Question

1. I am interested in asking people what they think about the current election and who their favorite candiate is. I decide to go to random subdivisons and city blocks and ask 15 people from each region who their favorite candiate is. I decide to go to random subdivisons and city blocks and ask 15 people from each region who their favorite candiate is. This is an example of:

a. Stratified sampling

b. Simple Random Sampling

c. Systematic Sampling.

d. Cluster Sampling

2. If we have two unbiased estimators, the next thing we are interested in checking is if they are:

a. Efficient

b. Consistent

3. 77% Of people have a gpa of 3.0 or higher. Suppose we take a random sample of 500 students.

a. What is the standard error of the proportion

b. What is the probabilty that 80% or more of those people will have a gpa higher than 3.0

4. In 2010, the average finshing time for marathons across the US was approximately 278 minutes, with a standard deviation of approximately 63 minutes. what finishing time defines the fastes 7.93% of runners?

a. 366.83

b. 189.17

c. 348.76

d. 405.78

Answer 1

Question 1

a) Stratified sampling

Explanation:

For the given scenario, researcher select random subdivisions and city blocks which are considered as strata and then from each stratum he/she selects a random sample of 15 people for the required survey.

Question 2

b) Consistent

Explanation:

A step by step criterion for good estimator in proper order is given as below:

Unbiasedness, Consistency, Efficiency, Sufficiency

Question 3

Part a

We are given p = 0.77, n = 500

Standard error = sqrt(p*q/n)

Where, q = 1 – p = 1 – 0.77 = 0.23

Standard error = sqrt(0.77*0.23/500) = sqrt(0.0003542) = 0.018820202

Standard error = 0.018820202

Part b

Here, we have to use the normal approximation to a binomial distribution.

Here, we have to find P(P>80%) = P(P>0.80) = P(X>0.80*500) = P(X>400)

P(X>400) = 1 – P(X<400)

Z = (X – mean) / SD

Mean = n*p = 500*0.77 = 385

SD = sqrt(n*p*q) = sqrt(500*0.77*0.23) = 9.410100956

Z = (400 - 385) / 9.410100956

Z = 1.594031782

P(Z<1.594031782) = 0.944535542

P(X<400) = 0.944535542

P(X>400) = 1 – P(X<400)

P(X>400) = 1 – 0.944535542

P(X>400) = 0.055464458

Required probability = 0.055464458

Question 4

We are given

Mean = 278

SD = 63

X = Mean + Z*SD

Z for upper 7.93% area or fastest runners is given as below:

Z = -1.409795757

X = 278 + (-1.409795757)*63

X = 189.17

Correct Answer: b. 189.17

***All z-scores, probabilities can be calculated by using z-table/excel/Ti-83/84 calculator/software.