Question

A sample proportion is calculated from a sample size of 418. How large of a sample would we need in order to decrease the standard error by a factor of 4?

Question 3 options:

	1) 12,958
	2) 7,106
	3) 836
	4) 6,688
	5) 1,672

Question 4 (1 point)

Historically, 71.15% of packages delivered by UPS are on time. Suppose 121 deliveries are randomly selected for quality control. What is the probability that greater than 74.74% of the deliveries were on time?

Question 4 options:

	1) 0.5000
	2) 0.1917
	3) 0.8083
	4) <0.0001
	5) -5.6248

Question 5 (1 point)

Suppose that 28.49% of all vehicles on the road get a fuel economy of at least 35 miles per gallon (MPG). You conduct an observational study on a stretch of road outside of campus and record the make and model of 703 vehicles over a month long period. What is the probability that greater than 30.22% of the cars you observed get at least 35 MPG?

Question 5 options:

	1) <0.0001
	2) 0.1548
	3) 0.5000
	4) -12.9831
	5) 0.8452

Question 6 (1 point)

Suppose the lifetime of incandescent light bulbs has a mean of 1105.049 hours and a standard deviation of 71.4078 days. A random sample of 72 is taken from the population. What is the distribution of the sample mean?

Question 6 options:

	1) Approximately normal with mean 130.23 and standard error 8.415.
	2) Approximately normal with mean 1,105.049 and standard error 8.415.
	3) 1105.049 give or take 71.4078.
	4) Approximately normal with mean 1105.049 and standard error 71.4078.
	5) 68% of sample averages will fall between 1,033.64 and 1,176.457.

Question 7 (1 point)

Suppose that the scores of golfers in one round on the PGA tour has an average of 66.5 and standard deviation of 4.19. A random sample of 42 is taken from the population. What is the distribution of the sample mean?

Question 7 options:

	1) Approximately normal with mean 66.5 and standard error 4.19.
	2) Approximately normal with mean 10 and standard error 0.6.
	3) 68% of sample averages will fall between 62 and 70.7.
	4) Approximately normal with mean 66.5 and standard error 0.6.
	5) 66.5 give or take 4.19.

Question 8 (1 point)

Suppose that in the United States the height of a typical adult male is normally distributed with an average of 67.46 inches tall and a standard deviation of 5.579. You take a random sample of 17 adult males. What is the probability that the mean height of the sample is between 67.46 and 68.22?

Question 8 options:

	1) 0.0542
	2) 0.2128
	3) The sample mean will never fall in this range.
	4) -0.0430
	5) 1.2128

Question 9 (1 point)

Suppose that NBA players average 32.1 points per game with a standard deviation of 7.69. A random sample of 150 players is taken. What is the probability that the sample mean is less than 31.7?

Question 9 options:

	1) 0.4793
	2) 0.5207
	3) 0.5187
	4) 0.7380
	5) 0.2620

Question 10 (1 point)

Fill in the blank. Speed Car Rental company found that the tire lifetime for their vehicles has a mean of 53,579.37 miles and standard deviation of 5,780.67 miles. In a sample of 67 tires tested, there is a 57% chance that the average tire lifetime is less than ________ miles.

Question 10 options:

	1) 53,703.93
	2) There is not enough information to determine this.
	3) 54,598.93
	4) 52,559.81
	5) 53,454.81

Question 11 (1 point)

Fill in the blank. Suppose that the average starting salary for student with an Economics degree is $70,291.07 with a standard deviation of $8,104.85. A random sample of 185 recent graduates with a job is taken. There is a 28% chance that the average salary is greater than $ ________.

Question 11 options:

	1) 70,638.37
	2) 69,943.77
	3) 75,014.91
	4) There is not enough information to determine this.
	5) 65,567.23

(Just show answers)

Answer 1

3.

let Proportion is P and sample size is 418 then standard error of P is given by

let New sample size is n1 then new SE(P) is given by

since SE decreased by 1/4 times

so

this implies

Option (4).6688 is correct

4.

let P is the proportion

given

n=121

we have to find P( P >0.7474)=?

=P(Z>0.8713) =1-P(Z<0.8713) =1-0.80825 =0.1917

option (2) is correct

5)

let P is the proportion

given

n=703

we have to find P( P >0.3022)=?

=P(Z>0.1.016) =0.1548

Option (2) is correct

6)

let X is life time so

E(X) =1105.049

SD(X) =71.4078 days

n=72

then distribution of sample mean is given by

option (2) is correct

7)

let X is scores of golfer

E(X) =66.5

SD(X) =4.19

n=42

then distribution of sample mean is given by

option (4) is correct

8)

let X is the height

E(X)=67.46 SD(X)=5.579 n=17

we have to find

=P(0<Z<0.5617) =0.2128

option (2) is correct

9)

given

E(X)=32.1

SD(X)=7.69

n=150

we have to find

so Ans (4) is correct

10)

let lifetime is X

E(X)=53,579.37 SD(X)= 5,780.67 miles. n=67 tires tested,

let required life time is U so

from Z table

P(Z<0.176374) =0.57 so

option (1) is correct

11).

let X is salary

E(X)=$70,291.07 SD(X)= $8,104.85. n=185

let rquired salary is L so

from Z table

so L =69943.766

option (2) is correct