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.

Ninth-grade students and teachers were surveyed to determine the
level of bullying that the students experienced. Higher scores on
the survey indicated more experience with bullying. Then the
researchers were given permission to access student's scores on the
EQAO Mathematics Assessment. The EQAO scores are given as deciles
instead of percentages to make your calculations easier. The
researchers hypothesized that students who were bullied more would
have lower EQAO Math scores. Their data is given below.
X - Bullying Score...

BACKGROUND: According to the Educational Testing Service (ETS),
the national average on the Graduate Record Examinations (GRE), a
standardized test that is an admissions requirement for most
graduate schools in the United States, is 302.60 (with the verbal
and quantitative subsections combined). Unfortunately, ETS does not
provide a standard deviation for total GRE score (only standard
deviations for the two subsections), so let’s just use a standard
deviation of 12.
Pretend the ETS revises the current GRE test (the one...

BACKGROUND: According to the Educational Testing Service (ETS),
the national average on the Graduate Record Examinations (GRE), a
standardized test that is an admissions requirement for most
graduate schools in the United States, is 302.60 (with the verbal
and quantitative subsections combined). Unfortunately, ETS does not
provide a standard deviation for total GRE score (only standard
deviations for the two subsections), so let’s just use a standard
deviation of 12.
PROBLEM (FICTIONAL): ETS has received number complaints from
universities that...

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