A school administrator wants to know what proportion of the approximately 80,000 teachers in their state
have a Master's degree. The administrator takes an SRS of 100 teachers from a statewide database
containing every teacher, and they find 55 teachers in the sample have a Master's degree.
Based on this sample, which of the following is a 99% confidence interval for the proportion of teachers
in the state with a Master's degree?
Choose 1
~
0.55 +0.128
Ⓡ
0.55 = 0.098
©
55 +0.128
©
55 = 0.098

0.55 ± 0.128

Step-by-step explanation:

Confidence interval is written as

Sample proportion ± margin of error

Margin of error = z × √pq/n

Where

z represents the z score corresponding to the confidence level

p = sample proportion. It also means probability of success

q = probability of failure

q = 1 - p

p = x/n

Where

n represents the number of samples

x represents the number of success

From the information given,

n = 100

x = 55

p = 55/1)00 = 0.55

q = 1 - 0.55 = 0.45

To determine the z score, we subtract the confidence level from 100% to get α

α = 1 - 0.99 = 0.01

α/2 = 0.01/2 = 0.005

This is the area in each tail. Since we want the area in the middle, it becomes

1 - 0.005 = 0.995

The z score corresponding to the area on the z table is 2.58. Thus, confidence level of 99% is 2.58

Therefore, the 99% confidence interval is

0.55 ± 2.58√(0.55)(0.45)/100

= 0.55 ± 0.128

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.

4.08%

step-by-step explanation: