Unit 5 Test Review
pdf
keyboard_arrow_up
School
University of California, Los Angeles *
*We aren’t endorsed by this school
Course
41
Subject
Industrial Engineering
Date
Feb 20, 2024
Type
Pages
5
Uploaded by scholarshipsdeltaeta
Unit 5 –
Sampling Distributions Name: _______________________ Unit 5 Test Review Multiple Choice Practice ______ 1) Suppose a normal population exists that has a mean of 42 and a standard deviation of 15. You select a random sample of size 8 from the population. What is the probability that your sample mean will be between 30 and 60? (A) 0.9878 (B) 0.6731 (C) 0.4558 (D) 0.3269 (E) 0.0122 ______ 2) Suppose a population exists that has p = 0.35. If you take a sample of 10 from the population and record 𝑝̂
, what is the 85
th
percentile of the sampling distribution of 𝑝̂
? (Assume Normal) (A) 1.036 (B) 0.151 (C) 0.506 (D) 0.35 (E) None of the above Use the following situation to answer questions 3 –
6: A Pew Research Poll recently asked a random sample of 500 adults if they have been to the gym in the past week. Assume that the population of all adults who have been to the gym in the past week is 58%. ______ 3) Which of the following is the appropriate mean and standard deviation of the sampling distribution for 𝑝̂
? (A) 𝜇
𝑝̂
= 0.58
and 𝜎
𝑝̂
= 0.0221
(B) 𝜇
𝑥̅
= 0.58
and 𝜎
𝑥̅
= 0.0221
(C) 𝜇
𝑝̂
= 290
and 𝜎
𝑝̂
= 0.42
(D) 𝜇
𝑥̅
= 290
and 𝜎
𝑥̅
= 0.42
(E) You cannot answer the question without knowing the standard deviation of the population ______ 4) Which of the following is the correct condition to check that you can use the normal approximation for the distribution of 𝑝̂
? (A) A random sample of adults was chosen from the population (B) 500
0.1(all adults in the population) (C) 500(0.58)
10 and 500(0.42)
10 (D) 500
30 (E) None of the above represents the correct condition for the normal approximation
______ 5) What is the probability that between 54% and 60% of the sample of adults have been to the gym in the past week? (A) 0.0600 (B) 0.5664 (C) 0.2355 (D) 0.6981 (E) 0.7821 ______ 6) Decreasing the sample size from 500 to 250 would multiply the standard deviation by (A) 2 (B) 1/2 (C) √2
(D) 1/√2
(E) None of these ______ 7) YouTube has stated that 62% of Internet users access YouTube daily. A sample survey was given out to an SRS of 800 Internet users and the proportion of the sample who accessed YouTube that day was recorded. If the sample size were changed from 800 to 1800, how would this change the sampling distribution of 𝑝̂
? (A) A larger sample size would result in a larger range of values for the center of the distribution, which would create more variability in the sampling distribution of 𝑝̂
. (B) A larger sample size would result in a larger standard deviation, which would create less variability in the sampling distribution of 𝑝̂
. (C) A larger sample size would result in a larger standard deviation, which would create more variability in the sampling distribution of 𝑝̂
. (D) A larger sample size would result in a smaller standard deviation, which would create less variability in the sampling distribution of 𝑝̂
. (E) A larger sample size would result in a smaller standard deviation, which would create more variability in the sampling distribution of 𝑝̂
. ______ 8) To create a sampling distribution of 𝑥̅
, does the population need to be normally distributed for the sampling distribution to be approximately normal? (A) Yes, because the Central Limit Theorem states that the variability the sampling distribution of any non-
normal population will increase as your sample size increases. (B) Yes, because the sampling distribution of 𝑥̅
will approach the same distribution shape as the population as your sample size increases. (C) No, because the Central Limit Theorem states that when the sample size is sufficiently large, the sampling distribution of 𝑥̅
will be approximately normally distributed. (D) No, because the large counts condition states that as long as we have enough “
successes
”
and “
failures
”
in our sample, the sampling distribution of 𝑥̅
will be approximately normally distributed. (E) No, because the sampling distribution of 𝑥̅
will always be approximately normal distribution due to the nature of averages.
______ 9) The average weight of an adult male is 198 pounds, and the population distribution is normal with a standard deviation of 25 pounds. If you select an adult male at random, what is the probability that he will weigh over 210 pounds? (A) 0.6844 (B) 0.5523 (C) 0.4789 (D) 0.3156 (E) 0.1401 ______ 10) The average weight of an adult male is 198 pounds, and the population distribution is normal with a standard deviation of 25 pounds. If you select an SRS of 16 males, that is the probability that the average weight of those men will weigh over 210 pounds? (A) 0.0021 (B) 0.0111 (C) 0.4142 (D) 0.3156 (E) 0.0274 Free Response Practice 1) A recent poll given to high school students asked who their favorite Harry Potter character was. Hermione Granger was the overwhelming favorite at 45%. We will assume that this is the parameter value for the entire population of high school students who have read the Harry Potter books. At your school, you take an SRS of 30 students who have read the Harry Potter books and ask if their favorite character is Hermione Granger. What is the probability that over 15 of them said that she was their favorite character?
Your preview ends here
Eager to read complete document? Join bartleby learn and gain access to the full version
- Access to all documents
- Unlimited textbook solutions
- 24/7 expert homework help
2) Newborns born at full term (after 37 weeks) in the US vary according to a population with a normal distribution and have a mean of 3,510 grams and a standard deviation of 390 grams. At a large city hospital, a random sample of 30 full term baby records were obtained and their weight recorded. What is the probability that the sample weight was below 3,400 grams? 3) In the 400-meter freestyle relay race, four swimmers each swim 100 meters. The coach places the four best female freestyle swimmers on the relay, in hopes to win 1
st
. The times, in seconds, for each of the four swimmers are given below (assume that the times are independent). Find the probability that the total team time in the 400-meter freestyle relay race is less than 215 seconds. Swimmer Mean Std. dev. Halle 55.2 2.8 Morgan 58.0 3.0 Jordan 56.3 2.6 Stephanie 54.7 2.7
4) Schools keep track of how many absences a student has. For freshman boys, the average number of days absent is 8.5 days with a standard deviation of 2 days. For freshman girls, the average number of days absent is 7.2 days with a standard deviation of 2.1 days. Both population distributions are normally distributed. You take two separate random sample of freshman boys and freshman girls at your school. What is the probability that in your sample of 20 freshman boys and 30 freshman girls, that the girls will have a higher average number of absences?