4/26 stats test
The number of hybrid cars a dealer sells weekly has the following probability distribution: The dealer purchases the cars for $21,000 and sells them for $24,500. What is the expected weeky profit from selling hybrid cars?
$5355 U= 0(.32)...5(.06) =1.53(24500-21000) =$5355
FR 1.1 A bonus is to be given to 20 percent of the sales agents. Those who achieved the highest monthly sales volume during the preceding month will receive a bonus. What is the minimum monthly sales volume an agent must have achieved to qualify for the bonus.
$800,000
FR 2.2A Suppose this study is to be conducted using a completely randomized design. Describe a randomization process and identify an inference procedure for the study.
-use a random integer ot pull 50 #s from 00-99, putting 00-49 w/new, and 50-99 with old. -compare the mean # of mosquito bites for each compound using a two sample t test
FR 2.1A Describe an appropriate design for the new study. Your discussion should briefly address treatments used, methods of treatment assignment, and what variables would be measured. Do not describe how the data would be analyzed.
-use magnets and a placebo of equally weight & treatment -# males 00-99, 00-49= magnets, 50-99= placebos 100 male patients to 50-50 (one w magnets, one w placebo) then compare
A government statistician claims that the mean income level of families living in subsidized house is $9250 with a standard deviation of $2575. A reporter plans to test this claim through interviews with a random sample of 50 families. If she finds a sample mean more than $500 different from the claimed $9250, she will dispute the statistician's claim. What is the probability that the reporter will mistakenly reject a true claim?
.170
In a random sample of 1250 adult drives 450 said that they would cut their driving by 10 % if this significantly helped the environment. Find a 95% percent confidence interval estimate of the proportion of adult drivers who are willing to cute their driving by 1-% to help the environment.
.36-+1.96-/((.36)(.64)/1250)
Given the probabilities P(A) = .3 and P (A U B)= .7, what is the probability P(B) if A and B are mutually exclusive? If A and B are independent?
.4, 4/7
The Air Force receives 40 percent of its parachutes from company C1 and the rest from company C2. The probability that a parachute will fail to open is .0025 or .002, depending on whether it is from company C1 or C2, respectively. if a randomly chosen parachute fails to open, what is the probability that it is from company C1?
.4545
Suppose that 62% of the graduates from your high school go on to four-year colleges, 15 percent go on to two-year colleges, and 18 % find employments, and the remaining graduates search for a job. If a randomly selected student is not going on to a four-year college, what is the probability he or she will find employment?
.474 P(E/not 4)
A new soft drink product has an average number of 77 calories per bottle with a standard deviation of 4.5 calories. In a random sample of 40 bottles, what is the probability that the mean number of calorie is between 75 and 80?
.9975
FR 1.1 What proportion of sales agents achieved monthly sales volumes between $700,000 and $800,000?
10% (80%-70%)
Suppose X and Y are random variables with Ux=38, O-x= 12, Uy=35, and O-y=9. Given that X and Y are independent, what is the standard deviation of the random variable X-Y?
15: basically just variance of X+Y (square root the O-^2 added together)
Four pairs of data are used in determining a regression line y= -2+6x. If the four values of the independent variable are 37, 52, 18, and 23 respectively, what is the mean of the four values of the dependent variable?
193
Suppose the scores on an exam have a mean of 75 with a standard deviation of 8. If one student has a test result with a z-score of -1.5 and a second student has a test result with a z-score of 2.0, how many points higher was the second student's result than the first?
28
FR 1.1 In the context of this question, explain what information is conveyed by the circled point.
40% of sales associates sold $300 thousand or less
A guidance counselor wishes to determine the mean number of changes in academic major by college students to within -+0.1 at a 90 percent confidence level. What sample size should be chosen if it is known that the standard deviation is 0.45?
55 1.645(.45/-/n)=.1
There are 8253 men and 10327 women at a state university. If 43 % of the men and 27 % of the women are business majors, what is the expected number of business majors in a random sample of 200 students?
68.2
Suppose we have a random variable X where the probability associated with the value k is (12/k)(.34)^k(.66)^12-k for k=0...12. what is the mean of X.
C) 4.08 (np)
A small appliance manufacturer sets up three locations to provide service for its customers. Logs are kept noting whether or not calls about problems are solved successfully. Data from a sample of 500 cells are summarized in the following table. Assuming there is no association between location and whether or not a problem is resolved successfully, that is H0: independence, what is the expected number of successful calls (problem solved) from location 2?
E) (161)(325)/500 (row)(columns)/total
Suppose two events, E and F, have nonzero probabilities p and q, respectively. Which of the following is impossible?
E) E and F are both independent and mutually exlusive
FR 4.2 Is there a significant difference in the mean amount of E. coli bacteria detected by the two methods for this type of beef? Provide a statistical justification to support your answer.
I want to infer abt u, the mean difference in the amount of E coli bacteria detected by method A and method B in millimicrobes/liter. Ho: u=0. No difference in amt of bacteria Ha: u DOES NOT = 0. Difference SRS, 10%, n=10 is too small for CLT I will conduct a one-sample t test of the difference. P(X<-0.29 or X>0.29) 2P(X>0.29) 2P(t>(0.29-0)/(0.6297/-/10) 2P(t>1.456) =0.1793 INSUFFICIENT EVIDENCE we cannot conclude that there is a difference.
Which of the following are true statements about sampling error? I. Sampling error can be eliminated only if a survey is both extremely well designed and extremely well conducted. II. Sampling error concerns natural variation between samples, is always present and can be described using probability. III. Sampling error is generally smaller when the sample size is larger.
II and III
Which of the following are true statements? I. If the sample has variance zero, the variance of the population is also zero. II. If the population has variance zero, the variance of the sample is also zero. III. If the sample has variance zero, the sample mean and sample median are equal.
II and III
Which of the following are true statements? I. The larger the sample, the larger the spread in the sampling distribution. II. Provided that the population size is significantly greater than the sample size, the spread of a sampling distribution is about the same no matter what the population size. III. Bias has to do with the center, not the spread, of a sampling distribution.
II and III
Given this back-to-back stemplot, which of the following is true? I. The Empirical Rule applies to both A and B. II. In one set, the mean and median should be about the same, while in the other the mean appears to be less than the median. III. The ranges of the two sets are equal.
II only
Which of the following are true statements about the correlation coefficient r? I. A correlation of 0.3 means that 30 percent of the points are highly correlated. II. The square of the correlation measure the proportion of the y-variance that is predictable from a knowledge of x. III. Perfect correlation, that is, when the points lie exactly on a straight line, results in r=0.
II only
Suppose that the scatterplot of log X and log Y shows a strong positive correlation close to 1. Which of the following is true? I. The variables X and Y will also have a correlation close to 1. II. A scatterplot of the variables X and Y will show a strong nonlinear pattern. n III. The residual plot of the variables X and Y will show a random pattern.
II only: A scatterplot of the variables X and Y will show a strong nonlinear pattern.
In which of the following studies are cause-and-effect (rather than simple association) conclusions probably reasonable? I. Studies noting heights and ages at death tend to show that taller people live longer than shorter people. II. Studies noting that children born prematurely tend to engage in less risky behavior as adults. III. Studies showing that animals fed low-calories diets tend to live longer than animals on normal diets.
III only
FR 1.2 Suppose that you want to describe the relationship between operating cost per hour and number of passenger seats in the plane for planes only in the range of 250 to 350 seats. Does the line shown in the scatterplot still provide the best description of the relationship for data in this range? Why or why not?
No, because then the slope would be negative.
If quartiles Q1=50 and Q3=70, which of the following must be true? I. Median=60 II. Mean is between 50 and 70 III. The standard deviation is at most 20.
None may be true.
A linear regression analysis is performed on the data from two scatterplots, A and B, resulting in identical least squares regression lines with positive slopes. Which of the following statements are true?
None of the above are true statements.
FR 3.2C Sam will take 1-4 flights next year. Would you be surprised if Sam receives more than 20 upgrades to fist class during the year? Justify
P(X>20)=1-P(X-<20) =1-[104\0(0.1)^0(0.9)^104+...+(104\20)(0.1^20)(0.9)^84 =1-0.9986 =0.0014
FR 3.2A What is the probability that Sam's first upgrade will occur after the third flight?
P(x->4)=1-P(X->3) =1-[P(x=1)+P(x=2)+P(x=3) =1-[0.1+0.09+0.081] =1-0.271 =0.729
FR 3.2B What is the probability that Sam will be upgraded exactly 2 times in his next 20 flights?
P(x=2)=(20\2)(0.1)^2(0.9)^18 =20!/2!18!(0.1)^2(0.9)^18 =190(0.01)(0.15) =0.2852
FR 3.1A What is the probability that a randomly selected full carton of Grande A eggs will weigh more than 850 grams?
P(x>850) P(Z> 850-840/ 7.9) P(Z>1.27) =0.102
FR 3.1B The weights of the empty cardboard containers have a mean of 20 grams and a standard deviation of 1.7 grams. It is reasonable to assume independence between the weights of the empty cardboard containers and the weights of the eggs. It is also reasonable to assume independence among the weights of the 12 eggs that are randomly selected for a full carton. i)What is the mean of X ii)What is the standard deviation of X?
P= weight of packaging X- weight of the ith egg W- weight of a full carton i) W=P+X1+X2+..+X12 W= P+12X Uw=Up +12Ux 840=20+12Ux 820=12Ux Ux=68.3 grams ii)O-2w= O-2p+12O-2x 62.31=2.89+12O-2x O-2x=4.96 Ox=2.23 grams
FR 4.1A Construct a 99 percent confidence interval for the proportion of vaccine-eligible people who had received fly vaccine. Use your confidence interval to comment on the belief that 45 percent of the vaccine-eligible people had received flu vaccine.
SRS, 10%, sample size n(p) & n(1-p) is greater than or equal to 10 a will construct a one-proportion z interval at the 99% confidence level p(hat)-+ Zstar(-/pH(1-pH)/n) 0.4162-+ 2.5758(0.0102) (0.38998, 0.44236)
A botanist is running an experiment on two fertilizers that require different amounts of watering. She has 40 test plot, half of which are in sunny locations, and half are in the shade. She randomly selects 10 sunny plots and 1- shady plots for which to use one fertilizer with its appropriate watering, while the remaining plots are for the other fertilizer with its appropriate watering. Of the following, which is the most important observation about this procedure?
The variable, fertilizer and water, are confounded.
FR 1.1 For values between 10 and 11 on the horizontal axis, the cumulative relative frequency plot is flat. In the context of this question, explain what that means.
This means no agents sold $1.1 to 1.0 million.
Two antidepressants are to be compared in the treatment of elderly patients in a nursing home. Each patient has his or her own room, some with spectacular views of the ocean. The experimental design is to create homogeneous blocks with respect to window view. How should randomization be used for a randomized block design?
Within each block, randomly pick half the patients to receive each antidepressant.
FR 2.1B Would you modify the design above if, instead of 100 male patients, there were 50 male and 50 female patients available for the study? If so, how would you modify your design? If not, why not?
Yes, I would block on gender, males & females, then put 50 randomly into magnet and placebo using the same 00-99 SRS technique.
An office manager believes that the percentage of employees arriving late is even greater than the previously claimed 7$. She conducts a hypothesis test on a random 200 employee arrivals and find 23 punching in late. Is this strong evidence against the 0.07 claim?
Yes, because the P-value is 0.0062
Which of the following is most useful in establishing cause-and-effect relationships?
a controlled experiment
Which of the following are unbiased estimators for the corresponding population parameters? I. Sample means II. sample proportions III. difference of smaple means IV. Difference of sample proportions
all are unbiased
A critical difference between experiments and observational studies is
an experiment often suggests a causal relationship, whereas an observational study only suggest an association
Sampling error occurs
because a sample statistic is used to estimate a population parameter
A researcher believes that a new diet should improve weight gain in lab mice. If the average gain for 12 mice is 5.3 ounces with a standard deviation of 0.5 oz, while 15 control mice on the old diet gain an average of 5 oz with a standard deviation of 0.4 oz, what is the P-value?
between .05 and .10
Which of the following is most important in minimiting the placebo effect?
blinding and a control
A candy manufacturer wants to test the consistency of the sugar content of chocolate covered cherries produced in one factory. The company decides to randomly select three boxes of chocolate covered cherries from each day's production run at the factory and analyze every cherry in each of these boxes as to sugar content. What type of sampling in this?
cluster (choose random, then test all in the GROUP)
A television network conducts a weekly survey to determine the proportion of viewers who watch various programs. For the coming year, they decide too double the sample size. The main benefit of this is to:
decrease the standard deviation of the sampling distribution
In general, how does doubling the sample size change the confidence interval size?
divides the interval size by 1.414
FR 4.1B Suppose a similar survey will be given to vaccine-eligible people in Canada by Canadian health officials. A 99 percent confidence interval for the proportion of people who will have received flu vaccine is to be constructed. What is the smallest sample size that can been used guarantee that the margin of error will be less than or equal to 0.02?
margin of error Zstar -/pH(1-pH)/n 2,5758-/(.25/n)<- 0.02
A real estate agent, working entirely on commission, weekly makes an average of $850 with a standard deviation of $260 selling property in the city and an average of $1340 with a standard deviation of $390 selling property in the suburbs. Assuming independence of what she sells in the two locations, what the mean and standard deviation of her total weekly sales?
mean $2190 and standard deviation $469
Which of the following are true statements? I. Test of significance are designed to measure the strength of evidence against the null hypothesis. II. A well-planned test of significance should result in a statement whether that the null hypothesis is true or that it is false. III. The null hypothesis is one-sided and expressed using either > or < if there is interest in deviations in only one direction.
none of the above gives the complete set of true responses
FR 1.2 What is the value of the correlation coefficient for operating cost per hour and number of passenger seats in the plane? Interpret this correlation.
r: 0.755
FR 2.2B Suppose this study is to conducted using a matched-pairs design. Describe a randomization process and identify an inference procedure for the study.
random assign a bin, & then spray one arm with new and one with old. randomly assign arm,s and compare the difference for each subject (old-new) & conduct a one-sample t test for the mean of the difference
FR 2.2C Which of the designs, the one in part or the one in part b, is better for testing the effectiveness of the new compound versus that of the current compound? Justify your answer.
the second (match pairs) b/c it eliminates one source of variability, as some people are more susceptible to bites.
A geneticist claims that four species of fruit flies should appear in the ratio 1:3:3:9. Suppose that a sample of 480 flies contained 25, 92, 68, and 295 flies of each species, respectively. Does a chi-squared test show sufficient evidence to reject the geneticist's claim?
the test gives sufficient evidence to reject the geneticist's claim
What is the probability of a Type II error when a hypothesis test is being conducted at the 5% significance level (a=.05)
there is insufficient information to answer this question
FR 1.2 What is the equation of the least squares regression line that describes the relationship between operating cost per hour and number of passenger seats in the plane? Define any variables used in this equation?
y(hat)= a + bx , y(hat)=1136+14.673x, y(hat)= cost per hour, x= # of seats
