Question

2. Mr.Jones suspects that the majority of his students (more than a proportion of .5) prefer projects to exams. He decides to conduct a hypothesis test to investigate this. He asks a random sample of 25 students whether they prefer projects or exams and 14 of them say they prefer projects. Use this information to answer the following questions.

a. (2 points) What is the null hypothesis about the proportion of students that prefer projects?

b. (2 points) What is the alternative hypothesis about the proportion of students that prefer projects?

c. (2 points) What is the sample proportion?

d. (2 points) What is the standard score (z statistic) for the sample proportion?

e. (2 points) What is the P-value?

f. (2 points) Should he reject the null hypothesis at the 5% significance level?

g. (2 points) Based on your answer to part (f), does he have sufficient evidence to conclude that the majority of students prefer projects to exams?

Answer 1

given data are:-

sample size (n) = 25

x = number of students who prefer projects.

a).the null hypothesis:-

b).the alternative hypothesis:-

[this is the suspect of MR. jones, i.e, this is the claim ]

c).the sample proportion is:-

d).the standard score (test statistic) is:-

e).the p value is :-

[ using standard normal table ]

f).decision:-

p value = 0.2743 > 0.05 (alpha)

so, we fail to reject the null hypothesis.

g).conclusion:-

he does not have sufficient evidence to conclude that the majority of students prefer projects to exams.

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