A teacher wants to know if more than 15% of her students use online resources to complete their home

gvaldytist

gvaldytist

Answered question

2022-06-13

A teacher wants to know if more than 15% of her students use online resources to complete their homework assignments instead of doing the homework independently. The teacher would like to carry out a test at the 0.05 significance level of
H 0 : p = 0.40
H a : p > 0.40
where p = the true proportion of students that use online resources to complete their homework assignments. One day after school, the teacher asked the 40 students studying in her classroom if they used online resources to complete their homework assignments or if they did their homework independently. Are the conditions to perform the significance test met?
No, the students do not represent a random sample and the Large Counts condition is not satisfied.
No, the students do not represent a random sample even though the Large Counts condition is satisfied.
No, the students represent a random sample, but the Large Counts condition is not satisfied.
Yes, the students represent a random sample and satisfy the Large Counts condition.

Answer & Explanation

Angelo Murray

Angelo Murray

Beginner2022-06-14Added 23 answers

sample size (n) = 40
sample proportion (P) = 15% = 0.15
true population (p) = 0.40
significance level ( α) = 0.05
1) Null and alternative hypothesis
H 0 : p = 0.40
H a : p > 0.40
2)Test statistics
( z ) = ( P p ) p ( 1 p ) n = ( 0.15 0.40 ) 0.40 × ( 1 0.40 ) 40 = ( 0.25 ) 0.0122 = 20.4124
3)degree of freedom (df) = n -1 = 40 -1
this is a right tailed test and α = 0.05. The Z c r i t i c a l = 1.6849
4) Zcritical > z, we reject the null hypothesis at α = 0.05.
Question : Are the conditions to perform the significance test met?
Answer : Yes,the students represent a random sample and satisfy the large counts condition.

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