Unit 1- One Variable Data
True/False: A Dot Plot is easy to see the pattern in the data where a Histogram is easy to see Individual data
FALSE
Dot Plot- Easy to see individual data
Histogram- Easy to see the pattern in the data
For the following situation determine if it is a binomial setting, geometric setting or neither. Explain your Answer
You flip a coin and get tails
Geometric because there is not a fixed number of trials
how do we conclude independence?
What is the 10% condition
Which of the following statements are true?
1) One sample z intervals for means are constructed when er know the population standard deviation.
2) the t-distribution is similar to the standard normal distribution for small values of n
3) The central limit theorem tells us that the t-distribution will be approximately normally for small values of n
A) 1 only
B) 1&2
C) 1&3
D) 2 only
E) 3 only
A
One Sample z intervals for means are constructed when we know the population standard deviation
How many conditions do you have to check?
5
Linear,Independence,Normal Distribution,Equal SD,Random
In a distribution of 3000 scores the mean is 78 and the median is 95 one would expect this distribution to be ...
A) Skewed to the Right
B) Skewed to the Left
C) Symmetrical and Mound Shaped
D) Symmetrical and Uniform
B
I get sick 10 times each year. Assume each sickness is independent of the next sickness
Let X represent the number of times I get sick in a year
find and interpret the probability
P(X=8)
P(X=8) = 0.113
The probability I get sick 8 times in one year is 0.113
Suppose a large candy machine has 15% orange candies. imagine taking a SRS of 25 candies from the machine and observing the sample proportion P^ of orange candies.
WHat is the mean of the sampling distribution of P^? why?
Because the sample is a SRS the sample proportion mean can be approximated by the population proportion
SRS~MP^=P=0.15
A 95% confidence interval estimate for population mean M is (23,45) which of the following is a true statement?
A) there is 0.95 probability that M is between 23 and 45
B) if 95% confidence intervals are calculated from all possible samples of the given size M will be 95% of these intervals
C) if 95% confidence Intervals are calculated from all possible samples of the given size 95% of them will be ( 23,45)
B
If 95% confidence intervals are calculated from all possible samples of the given size M will be in 95% of these intervals
Inference for regression on the population regression slope B is based on which of the following distributions?
A) the t distribution with n-1 degrees of freedom
B) the standard Normal distribution
C) the t distribution with n-2 degrees of freedom
C
If you have 20% of your data lying below a Z-Score what is that Z-Score?
Z= -0.8416
InvNorm(0.2)
In the past 72 years there have been 59 EF-5 (wind speeds the exceed 200 mph) tornadoes recorded in the United States. what is the probability that this year we will have 2 or more EF-5 Tornadoes?
0.198
The probability we will have 2 or more EF-5 tornadoes this year is 0.198
The Wechsler Adult intelligence Scale WAIS is a common IQ test for adults. The distribution of WAIS scores for people over 16 years of age is approximately normal with mean 100 and standard deviation 15. What is the probability that the average WAIS score of a SRS of 60 people is 105 or Higher?
Are all conditions Met? How or how not were they met
Yes all conditions are met
Random- SRS
Independent- 10 % condition
Normal- n>- 60 ( and population is normally distributed)
Find the t-value
The area in the right tail is 0.10 with 25 degrees of freedom
t=1.32
invT( 0.9,24)
A 95% confidence interval was computed to be ( 30.28,40.695) Based on this interval and the data given what is the standard error of the slope of the regression line.
b=35.488
p=<0.001
s=282
R-Sq=0.943
2.411
b+- t*Sb
If Z= -0.55 X( bar)= 13.4 and S= 2 What is your X Value?
-0.55
a large fast food chain runs a promotion where 1 in 4 boxes of French fries include a coupon for a free box of French fries. Suppose that some location sells 100 of these boxes of fries per day. let X be the number of coupons won per day
Find the Mean
MX= 25
MX=np=100(0.25)
The Wechsler Adult intelligence Scale WAIS is a common IQ test for adults. The distribution of WAIS scores for people over 16 years of age is approximately normal with mean 100 and standard deviation 15. What is the probability that the average WAIS score of a SRS of 60 people is 105 or Higher?
P=0.0049
The probability that the average score of a SRS of 60 people is greater than 105 is 0.0049
The trade magazine QSR routinely checks the drive through service times of fast food restaurants. A 90% confidence interval that results from examining 607 customers in taco Bell's drive through has a lower bound of 161.5 seconds and an upper bound of 164.7 seconds. explain what this means.
we are 90% confident that the mean drive thru service time as taco bell restaurants in between 161.5 and 164.7 seconds.
Which of the following is NOT a condition needed for a regression inference
A) The scatter plot should show a linear pattern
B) The data should be collected using random sampling techniques
C) A histogram of the residuals should look uniform with no outliers
D) A residual plot should show random scatter and not obvious pattern
C
A histogram of the residuals should look uni modal and symmetric close to normal NOT uniform with no outliers
A special task force of a military unit requires that the recruits not to be too tall or too short. Suppose 12% of the applicants are rejected because they are too tall and 18% because they are too short. If the height of an applicant is normally distributed with a mean of 69.4 inches and a standard deviation of 3.5 inches, determine the heights that define weather and applicant is accepted or rejected
Applicants must be between 66.2 inches and 73.5 inches
Jeremiah makes 25% of the three point shots he attempts. for a warm up Jeremiah likes to shoot three point shots until he successfully makes one. let M be the number of shots it takes Jeremiah to successfully make his first three point shots. Assume that the result of each shot is independent.
Write a formula for determining the probability that Jeremiahs first made shot is on his 7th attempt
P(X=7)=0.044
P(X=7)=(0.75)6(0.25)
Voter registration records show that 68% of all voters in Indianapolis are registered as Republicans. To test weather the numbers dialed by a random digit dialing service device really are random you use the device to call 150 randomly chosen residential telephones in Indianapolis. Of the registered voters contacted 73% are registered Republicans. Find the probability of obtaining an SRS of size 150 from the population of Indianapolis voters in which 73% or more are registered Republicans. How well is your random digit device.
Assume all conditions are met
p=0.095
The probability of obtaining a SRS in which 73% or more are registered Republicans 0.095. This is not highly unlikely so the device seems to be working well.
According to the crown ATM Network the mean ATM withdrawal is $67. payEase inc manufactures an ATM that allows one to pay bills as well as withdraw money. A review of 40 withdraws shows the mean withdrawal is $73 from a payEase ATm machine. you are trying to determine if people withdraw more money from a payEase machine
State your hypotheses
Ho: M= 67
Ha: M>67
A teacher asked her 8 introductory statistics students to record the total amount of time they spent studying for a particular test. the amounts of study time x ( in hours) and the resulting test grades y are given below.
X= 2,1,1.5,0.5,1,3,0,2
y=92,81,84,68,85,96,48,74
Calculate and interpret SEb
SEb=3.545
If we were to repeat this study many times the slope of the sample regression line predicting test grades from study times