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
Archy [21]
3 years ago
15

Of 575 broiler chickens purchased from various kinds of food stores in different regions of a country and tested for types of ba

cteria that cause​ food-borne illnesses, 68​% were infected with a particular bacterium. ​a) Construct a 99​% confidence interval. ​b) Explain what your confidence interval says about chicken sold in the country. ​c) A government spokesperson claimed that the sample size was too​ small, relative to the billions of chickens slaughtered each​ year, to generalize. Is this criticism​ valid?
Mathematics
1 answer:
chubhunter [2.5K]3 years ago
4 0

Answer:

a) 0.68 - 2.58 \sqrt{\frac{0.68(1-0.68)}{575}}=0.630  

0.68 + 2.58 \sqrt{\frac{0.68(1-0.68)}{575}}=0.730  

And the 99% confidence interval would be given (0.630;0.730).  

b) We are 99% confident that the true proportion of infected chickens are between 0.63 (63%) and 0.73 (73%)

c) For this case the answer would be No. Since all the required assumptions in order to construct the confidence interval  are satisfied, so then the results can be assumed for all the population

Step-by-step explanation:

Previous concepts

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".  

p represent the real population proportion of interest  

\hat p =0.68 represent the estimated proportion

n=575 is the sample size required (variable of interest)  

z represent the critical value for the margin of error  

The population proportion have the following distribution  

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

Part a

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:  

0.68 - 2.58 \sqrt{\frac{0.68(1-0.68)}{575}}=0.630  

0.68 + 2.58 \sqrt{\frac{0.68(1-0.68)}{575}}=0.730  

And the 99% confidence interval would be given (0.630;0.730).  

Part b

We are 99% confident that the true proportion of infected chickens are between 0.63 (63%) and 0.73 (73%)

Part c

For this case the answer would be No. Since all the required assumptions in order to construct the confidence interval  are satisfied, so then the results can be assumed for all the population

You might be interested in
You are traveling in a car. your speed is 15 miles an hour. what is your speed in feet per minute
dimaraw [331]

15 miles * 5280 ft/mile = 79200 ft

1 hour * 60 minutes/hr = 60 minutes

79200ft/ 60 minutes

1320 ft/min

4 0
3 years ago
Esmeralda rent a car from a company that race cars by an hour she has a pair nishal fee of $52 and then they charged her $8 per
tatuchka [14]

Answer:

11 hours is the most she can afford

Step-by-step explanation:


7 0
3 years ago
Simplify 2^-6 times 2^3
IgorC [24]

Answer:

(2^-6)*(2^3)

=2^(-6+3)

=2^-3

=1/(2^3)

=1/8

3 0
3 years ago
Read 2 more answers
Order these numbers from least to greatest.
PSYCHO15rus [73]
<h3>Answer:  3.1691, 5.8, 5.802, 5.82</h3>

Explanation:

The smallest item is 3.1691 which is listed first. This is because 3 is smaller than 5.

Now to sort the values that start with 5.

Think of 5.82 as 5.820; think of 5.8 as 5.800

We can see that 820 is larger than 800, which means 5.820 is larger than 5.800; in short, 5.82 > 5.8

Through similar logic, we can see that 5.82 > 5.802 and it further means 5.82 is the largest item. The next largest is 5.802

The sub-list {5.802, 5.82, 5.8} sorts to {5.8, 5.802, 5.82}. These values are then written after the 3.1691 mentioned. This will produce the fully sorted list from smallest to largest.

4 0
2 years ago
Help i need it its math
Vanyuwa [196]
The scale factor is 1/2 or a half
8 0
2 years ago
Read 2 more answers
Other questions:
  • Which equation is modeled below?
    13·1 answer
  • A restaurant manager needs to rope off a rectangular section for a private party. The length of the section must be 7.4 m. The m
    9·1 answer
  • Question 1 (Multiple Choice Worth 2 points)
    12·2 answers
  • I am confused by this question. Can someone help​
    6·1 answer
  • Simplify 27x^7y^2/9x^6y^5
    6·1 answer
  • Play with the interactives to view the line graphs of various equations. Use positive and negative values for the slope, or m. T
    14·1 answer
  • Which is bigger 5/9 or 11/20
    12·1 answer
  • Math, help please I give points and brainlist<br> -ASAP
    9·2 answers
  • State if the two triangles are congruent. If they are, state how you know.
    7·1 answer
  • Solve for u. m/u^2+r=−k−y
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!