Question

n a large high school, 37% of the teachers believe that five minutes is not enough time for students to change classes. However, 89% of the students believe that five minutes is not enough time for students to change classes. Let p hat Subscript Upper F and p hat Subscript Upper S be the sample proportions of teachers and students, respectively, who believe that five minutes is not enough time for students to change classes. Suppose 28 teachers and 100 students are selected at random and asked their opinion on the amount of time students have to change class. Which of the following is the correct shape and justification of the sampling distribution of p hat Subscript Upper F Baseline minus p hat Subscript s ?

Answer 1

The difference (faculty-student) in the sample proportions of those who believe that five minutes is not enough time for students to change classes typically varies about 0.096 from the true difference in proportions. Option D is correct.

What is the standard deviation?

It is a measurement of statistical data dispersion. The degree to which the value varies is known as standard deviation.

The standard deviation of the sampling distribution is found as;

$\rm \sigma_F-\sigma_s= \sqrt{\frac{0.37 \times (1-0.37)}{28}+\frac{0.89 \times (1-0.89)}{100} } \\\\ \sigma_F-\sigma_s=0.096$

The difference in the sample proportions of those who think five minutes is not enough time for students to switch classrooms generally differs by roughly 0.096 from the actual difference in proportions.

Hence option D is correct.

To learn more about the standard deviation, refer to: brainly.com/question/16555520.

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