Q.34 - The Practice of Statistics for AP

Question

Check that the conditions for carrying out a one-sample z test for the population proportion p are met. A Gallup Poll report on a national survey of 1028 teenagers revealed that 72% of teens said they rarely or never argue with their friends. Yvonne wonders whether this national result would be true in her large high school, so she surveys a random sample of 150 students at her school.

Step-by-Step Solution

Answer

The conditions for carrying out a one-sample z test for the population proportion p are met 

Step 1: Introduction

Population Survey tries to decide the segment attributes and business status of all people of a family who are of working age.

Step 2: Explanation

The sample size is n= $150$

The population proportion is p = $72\%=0.72$

The number of successes = n$\times$pdata-custom-editor="chemistry" $=150\times 0.72=108$ 

The number of failures = n(1-p)

$=150\times (1-0.72)=42$

The normal condition is satisfied as the success and failures are larger than ten and since the sample size is less than$10\%$of the population.

hence the conditions for carrying out a one-sample z test for the population proportion p are met