Following classes has a ratio of girls to total students of 7: 10
1 answer:
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Complete Question
A magazine provided results from a poll of 500 adults who were asked to identify their favorite pie. Among the 500 respondents, 12 % chose chocolate pie, and the margin of error was given as plus or minus 5 percentage points.What values do , n, E, and p represent? If the confidence level is 90%, what is the value of
?
Answer:
a
is the sample proportion
is the sample size is
is the margin of error is
represents the proportion of those that did not chose chocolate pie i.e
b
Step-by-step explanation:
Here
is the sample proportion
is the sample size is
represents the proportion of those that did not chose chocolate pie i.e
is the margin of error is
Generally is the level of significance and it value is mathematically evaluated as
Where is the confidence level which is given in this question as
So
Answer:
12%
Step-by-step explanation:
The equation for the growth is ...
f(t) = (initial value)×(growth multiplier per period)^(number of periods)
where the growth multiplier is often expressed as a percentage added to 1:
multiplier = 1+r
growth rate = r
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This equation has two unknowns:
- initial value
- growth multiplier
In order to find these, you can make use of two of the supplied data points. I like to choose the ones that are farthest apart, as they tend to average out any errors due to rounding.
Clearly, the table tells you the initial value is 210. If you don't believe, you can put the numbers in the equation to see that:
f(0) = (initial value)×(growth multiplier)^0
210 = (initial value)×1
(initial value) = 210
__
Using the last data point, we get ...
f(7) = 210×(growth multiplier)^7
464 = 210×(growth multiplier)^7 . . . . . . . . . fill in table value
2.209524 = (growth multiplier)^7 . . . . . . . divide by 210
You can solve this a couple of ways. My calculator is able to take the 7th root, so I can use it to find ...
Alternatively, you can use the 1/7 power:
2.209524^(1/7) = (growth multiplier)
Another way to solve this is to use logarithms:
log(2.209524) = 7×log(growth multiplier) . . . . . take the log
log(2.209524)/7 = log(growth multiplier) . . . . . divide by 7
0.04918553 ≈ log(growth multiplier)
growth multiplier = 10^0.04918553 ≈ 1.11992 . . . . take the antilog
So, our growth multiplier is ...
1 + r ≈ 1.11992
r ≈ .11992 ≈ 12.0%
The rate of growth is about 12% in each period.
_____
Collapsing all of that to a single calculation:
growth rate = (464/210)^(1/(7-0)) -1 ≈ 12.0%
