Question

A sample proportion is calculated from a sample size of 363. How large of a sample would we need in order to decrease the standard error by a factor of 9?

Question 3 options:

1)

6,171

2)

11,253

3)

1,089

4)

29,403

5)

3,267

Question 4 (1 point)

Suppose the nationwide high school dropout rate for 2014 was around 7.85%. If you checked the records of 781 students in high school in 2014, what is the probability that between 6.59% and 7.19% of them ended up dropping out?

Question 4 options:

1)

50.3598

2)

0.1512

3)

15.1731

4)

0.3417

5)

0.8488

Suppose you are interested in measuring the amount of time, on average, it takes you to make your commute to school. You've estimated that the average time is 38.52 minutes with a standard deviation of 6.979 minutes. Assuming that your estimated parameters are correct and the commute time is normally distributed, what is the probability that the average commute time of 10 random days is greater than 40.89 minutes?

Question 9 options:

1)

0.1414

2)

0.3671

3)

0.6329

4)

0.8984

5)

0.8586

Fill in the blank. Suppose that the average starting salary for student with an Economics degree is $79,120.51 with a standard deviation of $6,811.9. A random sample of 181 recent graduates with a job is taken. There is a 93% chance that the average salary is less than $ ________.

Question 11 options:

1)	There is not enough information to determine this.

2)

89,173.45

3)

69,067.57

4)

79,867.74

5)

78,373.28

Answer 1

3)

sample size =363*9² =29403

4)

std error of proportion=σp=√(p*(1-p)/n)=0.0096

probability =P(0.0659<X<0.0719)=P((0.0659-0.0785)/0.01)<Z<(0.0719-0.0785)/0.01)=P(-1.31<Z<-0.69)=0.2459-0.0947=0.1512

9)

for normal distribution z score =(X-μ)/σ
here mean=       μ=	38.52
std deviation   =σ=	6.9790
sample size       =n=	10
std error=σx̅=σ/√n=	2.2070

probability =P(X>40.89)=P(Z>(40.89-38.52)/2.207)=P(Z>1.07)=1-P(Z<1.07)=1-0.8586=0.1414

11)

for 93th percentile critical value of z=		1.476
therefore corresponding value=mean+z*std deviation=			79867.74