We know that 60% of STAT 201 students have taken STAT 110. 80 STAT 201 students

Question

We know that 60% of STAT 201 students have taken STAT 110. 80 STAT 201 students are randomly selected and asked whether they have taken STAT 110, 40 of them response “Yes”.

a. Calculate the sample proportion.

b. Find the mean and standard error of the sampling distribution of the sample proportion

c. Can we assume the sampling distribution of the sample proportion in this problem is normal distribution? Why?

d. Perform a 95% confidence hypothesis test to test whether the true population proportion is less than 60%

i. Write the hypothesis, H0 and Ha.

ii. Check assumptions.

iii. Calculate test-statistic ?? ? .

iv. Find P-value with z from last step using z-table.

v. Make your decision and provide an interpretation.

Explanation / Answer

Ans:

a)sample proportion=40/80=0.5

b)mean=p=0.6

stnadard deviation=sqrt(0.6*(1-0.6)/80)=0.0548

c)Yes,as,np>10,nq>10(number of successes and failures are greater than 10)

d)

Ho:p=0.6

Ha:p<0.6

Test statistic:

z=(0.5-0.6)/0.0548

z=-1.826

p-value=P(z<-1.826)=0.0339

As,p-value<0.05,we reject null hypothesis,we can conclude that true population proportion is less than 60%.

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.