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ANTONII [103]
3 years ago
10

In a study comparing calories in vegetarian and non vegetarian entrees the average number of calories in 28 vegetarian entrees w

as found to be Y¯ = 351 with a standard deviation S = 119 while the number of calories in 28 non vegetarian entrees was Y¯ = 305 with S = 125.
A) Find a 99% confidence interval for µV − µNV.
B) Test at α = .05 that vegetarian entrees have more calories. State the hypothesis, test statistic and your conclusion.
C) If non vegetarian meals have on average 25 more calories (which all other things being equal would lead to a 7.8 kg weight increase per year), how large do the samples need to be to detect such an increase with power .8 at the above level of significance α = .05. Use the statistics obtained above as the parameter values needed for the power calculation.
Mathematics
1 answer:
Lera25 [3.4K]3 years ago
5 0

Solution:

Calculating the polled variance

$ S_p^2 = \frac{(n_1-1)S_1^2+(n_2-1)S_2^2}{n_1+n_2-2}$

    = $ \frac{(28-1)\times 119^2+(28-1)\times 125^2}{28+28-2}$

   = 14893

Now we calculate the estimated standard error

$ S_{M1-M2} =\sqrt {\frac{S_p^2}{n_1}+\frac{S_p^2}{n_2}}$

            $=\sqrt{\frac{14893}{28}+\frac{14893}{28}} = 32.61$

Thus , the 99 percent confidence interval is

= $(M_1-M_2) \pm t_{54.001}\times S_{M_1-M_2}$

= 351 - 305 ± 2.660 x 32.6

= (46) ± 86.74

= (-40.74, 132.74)

Now the null hypothesis is :

$H_0 : u_1-u_2 = 0$

Against the alternative hypothesis

$H_0 : u_1-u_2 > 0$

Computing the statistics ,

$t = \frac{(M_1-M_2)-(u_1-u_2)}{S_{M_1-M_2}}$

 $= \frac{(351-305)-0}{32.61}$

 = 1.41

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adell [148]

Answer:

The price per wind chime that will maximize revenue = $ 315

Step-by-step explanation:

Given - A gift shop sells 160 wind chimes per month at $150 each. the owners estimate that for each $15 increase in price, they will sell 5 fewer wind chimes per month.

To find - Find the price per wind chime that will maximize revenue.

Proof -

Given that,

Total Wind chimes selling = 160

Price of each Wind chime = $150

Now,

Given that, for each $15 increase in price, they will sell 5 fewer wind chimes per month.

So,

Let the price = 150 + 15x

So,

Number of wind Chimes sold per month = 160 - 5x

So,

Total Revenue, R = (150 + 15x)(160 - 5x)

                             = 24000 - 750x + 2400x - 75x²

                             = 24000 + 1650x - 75x²

⇒R(x) = 24000 + 1650x - 75x²

Differentiate R with respect to x , we get

R'(x) = 1650 - 150x

Now,

For Maximize Revenue, Put R'(x) = 0

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⇒150x = 1650

⇒x = 1650/150

⇒x = 11

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Price per Wind chime = $ 150 + 15(11)

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                                    = $ 315

So,

The price per wind chime that will maximize revenue = $ 315

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Answer:

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A publishing company claims that in fall 2019, the average price of college textbooks for a single semester is $385. Suppose you
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Answer:

We accept H₀ . We don´t have enough evidence to express the publisher claim is not true

Step by Step explanation:

We must evaluate if the mean of the price of college textbooks is different from the value claimed by the publisher

n < 30 then we must use t - distrbution

degree of freedom   n  - 1     df = 22 - 1     df = 21

As the question mentions " different " that means,  a two-tail test

At 0,01 significance level     α  = 0,01       α/2  =  0,005

and t(c)  = 2,831

Test Hypothesis

Null Hypothesis                      H₀          μ  =  μ₀

Alternative hypothesis           Hₐ          μ  ≠  μ₀

To calculate t(s)

t(s)  =  (  μ  -  μ₀ ) /σ/√n

t(s)  =  (  433,50 - 385 ) / 86,92 / √22

t(s)  =  2,6171

Comparing   t(c)   and t(s)

t(s) < t(c)

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