Download SP15_226_Ex_T2_Molly

STP 226
Spring
2015
Diane Richardson:
EXAM #2
Material from chapters 6-8
Honor Statement:
I have neither given nor received information regarding this exam, and I will not do so
until all exams have been graded and returned.
Signed ______________________
Date_________________________
_Molly Lawson_____________
PRINTED NAME
_Noon TTh___________
CLASS TIME
DIRECTIONS:
This is a closed book examination. You may use one page 8X11 (one side only) with
hand written notes and a graphing calculator.
Formulas , z-tables and t-tables are included at the end of the test.
For the first 5 questions you need to provide complete and well-organized answers,
Include sketches as requested to explain your answers, Round up all answers to required
decimal places (if specified).
For multiple choice questions #6-#15 place letter answers in the tables below. You can
earn 105 points (5 points are extra credit points ).
RELAX and Good Luck!
Part one: Show all work for questions #1-# 4
Use following information in questions #1-#2
We are interested in estimating the mean weight (𝜇) of seven female Great Dane dogs .
The sample of 25 randomly selected dogs had a mean weight
𝑥¯ =105.84 pounds.
Assume that Great Dane weights are normally distributed with standard deviation of
𝜎 =15 pounds.
Question#1 (25 points)
Obtain 90% confidence interval for 𝜇, show all work by hand and your step by step
process.
Assumptions: Circle the correct ones
1. Simple Random Sample
2. Large Sample or Normally Distributed
3. Sigma known
4. Sigma unknown
Step 1: Circle the correct answer and fill in the blank for the correct one.
1. t / 2  _____
2. z / 2  _____
Step 2: What is the correct answer? Circle the correct one.
1. ( 99.65, 112.03)
2. (100.91, 110.78)
Step 3: What is the correct answer? Circle the correct one.
1. With a confidence percentage of 90%, the mean weight of all female Great Dane
dogs is between 99.65 lbs to 112.03 lbs.
2. With a confidence percentage of 90%, the mean weight of all female Great Dane
dogs is between 100.91 lbs to 110.78 lbs.
Question#2 (4 points)
What sample size is needed for the margin of error in 90% confidence interval for 𝜇to be
no more than 2 pounds? Assume that 15 pounds is a reasonable guess for population
standard deviation 𝜎
Use following information for Questions #3 and #4
An insurance company knows that in the entire population of millions of insured workers,
the mean annual cost of workers compensation claims is only 𝜇=$439 per worker and the
standard deviation is 𝜎=$20,000. The distribution of loses is strongly right-skewed: Most
policies have no or very little loss, but few have large losses up to millions of dollars. Use
Central Limit Theorem to answer Questions #1 and #2
Question #3 (4 points)
Suppose the company sells n=40,000 of policies and 𝑥¯ is to be their average annual loss
from these policies. The sampling distribution of 𝑥¯is Approximately Normal. Give the
mean and the standard deviation of that distribution.
𝜇𝑥¯ =_________________________
𝜎𝑋¯ =________________________
Question #4 (6 points)
Company works under the assumption that the average loss will not exceed $500.
Compute the probability that their assumption is incorrect, so that for 40,000 policies the
average loss X will be greater than $500.
P(500  X ) =________________________
Part two: Multiple choice questions. Select one from A to E as appropriate.
Use following information in Questions #5 - #6
Suppose that you measure the heights of eight-year-old American girls. Population mean
height is 𝜇 = 140cm and standard deviation is 𝜎 = 8cm. The mean 𝑥¯of a simple random
sample of n=400 measurements will vary if you take repeated samples. The sampling
distribution of a sample mean 𝑥¯ is Normal, with mean 𝜇𝑥¯ = 140cm and SD𝜎𝑥¯ = 0.4cm
Question#5 (6 points) What percentage of samples of size 400 will have a sample mean
𝑥¯ within  0.8 cm from the population mean?
A) 68.26%
B) 95.44% C) 99.7% D) 90% E) none of these
Question#6 ( 6 points) Compute the probability that randomly selected samples of size
400 will estimate the population mean within 139 cm to 141 cm. Round your answer to 2
decimal places.
A) 0.90
B) 0.95
C) 0.68
D) 0.99
E) none of these
Question#7 ( 6 points) What is the probability that a sample mean from a size 400 girls
will be less than 140.5 cm? Round your answer to 2 decimal places.
A) 0.89
B) 0.95
C) 0.68
D) 0.99
E) none of these
Use following for Questions #8 - #10
A survey asked the following question: “ About how much time (in minutes) do you
study on a typical weeknight?” of randomly selected 40 first-year ASU students. The
sample mean was 118 minutes, sample standard deviation was 65 minutes. Let 𝜇 be
the mean study time of all first-year ASU students.
Question #8 (6 points) Construct a 95% confidence interval for 𝜇. Give 1 decimal place
for the final answer.
A) (-13.5, 249.5)
E) none of these
B) (97.9, 138.1)
C) (97.2, 138.8)
D) (-8.8, 244.8)
Question #9 (6 points) From your confidence interval would you expect the population
mean   160 minutes?
A) Yes, it is outside of the confidence interval
B) Yes, it is inside of the confidence interval
C) No, it is outside of the confidence interval
D) No, it is inside of the confidence interval
E) None of these
Question 10# (6 points) Would you expect another random sample of 40 ASU students
to have the same exact sample mean as this first sample?
A) Yes, all samples have the same sample mean.
B) Yes, the sample size is 40.
C) No, there is variation between the samples (sampling error)
D) None of these
Use following information in Questions #11 - #13:
The data for this example is for the full grown dog breed known as the Beagle (think
Snoopy). The weight of this breed is normally distributed with a mean of 22.5 pounds and
a standard deviation of 2.2 pounds.
11. What is the z-score of a dog that weighs 23.6 pounds?
A 0.5
B - 0.5
C 0.6915
D 0.3085
E None of the Above
12. Compute the probability that the dog will weigh less than 21.2 pounds
A 0.2776
B 0.7224
C 0.59
D 0.41
E None of the Above
13. If the doctor reports that a Beagle dog was at the 85th percentile for his weight, how
much did he weigh?
A. 20.21 lbs
B. 24.27lbs
E. None of these
C. 24.79 lbs
D. 23.73 lbs
Question#14 (6 points)
Suppose the mean annual income for adult men in one city is $28,520 with standard
deviation of $5190 and the distribution is left skewed. What is the sampling distribution
of the sample mean 𝑥¯ for samples of size 49
A) approximately normal distribution
C) left skewed
B) right skewed
D) can't specify, because sample is not large enough
Question#15 (6 points)
After performing a normal probability plot, if our data appears to be skewed, then we can
transform it using a transformation on the data such as the square root, or the log.
A True
B False
Place answers to multiple choice questions below, use capital letters A-E as
appropriate:
Question #5
Answer:
#6
#7
#8
#9
#10
#11
#12
#13
#14
#15
FORMULAS
𝜎
Sampling Distribution of 𝑥¯: 𝜇𝑥¯ = 𝜇 , 𝜎𝑥¯ = √𝑛
,
Standardized version of 𝑥¯: 𝑧 = 𝜎𝑥¯−𝜇
⁄√𝑛
Studentized version of : 𝑥¯:𝑡 = 𝑠𝑥¯−𝜇
⁄√𝑛
Confidence Intervals for 𝜇, Confidence level percentage C=(1 − 𝛼) ∗ 100%
𝜎
Z-interval: 𝑥¯ ± 𝑧𝛼⁄2 √𝑛
𝜎
Margin of error: 𝐸 = 𝑧𝛼⁄2 √𝑛
𝑠
T-interval: 𝑥¯ ± 𝑡𝛼⁄2 √𝑛
, df=n-1, Margin of error: E  t / 2 
Sample size estimation: 𝑛 = (
𝑧𝛼⁄2 𝜎 2
𝐸
)
s
n