Prompt:

Suppose it is reported that 80% of all people subscribe to a cable television service versus others. A student believes it is different and decides to test this claim by randomly sampling 30 people and 20 responded that they subscribe to cable or satellite television versus others at a 0.05 level of significance.

Student Work:

H0 : p=0.80

Ha : p0.80

The test z-statistic is z=1.8257 , and the P-value is 0.0679.

Since 0.06790.05 we fail to reject H0. Therefore, there is not sufficient evidence at 0.05 level of significance to conclude the proportion of people who subscribe to a cable television service versus others is different from 80%.

Task:

The student who submitted their work failed to check the conditions for the problem. Let's help them out.

1. Remind the student of the conditions and how to check them.
2. Tell the student why we need to check each condition.

3. A statistic student condusts a random sample of 1000 people and finds that 285 are living alone.

Find the Standard Error. Round your answers to four decimals.

The Standard Error is [a].