In a survey of 23312331 adults, 730730 say they believe in UFOs. Construct a 99 %99% confidence interval for the population pro
portion of adults who believe in UFOs. A 9999% confidence interval for the population proportion is (nothing,nothing). (Round to three decimal places as needed.) Interpret your results. Choose the correct answer below. A. With 9999% probability, the population proportion of adults who do not believe in UFOs is between the endpoints of the given confidence interval. B. The endpoints of the given confidence interval shows that 9999% of adults believe in UFOs. C. With 9999% confidence, it can be said that the sample proportion of adults who believe in UFOs is between the endpoints of the given confidence interval. D. With 9999% confidence, it can be said that the population proportion of adults who believe in UFOs is between the endpoints of the given confidence interval.
1 answer:
Answer:
0.288 < p < 0.338
Step-by-step explanation:
We have 2331 adults polled and 730 said they believe in UFOs. We are to construct a 99% confidence interval for the population proportion. We are told to round to 3 decimal places as needed.
We need to find p-hat and q-hat
p-hat = 730/2331 = 0.313
q-hat = 1 - p-hat = 1 - 0.313 = 0.687
Since the sample size is greater than 30, we use a z-value for 99% confidence, which is 2.575
See attached photo for the construction of the confidence interval
You might be interested in
Answer:
Costs $2.75
Step-by-step explanation:
Set up:
Cross Multiply:
12x = 33
Divide by 12:
x = $2.75
Functions can be used to model real life scenarios
- The reasonable domain is
.
- The average rate of change from t = 0 to 2 is 20 persons per week
- The instantaneous rate of change is
.
- The slope of the tangent line at point (2,V(20) is 10
- The rate of infection at the maximum point is 8.79 people per week
The function is given as:
<u>(a) Sketch V(t)</u>
See attachment for the graph of
<u />
<u>(b) The reasonable domain</u>
t represents the number of weeks.
This means that: <em>t cannot be negative.</em>
So, the reasonable domain is:
<u />
<u>(c) Average rate of change from t = 0 to 2</u>
This is calculated as:
So, we have:
Calculate <em>V(2) and V(0)</em>
So, we have:
Hence, the average rate of change from t = 0 to 2 is 20
<u>(d) The instantaneous rate of change using limits</u>
The instantaneous rate of change is calculated as:
So, we have:
Expand
Subtract V(t) from both sides
Substitute
Cancel out common terms
becomes
Limit h to 0
<u>(e) V(2) and V'(2)</u>
Substitute 2 for t in V(t) and V'(t)
So, we have:
<em>Interpretation</em>
V(2) means that, 20 people were infected after 2 weeks of the virus spread
V'(2) means that, the rate of infection of the virus after 2 weeks is 4 people per week
<u>(f) Sketch the tangent line at (2,V(2))</u>
See attachment for the tangent line
The slope of this line is:
The slope of the tangent line is 10
<u>(g) Estimate V(2.1)</u>
The <em>value of 2.1 </em>is
<u />
<u>(h) The maximum number of people infected at the same time</u>
Using the graph, the maximum point on the graph is:
This means that:
The maximum number of people infected at the same time is approximately 21.
The rate of infection at this point is:
The rate of infection is <em>8.79 people per week</em>
Read more about graphs and functions at:
