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nordsb [41]
3 years ago
6

A bottled water distributor wants to determine whether the mean amount of water contained in 1-gallon bottles purchased from a n

ationally 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?
Mathematics
1 answer:
mash [69]3 years ago
7 0

Answer:

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)

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6 0
3 years ago
Suppose that you take 120 mg of an antibiotic every 4 hr. The​ half-life of the drug is 4 hr​ (the time it takes for half of the
vodomira [7]

Answer:

The steady state amount of antibiotic in the bloodstream when t --> ∞ is 240 mg.

Step-by-step explanation:

Let the amount of antibiotic in one's bloodstream be given as Aₙ (where n = the number of half lives since the start of usage)

Let's follow the time line of events.

At t = 0 hr, the drug is taken

A₀ = 120 mg

At t = 4 hrs, n = 1, the drug is taken again

A₁ = (0.5×A₀) + 120

A₁ = (0.5×120) + 120 = 180 mg

At t = 8 hrs, n = 2, the drug is taken again,

A₂ = (0.5×A₁) + 120

A₂ = (0.5×180) + 120 = 210 mg

At t = 12 hrs, n = 3, the drug is taken again

A₃ = (0.5×A₂) + 120

A₃ = (0.5×210) + 120 = 225 mg

At this point, it becomes evident that at t = 4n hrs, n = n i.e. n half lives later, the general formula for the amount of the antibiotic in the bloodstream is

Aₙ = 0.5Aₙ₋₁ + 120

where Aₙ₋₁ = The amount of antibiotic in the bloodstream at the time t = 4(n-1) and (n-1) half lives later.

For infinite series, that are increasing in this order, as the value of n --> ∞,

Aₙ = Aₙ₋₁ = K

And our general formula becomes

K = 0.5K + 120

0.5K = 120

K = (120/0.5)

K = 240 mg

Hence, the steady state amount of antibiotic in the bloodstream when t --> ∞ is 240 mg.

Hope this Helps!!!

5 0
3 years ago
Evaluate 5- t/3 when t = 12
raketka [301]

Answer:

the answer hopefully should be 1

3 0
3 years ago
Read 2 more answers
The compound interest on the account with .01% interest rate in 5 years
Alina [70]

Answer:

The interest generated will be $ 51.20.

Step-by-step explanation:

To determine the compound interest on the account with 0.01% interest rate in 5 years compounded quarterly with an initial deposit of $ 1,000, the following calculation must be performed:

1,000 x (1 + 0.01 / 4) ^ 4x5 = X

1,000 x (1 + 0.0025) ^ 20 = X

1,000 x 1.0025 ^ 20 = X

1,000 x 1.05120 = X

1,051.20 = X

1,051.20 - 1,000 = 51.20

Therefore, the interest generated will be $ 51.20.

7 0
2 years ago
Rachel is a financial investor who actively buys and sells in the securities market. Now she has a portfolio of all blue chips,
Arturiano [62]

Answer:

(a) 41300 (b) 8.10 % (c) 3.41% (at real rates)

Step-by-step explanation:

Solution

Given:

(a) The  Weights of assets in Rachel's portfolio: = amount in each stock/ sum of amounts invested in all stocks

Share Amount Weights

A 13500 0.33

B 7600 0.18

C 14700 0.36

D 5500 0.13

THE TOTAL: 41300

(b) The Geometric average return of a portfolio = ((1+R1)*(1+R2)*(1+R3)....*(1+Rn))^(1/n) - 1

Now,

R1= return of period 1 Rn= return in nth period

Thus,

The Geometric average return of Rachel's portfolio= ((1+9.7%)*(1+12.4%)*(1-5.5%)*(1+17.2%))^(1/4) - 1

= 8.10 % (approx) per year.

(c) Using nominal rate of return (including inflation):

The CAPM: Required return= Risk free return + (Risk premium * Beta)

13.6 = Rf + (4.8*1.5)

So,

Rf= 6.4% (not inflation adjusted)

The inflation adjusted rate of return: ((1+return)/(1+inflation rate))-1

= ((1+13.6%)/(1+2.7%))-1  = 10.61%

Using CAPM: 10.61= Rf + (4.8*1.5)

Therefore, Rf= 3.41% (at real rates)

8 0
3 years ago
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