In: Statistics and Probability
There are 2567 students enrolled at a small college, with 2053 of them enrolled in a sociology course.
In the sampling distribution of sample proportions of size 230, above what proportion will 52% of all sample proportions be?
Select all answers that apply to your calculation below. Use the z-table given below to answer the question:
z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
-0.2 | 0.421 | 0.417 | 0.413 | 0.409 | 0.405 | 0.401 | 0.397 | 0.394 | 0.390 | 0.386 |
-0.1 | 0.460 | 0.456 | 0.452 | 0.448 | 0.444 | 0.440 | 0.436 | 0.433 | 0.429 | 0.425 |
-0.0 | 0.500 | 0.496 | 0.492 | 0.488 | 0.484 | 0.480 | 0.476 | 0.472 | 0.468 | 0.464 |
z | 0.00 | 0.01 | 0.02 | 0.03 | 0.04 | 0.05 | 0.06 | 0.07 | 0.08 | 0.09 |
0.0 | 0.500 | 0.504 | 0.508 | 0.512 | 0.516 | 0.520 | 0.524 | 0.528 | 0.532 | 0.536 |
0.1 | 0.540 | 0.544 | 0.548 | 0.552 | 0.556 | 0.560 | 0.564 | 0.567 | 0.571 | 0.575 |
0.2 | 0.579 | 0.583 | 0.587 | 0.591 | 0.595 | 0.599 | 0.603 | 0.606 | 0.610 | 0.614 |
Select all that apply:
z=0.05
z=−0.01
p̂ =0.80
p̂ =0.32
p̂ =0.75
Given,
2567 students enrolled at a small college, with 2053 of them enrolled in a sociology course.
Proportion of students enrolled in a sociology course : p = 2053/2567 = 0.800
sampling distribution of sample proportions of size 230
Sample size : n= 230
Sample proportion :
Sampling distribution of sample proportion follows normal distribution with mean : p: 0.800
and standard deviation :
let : sample proportion such that proportion(Probability) of sample proportion above is 52%
i.e
P( > ) = 52/100 = 0.52
P( > ) = 1 - P()
P() = 1-0.52 = 0.48
Let z1 be the score for
Then,
P(Zz1) = P() = 0.48
From the Given z-table ; z1 = - 0.05
z1 = ( - mean)/standard deviation = ( - 0.8)/0.0264
= 0.8 + 0.0264z1
Substitute z1 = -0.05 in the above
=0.8 +0.0264 x (-0.05)=0.8 - 0.00132= 0.79868 0.8
= 0.8
Ans :