6 less than the product of 3 and a number x

Of 580580 samples of seafood purchased from various kinds of food stores in different regions of a country and genetically compa

Lubov Fominskaja [6]

Answer:

a) The 99% confidence interval would be given (0.204;0.296).

b) We have 99% of confidence that the true population proportion of all seafood sold in the country that is mislabeled or misidentified is between (0.204;0.296).

c) No that's not true. Because the necessary assumptions and conditions for the confidence interval for the proportion are satisifed, so then we can use inferential statistics to interpret the interval to the population of interest.

Step-by-step explanation:

Part a

Data given and notation

n=580 represent the random sample taken

X represent the seafood sold in the country that is mislabeled or misidentified by the people

$\hat p=0.25$ estimated proportion of seafood sold in the country that is mislabeled or misidentified by the people

$\alpha=0.01$ represent the significance level (no given, but is assumed)

p= population proportion of seafood sold in the country that is mislabeled or misidentified by the people

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{\hat p(1-\hat p)}{n}})$

The confidence interval would be given by this formula

$\hat p \pm z_{\alpha/2} \sqrt{\frac{\hat p(1-\hat p)}{n}}$

For the 99% confidence interval the value of $\alpha=1-0.99=0.01$ and $\alpha/2=0.005$ , with that value we can find the quantile required for the interval in the normal standard distribution.

$z_{\alpha/2}=2.58$

And replacing into the confidence interval formula we got:

$0.25 - 2.58 \sqrt{\frac{0.25(1-0.25)}{580}}=0.204$

$0.25 + 2.58 \sqrt{\frac{0.25(1-0.25)}{580}}=0.296$

And the 99% confidence interval would be given (0.204;0.296).

Part b

We have 99% of confidence that the true population proportion of all seafood sold in the country that is mislabeled or misidentified is between (0.204;0.296).

Part c

A government spokesperson claimed that the sample size was too small, relative to the billions of pieces of seafood sold each year, to generalize. Is this criticism valid?

No that's not true. Because the necessary assumptions and conditions for the confidence interval for the proportion are satisifed, so then we can use inferential statistics to interpret the interval to the population of interest.

4 0

3 years ago

Solve the quadratic equation for x. What is the product when the roots are multiplied? (x + 2)2 = 1

tekilochka [14]

Regroup terms

2(x + 2) = 1

Divided both sides by 2

x + 2 = 1/2

Subtract 2 from both sides

x = 1/2 - 2

Simplify 1/2 - 2 to -3/2

4 0

3 years ago

Read 2 more answers

Dr. Green finds a note from another scientist. It says how many boxes of bug nets they should bring, but there is a smudge over

Marizza181 [45]

Answer:

The correct answer is the number in the note is 80 and the first digit is 8.

Step-by-step explanation:

Dr. Green finds a note from another scientist. It says how many boxes of bug nets they should bring, but there is a smudge over the first digit of the number.

Number of nets that they must bring is 320.

Each box contains 4 nets.

There number of boxes necessary to be brought is given by $\frac{320}{4}$ = 80.

Therefore the missing digit of number the number in the note is 8.

8 0

3 years ago

Read 2 more answers

a circle is centered at the point -3,2) and passes through the point (1,5). The radius of the circle is blank units. The point (

lianna [129]

It's important that you share the complete question. What is your goal here? Double check to ensure that you have copied the entire problem correctly.

The general equation of a circle is x^2 + y^2 = r^2. Here we know that the circle passes thru two points: (-3,2) and (1,5). Given that a third point on the circle is (-7, ? ), find the y-coordinate of this third point.

Subst. the known values (of the first point) into this equation: (-3)^2 + (2)^2 = r^2. Then 9 + 4 = 13 = r^2.

Let's check this. Assuming that the equation of this specific circle is
x^2 + y^2 = r^2 = 13, the point (1,5) must satisfy it.

(1)^2 + (5)^2 = 13 is not true, unfortunately.

(1)^2 + (5)^2 = 1 + 25 = 26 (very different from 13).

Check the original problem. If it's different from that which you have shared, share the correct version and come back here for further help.

3 0

3 years ago

What is the length of line PS

stiks02 [169]

$PQ^2 = PR \times PS$

$(4x + 4)^2 = (3x + 3)(3x + 3 + 21)$

$16x^2 + 32x + 16= (3x + 3)(3x + 24)$

$16x^2 + 32x + 16= 9x^2 + 81x + 72$

$7x^2 - 49x- 56 = 0$

$7(x^2 - 7x - 8)= 0$

$(x - 8)(x + 1) = 0$

$x - 8 = 0~~~or~~~x + 1 = 0$

$x = 8~~~or~~~x = -1$

x = -1 makes the lengths of segments PQ and PR equal zero.
That is not possible, so the solution x = -1 is discarded.

x = 8

PS = 3x + 3 + 21

PS = 3x + 24

PS = 3(8) + 24

PS = 24 + 24

PS = 48

4 0

3 years ago