Population Inferences

The Mitchell Junior High newspaper staff conducted two samples in which 40 students were randomly selected to represent the entire 600 member student

population. The results of the two surveys are shown below.

7:45 AM

START TIME

12

14

SAMPLE #1

SAMPLE #2

8:30 AM

START TIME

18

19

9:00 AM

START TIME

10

7

Read the headline and state of the headline is supported by the data.

OVER 300

STUDENTS

WANT TO

START AFTER

8:00 AM

A

Supported

Not Supported

Answer:

Over 300 students did not support start time after 8:00am

Step-by-step explanation:

Given

[tex]N = 600[/tex] --- population

[tex]n = 40[/tex] --- sample

See attachment for dataset

Required [True/False]

Over 300  wants start time after 8:00am

First, we calculate the number of samples that wants start time after 8:00am

[tex]x = 8:30am\ start + 9:00am\ start[/tex]

For sample 1

[tex]x_1 = 18[/tex]

The corresponding value of x1 in the overall population is:

[tex]X_1 = \frac{x_1}{n} * N[/tex]

[tex]X_1 = \frac{18}{40} * 600[/tex]

[tex]X_1 = \frac{18 * 600}{40}[/tex]

[tex]X_1 = \frac{10800}{40}[/tex]

[tex]X_1 = 270[/tex]

For sample 2

[tex]x_2 = 19[/tex]

The corresponding value of x2 in the overall population is:

[tex]X_2 = \frac{x_2}{n} * N[/tex]

[tex]X_2 = \frac{19}{40} * 600[/tex]

[tex]X_2 = \frac{19* 600}{40}[/tex]

[tex]X_2 = \frac{11400}{40}[/tex]

[tex]X_2 = 285[/tex]

None of X1 and X2 is greater than 300.

Hence, over 300 students did not support start time after 8:00am

None of X1 and X2 is greater than 300. so, over 300 students did not support start time after 8:00 am.

The population is 600 and the sample is 40.

The population of inference refers to the population (or universe) to which the results from a sample survey are meant to generalize.

Over 300 students did not support start time after 8:00 am

For sample 1

[tex]\rm x_{1} =18\\[/tex]

The corresponding value of x1 in the overall population is:

[tex]\rm X_{1} =\frac{x_{1} }{n} \times N\\\rm X_{1} =\frac{18}{40} \times 600\\\rm X_{1} =\frac{10800}{40}\\ \rm X_{1} =270\\[/tex]

For sample 2

[tex]\rm x_{2} =19[/tex]

The corresponding value of x2 in the overall population is:

[tex]\rm X_{2} =\frac{x_{2} }{n} \times N\\\rm X_{2} =\frac{19}{40} \times 600\\\rm X_{2} =\frac{11400}{40}\\ \rm X_{2} =285\\[/tex]

None of X1 and X2 is greater than 300.

Hence, over 300 students did not support start time after 8:00 am.

Learn more about the population of inference here:

https://brainly.com/question/3640262

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