 answer
  • Find the values of unknown angles in the following ​
    12·2 answers
  • A bag contains 5 red marbles, 7 blue marbles and 2 green marbles. If two marbles are drawn out of the bag, what is the probabili
    9·1 answer
  • Consider the line y=3/4x-7 what perpendicular, 6,3
    12·1 answer
  • Which decimal is equivalent to 8/11 ?
    11·2 answers
  • 1) If v2x - 4 = 13x – 8, what is the value of x?<br> A) 1.<br> B) 2<br> 4<br> D) 8
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!