Question

Hypothesis Testing of Proportions. According to the statistical abstract of the United States, in 2007, approximately 43% of sixth grade students reported being bullied at school. Due to increased education and outreach since 2007, many teachers now believe that the proportion of students being bullied at school has decreased. In a recent random sample of 75 sixth grade students, 40 respondents that they experienced bullying at school. Test the teachers’ hypothesis. Show all work and write a sentence stating your conclusion. Be sure to state the null hypothesis, alternative hypothesis, claim, determine if it is a one or two tailed test, use 0.05 for level of significance, report p-value and conclusion.

Answer 1

Null hypothesis

H0: P = 0.43

vs

Alternative hypothesis

H1 : P >0.43 (One tailed test )  

We can use here,

=1.81

P value is 0.0351

1-NORMSDIST(1.81)...............................p value by using Excel command.

1-P[Z<1.81] = 1 - 0.9649=0.0351........................p value by using normal probability table.

P value 0.0351 < 0.05

Therefore, We reject H0.

Conclusion: We have sufficient evidence to say that, at 5% level of significance  proportion of students being bullied at school has decreased.