A bottled water distributor wants to determine whether the mean amount of water contained in 1-gallon bottles purchased from a nationally known water bottling company is actually 1 gallon. You select a random sample of 100 bottles, the mean amount of water per 1-gallon bottle is 0.994 gallon, and standard deviation of the amount of water per bottle is 0.03 gallon. You select a random sample of 50 bottles, and the mean amount of water per 1-gallon bottle is 0.995 gallon.
a. Is there evidence that the mean amount is different from 1.0 gallon? (Use α-0.01.)
b. Compute the p-value and interpret its meaning
c. Construct a 99% confidence interval estimate of the population mean amount of water per bottle.
d. Compare the results of (a) and (c). What conclusions do you reach?

We fail to reject H0; Hence, we conclude that there is no significant evidence that the mean amount of water per gallon is different from 1.0 gallon

Pvalue = - 2

(0.98626 ; 1.00174)

Since, 1.0 exist within the confidence interval, then we can conclude that mean amount of water per gallon is 1.0 gallon.

Step-by-step explanation:

H0 : μ= 1

H1 : μ < 1

The test statistic :

(xbar - μ) / (s / sqrt(n))

(0.994 - 1) / (0.03/sqrt(100))

-0.006 / 0.003

= - 2

The Pvalue :

Pvalue form Test statistic :

P(Z < - 2) = 0.02275

At α = 0.01

Pvalue > 0.01 ; Hence, we fail to reject H0.

The confidence interval :

Xbar ± Margin of error

Margin of Error = Zcritical * s/sqrt(n)

Zcritical at 99% confidence level = 2.58

Margin of Error = 2.58 * 0.03/sqrt(100) = 0.00774

Confidence interval :

0.994 ± 0.00774

Lower boundary = (0.994 - 0.00774) = 0.98626

Upper boundary = (0.994 + 0.00774) = 1.00174

(0.98626 ; 1.00174)

i believe the answer is 68cm

step-by-step explanation:

i just took 34 x 2 because the space between v and y is the same as y to k.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3