Question

In: Statistics and Probability

There are 2567 students enrolled at a small college, with 2053 of them enrolled in a...

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=−0.05
  • z=−0.01

  • p̂ =0.80

  • p̂ =0.32

  • p̂ =0.75

Solutions

Expert Solution

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 :

  • z=−0.05
  • =0.80

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