STAT 2305 - Final Exam Review
Which measure of central tendency can be used for both numerical and categorical variables?
Mode
An appliance manufacturer claims to have developed a compact microwave oven that consumes a mean of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a population standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume a mean of 257.3 W. What is the population of interest?
the power consumption in all such microwave ovens
If P(B)=0.2, P(A | B)=0.7, P(B′)=0.8, and P(A | B′)=0.6, find P(B | A).
P(B | A)=0.226
A manager of the credit department for an oil company would like to determine whether the mean monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the mean owed is $83.40 with a sample standard deviation of $23.65. If you were to conduct a test to determine whether the auditor should conclude that there is evidence that the mean balance is different from $75, which test would you use?
t-test of population mean
The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. She performs a two-tail test of the null hypothesis that the mean for the stressed oak furniture is 650. The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test. Suppose the engineer had decided that the alternative hypothesis to test was that the mean was greater than 650. What would be the p-value of this one-tail test? Round to three decimal places.
0.040
The probability that a new advertising campaign will increase sales is assessed as being 0.80. The probability that the cost of developing the new ad campaign can be kept within the original budget allocation is 0.40. If the two events are independent, what is the probability that the cost is kept within budget and the campaign will increase sales?
0.32
The value of the cumulative standardized normal distribution at Z is 0.6255. What is the value of Z, rounded to two decimal places?
0.32
A sample of 200 students at a university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result. If the sample is a good representation of the population, what percent of those who did poorly on the midterm can be expected to have spent the weekend studying? Round to two decimal places.
22.22%
According to the empirical rule, if the data form a "bell-shaped" normal distribution, what percent of the observations will be contained within 3 standard deviations around the arithmetic mean?
99.7
Data on 1,500 students' height were collected at a larger university in the East Coast. Which of the following is the best chart for presenting the information?
A histogram
How many tissues should a package of tissues contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 tissue users yielded the following data on the number of tissues used during a cold: X=52, S=22. Suppose the test statistic does fall in the rejection region at α=0.05. Which of the following conclusion is correct?
At α=0.10, there is sufficient evidence to conclude that the mean number of tissues used during a cold is not 60 tissues.
If an economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000, which test should be used?
A one-tail test should be utilized.
Data on the number of credit hours of 20,000 students at a public university enrolled in a Spring semester were collected. Which of the following is the best for presenting the information?
A stem-and-leaf display
If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000, what type of test should be used?
A two-tail test should be utilized.
In a contingency table, what must be true about the number of rows and columns? - The number of rows and columns must always be the same. - The number of rows and columns must always be 2. - The number of rows and columns must add to 100% - None of the above
None of the above
If P(B)=0.55, P(A | B)=0.40, P(B′)=0.45, and P(A | B′)=0.80, find P(B | A).
P(B | A)=0.379
If you use a 0.05 level of significance in a two-tail hypothesis test, what decision will you make if ZSTAT=−2.18?
Reject H0 if ZSTAT<−1.961.96 or ZSTAT>+1.961.96. Since ZSTAT falls into the rejection region, reject H0.
For a one-tailed hypothesis test the critical value is 2.457. What is your statistical decision if tSTAT=+2.881?
Since the tSTAT value is greater than the critical value, reject H0.
Which of the following would be an appropriate null hypothesis?
The mean of a population is equal to 55.
Which of the arithmetic mean, median, mode, and geometric mean are resistant measures of central tendency?
The median and mode only
If the p-value is less than α in a two-tail test, what conclusion can be reached?
The null hypothesis should be rejected.
Construct an ordered array, given the following data from a sample of midterm exam scores in marketing. 88 78 78 74 94 78 85
The ordered array is 74, 78, 78, 78, 85, 88, 94.
In a one-tail hypothesis test where you reject H0 only in the upper tail, what is the p-value if ZSTAT=+2.30?
The p-value is 0.0107
Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of 23 years and a standard deviation of 3 years. If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?
The standard deviation of the sampling distribution is equal to 3 years.
A newspaper poll asked 2,150 adults in the U.S. a series of questions to find out their view on the U.S. economy. What is the population of interest?
all the adults living in the U.S. when the poll was taken
If the outcome of event A is not affected by event B, then what are events A and B said to be?
independent
If event A and event B cannot occur at the same time, then what are events A and B said to be?
mutually exclusive
How many tissues should a package of tissues contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 tissue users yielded the following data on the number of tissues used during a cold: X=52, S=22. Using the sample information provided, calculate the value of the test statistic, rounding to two decimal places.
t= -3.64
If, in a sample of n=25 selected from a normal population, X=59 and S=10, what is the value of tSTAT if you are testing the null hypothesis H0: μ=50?
tSTAT=4.5
An economist is interested in studying the incomes of consumers in a country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What is the width of the 90% confidence interval? Round to two decimal places.
$465.23
A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and analyzed with the following results: X=$50.50 and S=20. Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store in the mall if the amount spent follows a normal distribution. Round to two decimal places.
$50.50±$11.08
An alcohol awareness task force at a major university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The accompanying result was obtained. What is the probability that a randomly selected student did well on the midterm or went bar hopping the weekend before the midterm?
(80+30+70)/200 or (110+100-30)/200 or 90%
Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was no more than $3.0 million, rounding to four decimal places.
0.0151
Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players exceeded $3.5 million, rounding to four decimal places.
0.0228
The owner of a local nightclub has recently surveyed a random sample of n=250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the p-value associated with the test statistic, rounding to four decimal places?
0.0780
The employees of a company were surveyed on questions regarding their educational background (college degree or no college degree) and marital status (single or married). Of the 600 employees, 400 had college degrees, 100 were single, and 60 were single college graduates. What is the probability that an employee of the company does not have a college degree? Round to two decimal places.
0.33
The accompanying data are the duration in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier. What is the cumulative relative frequency for the percentage of calls that lasted 10 minutes or more?
0.41
According to a survey of American households, the probability that the residents own 2 cars if annual household income is over $50,000 is 80%. Of the households surveyed, 60% had incomes over $50,000 and 70% had 2 cars. What is the probability that the residents of a household own 2 cars and have an income over $50,000 a year?
0.48
The quality control engineer for a furniture manufacturer is interested in the mean amount of force necessary to produce cracks in stressed oak furniture. She performs a two-tail test of the null hypothesis that the mean for the stressed oak furniture is 650. The calculated value of the Z test statistic is a positive number that leads to a p-value of 0.080 for the test. Suppose the engineer had decided that the alternative hypothesis to test was that the mean was less than 650. What would be the p-value of this one-tail test? Round to three decimal places.
0.960
If two events are collectively exhaustive, what is the probability that one or the other occurs?
1.00
According to the Chebyshev rule, at least 75% of all observations in any data set are contained within how many standard deviations around the mean?
2
A sample of 200 students at a university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. If the sample is a good representation of the population, what percent of the students in the population can be expected to spend the weekend studying and do poorly on the midterm?
10%
An insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for automobile insurance. A representative from a local insurance agency selected a random sample of insured drivers and recorded, X, the number of claims each made in the last 3 years, with the accompanying results. How many total claims are represented in the sample?
111
Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are provided. Given that multiple vehicles were involved, what proportion of accidents involved alcohol? Round to two decimal places.
120/325 or 36.92%
At a meeting of information systems officers for regional offices of a national company, a survey was taken to determine the number of employees the officers supervise in the operation of their departments, where X is the number of employees overseen by each information systems officer. Across all the regional offices, how many total employees were supervised by those surveyed?
127
The accompanying data are the duration in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier. If 100 calls were sampled, how many of them would have lasted 20 minutes or more?
16
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation, rounding to three decimal places?
2.500
Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are provided. Given that 3 vehicles were involved, what proportion of accidents involved alcohol? Round to two decimal places.
20/50 or 40.00%
The accompanying data are the duration in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier. If 100 calls were randomly sampled, how many calls lasted 15 minutes or longer?
26
A sample of 200 students at a university was taken after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The following table contains the result. Of those who went bar hopping the weekend before the midterm in the sample, what percent of them did well on the midterm?
30%
An alcohol awareness task force at a major university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The accompanying result was obtained. What is the probability that a randomly selected student who went bar hopping did well on the midterm?
30/100 or 30%
If X=89, S=20, and n=16, and assuming that the population is normally distributed, construct a 90% confidence interval estimate of the population mean, μ.
80.23 ≤μ≤ 97.77
Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are provided. What proportion of accidents involved more than one vehicle?
325/400 or 81.25%
A survey was conducted to determine how people rated the quality of programming available on television. Respondents were asked to rate the overall quality from 0 (no quality at all) to 100 (extremely good quality). The stem-and-leaf display of the data is shown. What percentage of the respondents rated overall television quality with a rating of 80 or above?
4%
The owner of a fish market determined that the mean weight for a catfish is 3.2 pounds with a standard deviation of 0.8 pound. A citation catfish should be one of the top 2% in weight. Assuming the weights of catfish are normally distributed, at what weight (in pounds) should the citation designation be established? Round to two decimal places.
4.84 pounds
At a meeting of information systems officers for regional offices of a national company, a survey was taken to determine the number of employees the officers supervise in the operation of their departments, where X is the number of employees overseen by each information systems officer. How many regional offices are represented in the survey results?
40
Mothers Against Drunk Driving is a very visible group whose focus is to educate the public about the harm caused by drunk drivers. A study was recently done that emphasized the problem we all face with drinking and driving. Four hundred accidents that occurred on a Saturday night were analyzed. Two items noted were the number of vehicles involved and whether alcohol played a role in the accident. The numbers are provided. What proportion of accidents involved alcohol and a single vehicle?
50/400 or 12.5%
Form an ordered array, given the following data from a sample of n = 7 midterm exam scores in accounting. 86 73 62 60 98 66 68
60, 62, 66, 68, 73, 86, 98
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds? Round to the nearest percent.
67%
According to the empirical rule, if the data form a "bell-shaped" normal distribution, what percent of the observations will be contained within 1 standard deviation around the arithmetic mean?
68.26
If n=10 and π=0.70, what is the mean of the binomial distribution? Round to two decimal places.
7.00
If X=76, σ=8, and n=68, construct a 99% confidence interval estimate of the population mean, μ.
73.50 ≤μ≤ 78.50
The accompanying data are the duration in minutes of a sample of long-distance phone calls made within the continental United States reported by one long-distance carrier. If 100 calls were sampled, how many of them would have lasted less than 15 minutes?
74
According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within 2 standard deviations around the mean? Round to the nearest hundredth of a percent.
75.00%
A professor of economics at a small Texas university wanted to determine what year in school students were taking his tough economics course. A pie chart of the results is shown. What percentage of the class took the course prior to reaching their senior year?
86%
According to the Chebyshev rule, at least what percentage of the observations in any data set are contained within 3 standard deviations around the mean? Round to the nearest hundredth of a percent.
88.89%
You have collected data on the responses to two questions asked in a survey of 40 college students majoring in business: "What is your gender (Male=M; Female=F)?" and "What is your major (Accountancy=A; Computer Information Systems=C; Marketing=M)?." Which of the following is the best for presenting the data?
A contingency table
You have collected information on the market share of 5 different search engines used by U.S. Internet users in a quarter. Which of the following is the best for presenting the information?
A pie chart
Researchers suspect that the average number of units earned per semester by college students is rising. A researcher at Calendula College wishes to estimate the number of units earned by students during the spring semester at Calendula. To do so, he randomly selects 100 student transcripts and records the number of units each student earned in the spring term. He found that the average number of semester units completed was 12.96 units per student. Identify the population of interest to the researcher.
All Calendula College students enrolled in the spring.
In a one-tail hypothesis test where you reject H0 only in the lower tail, it was found that the p-value is 0.9945 if ZSTAT=+2.54. What is the statistical decision if you test the null hypothesis at the 0.05 level of significance?
Fail to reject the null hypothesis because the p-value is greater than or equal to the level of significance.
The owner of a local nightclub has recently surveyed a random sample of n=250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. What are the appropriate hypotheses to test?
H0: μ≤30 versus H1: μ>30
How many tissues should a package of tissues contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 tissue users yielded the following data on the number of tissues used during a cold: X=52, S=22. Suppose the alternative you wanted to test was H1: μ<60. State the correct rejection region for α=0.05.
Reject H0 if t< -1.6604
In a one-tail hypothesis test where you reject H0 only in the lower tail, it was found that the p-value is 0.0059 if ZSTAT=−2.52. What is your statistical decision if you test the null hypothesis at the 0.10 level of significance?
Reject the null hypothesis because the p-value is less than the level of significance.
A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the sample in the study.
The 250 randomly selected adult American pine trees.
In a one-tail hypothesis test where you reject H0 only in the upper tail, what is the critical value of the t-test statistic with 48 degrees of freedom at the 0.10 level of significance?
The critical value of the t-test statistic is 1.2994
If, in a sample of n=16 selected from a normal population, X=55 and S=20, what are the critical values of t if the level of significance, α, is 0.05, the null hypothesis, H0, is μ=50, and the alternative hypothesis, H1, is μ≠50?
The critical values of t are 2.13, -2.13
If, in a sample of n=25 selected from a normal population, X=59 and S=15, what is your statistical decision if the level of significance, α, is 0.10, the null hypothesis, H0, is μ=50, and the alternative hypothesis, H1, is μ≠50? Determine the critical value(s). Determine the test statistic, tSTAT. State your statistical decision. Choose the correct answer below.
The critical values are -1.7109, 1.7109. tSTAT= 3.0000 The test rejects the null hypothesis. The data provide sufficient evidence to conclude that the mean differs from μ=50.
If, in a sample of n=16 selected from a normal population, X=51 and S=20, how many degrees of freedom does the t test have if you are testing the null hypothesis
The degrees of freedom are 15
What does the width of each bar in a histogram correspond to?
The differences between the boundaries of the class
For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a right skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights.
The distribution is approximately normal with mean=10 minutes and standard error=0.8 minutes.
Which of the following is not a measure of central tendency?
The interquartile range
Which of the following would be an appropriate alternative hypothesis?
The population proportion is less than 0.65
For sample sizes greater than 30, when will the sampling distribution of the mean be approximately normally distributed?
The sampling distribution of the mean will be approximately normally distributed regardless of the shape of the population.
Which of the following statements about the sampling distribution of the sample mean is incorrect?
The standard deviation of the sampling distribution of the sample mean is equal to σ.
Which of the following statements is true about the Student's t distribution?
The t distribution: approaches the normal distribution as the sample size increases, has more area in the tails than does the normal distribution, and assumes the population is normally distributed.
The owner of a local nightclub has recently surveyed a random sample of n=250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. If she wants to have a level of significance at 0.01 what conclusion can she make?
There is not sufficient evidence that the mean age of her customers is greater than 30.
A study is under way in Yosemite National Forest to determine the adult height of American pine trees. Specifically, the study is attempting to determine what factors aid a tree in reaching heights greater than 60 feet tall. It is estimated that the forest contains 25,000 adult American pines. The study involves collecting heights from 250 randomly selected adult American pine trees and analyzing the results. Identify the population from which the study was sampled.
The 25,000 adult American pine trees in the forest.
Suppose we wish to test H0: μ=47 versus H1: μ>47. What will result if we conclude that the mean is greater than 47 when its true value is really 52?
We have made a correct decision.
How can a 99% confidence interval estimate can be interpreted?
We have 99% confidence that we have selected a sample whose interval does include the population mean. If all possible samples of size n are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval.
The chancellor of a major university was concerned about alcohol abuse on her campus and wanted to find out the proportion of students at her university who visited campus bars on the weekend before the final exam week. Her assistant took a random sample of 250 students. What is the answer on "whether you visited campus bars on the weekend before the final exam week" from students in the sample an example of?
a categorical variable
What is the classification of student major (accounting, economics, management, marketing, other) an example of?
a categorical variable
To monitor campus security, the campus police office is taking a survey of the number of students in a parking lot each 30 minutes of a 24-hour period with the goal of determining when patrols of the lot would serve the most students. If X is the number of students in the lot each period, what is X an example of?
a discrete variable
What is a summary measure that is computed to describe a characteristic of an entire population called?
a parameter
What is the universe or "totality of items or things" under consideration called?
a population
What is the portion of the universe that has been selected for analysis called?
a sample
What is the collection of all possible events called?
a sample space
What is a summary measure that is computed to describe a characteristic from only a sample of the population called?
a statistic
A recent survey reported that 40% of 18- to 29-year-olds in a certain country own tablets. Using the binomial distribution, complete parts (a) through (e) below. a. What is the probability that in the next six 18- to 29-year-olds surveyed, four will own a tablet? b. What is the probability that in the next six 18- to 29-year-olds surveyed, all six will own a tablet? c. What is the probability that in the next six 18- to 29-year-olds surveyed, at least four will own a tablet? d. What are the mean and standard deviation of the number of 18- to 29-year-olds who will own a tablet in a survey of six? e. What assumptions do you need to make in (a) through (c)? Select all that apply.
a. 0.1382 b. 0.0041 c. 0.1792 d. The mean number of 18- to 29-year-olds who own tablets out of six surveyed is 2.4000. The standard deviation of the number of 18- to 29-year-olds who own tablets out of six surveyed is 1.2000. e. Each observation is classified into one of two mutually exclusive and collectively exhaustive categories. The probability of an observation being classified as the event of interest, π, is constant from observation to observation. The outcome of any observation is independent of the outcome of any other observation.
The probability that a person has a certain disease is 0.03. Medical diagnostic tests are available to determine whether the person actually has the disease. If the disease is actually present, the probability that the medical diagnostic test will give a positive result (indicating that the disease is present) is 0.90. If the disease is not actually present, the probability of a positive test result (indicating that the disease is present) is 0.01. a. If the medical diagnostic test has given a positive result (indicating that the disease is present), what is the probability that the disease is actually present? b. If the medical diagnostic test has given a negative result (indicating that the disease is not present), what is the probability that the disease is not present?
a. 0.736 b. 0.997
A marketing researcher wants to estimate the mean amount spent ($) on a certain retail website by members of the website's premium program. A random sample of 96 members of the website's premium program who recently made a purchase on the website yielded a mean of $1500 and a standard deviation of $350. a. Construct a 95% confidence interval estimate for the mean spending for all shoppers who are members of the website's premium program. b. Interpret the interval constructed in (a).
a. 1,429.08 ≤μ≤ 1,570.92 b. With 95% confidence, the mean spending in dollars for all shoppers who are members of the website's premium program is between the lower and upper limits of the confidence interval.
A categorical variable has three categories, with the frequencies of occurrence below. a. Compute the percentage of values in each category. b. What conclusions can you reach concerning the categories?
a. 26, 54, 20 b. Category B occurs more than half of the time. The other two categories occur less than half of the time, with category C being the least likely to occur.
Planning and preparing for the unexpected, especially in response to a security incident, is one of the greatest challenges faced by information technology professionals today. An incident is described as any violation of policy, law, or unacceptable act that involves information assets. Incident Response (IR) teams should be evaluating themselves on metrics, such as incident detection or dwell time, to determine how quickly they can detect and respond to incidents in the environment. In a recent year, an institute surveyed organizations about internal response capabilities. The frequency distribution that summarizes the average time organizations took to detect incidents is given below. a. What percentage of organizations took fewer than 2 days, on average, to detect incidents? b. What percentage of organizations took between 2 and 31 days, on average, to detect incidents? c. What percentage of organizations took 31 or more days, on average, to detect incidents? d. What conclusions can you reach about average dwell time of incidents?
a. 40.16% b. 32.60% c. 27.24% d. Most of the incidents are detected in less than 31 days. Less than 35% of the incidents are detected after 31 days or more.
Given the probability distributions shown to the right, complete the following parts. a. Compute the expected value for each distribution. b. Compute the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A and Distribution B? d. Compare the results of distributions A and B.
a. A μ= 3.070; B μ=0.930 b. A σ=1.160; B σ=1.160 c. A P(x≥3)=0.73; B P(x≥3)=0.14 d. Distribution A is left-skewed, distribution B is right-skewed.
Given a normal distribution with μ=100 and σ=8, and given you select a sample of n=16, complete parts (a) through (d). a. What is the probability that X is less than 95? b. What is the probability that X is between 95 and 96.5? c. What is the probability that X is above 101.2? d. There is a 65% chance that X is above what value?
a. P(X<95)=0.0062 b. P(95<X<96.5)=0.0338 c. P(X>101.2)=0.2743 d. X=99.23
Given a standardized normal distribution (with a mean of 0 and a standard deviation of 1), complete parts (a) through (d). a. What is the probability that Z is less than 1.57? b. What is the probability that Z is greater than 1.86? c. What is the probability that Z is between 1.57 and 1.86? d. What is the probability that Z is less than 1.57 or greater than 1.86?
a. The probability that Z is less than 1.57 is 0.9418 b. The probability that Z is greater than 1.86 is 0.0314 c. The probability that Z is between 1.57 and 1.86 is 0.0268 d. The probability that Z is less than 1.57 or greater than 1.86 is 0.9732
The table to the right represents the annual percentage of smartphones sold in a certain region in 2011, 2012, and 2013 (projected). a. What conclusions can you reach about the market for smartphones in 2011, 2012, and 2013? b. What differences are there in the market for smartphones in 2011, 2012, and 2013?
a. Type 1 had the largest percentage of smartphones sold in all three years. Type 6 had the smallest or close to the smallest percentage of smartphones sold in all three years. Type 2 had the second largest percentage of smartphones sold in all three years. b. The percentages of Type 3 smartphones sold increased each year. In 2012, there were four types of smartphones that had percentages sold in the single digits, which is more types of smartphones than in 2011 and 2013. The percentages of Type 5 smartphones sold decreased each year. The percentages of Type 4 smartphones sold decreased each year.
The following is a set of data from a sample of n=5. 5, 2, 7, 4, 9 a. Compute the mean, median, and mode. b. Compute the range, variance, standard deviation, and coefficient of variation. c. Compute the Z scores. Are there any outliers? d. Describe the shape of the data set.
a. mean is 5.4, median is 5, There is no solution b. range is 7, variance is 7.3, standard deviation is 2.7, coefficient of variation is 50.03% c. -0.15, -1.26, 0.59, -0.52, 1.33; No outliers d. Positive (right-skewed)
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. What is the population of interest?
all the customers who have bought a Blu-ray player made by the company over the past 12 months
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. Classify the possible responses to the question "What brand of Blu-ray player did you purchase?."
categorical variable
If either event A or event B must occur, then what are events A and B said to be?
collectively exhaustive
When studying the simultaneous responses to two categorical questions, what representation of the data should you set up?
contingency table
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. Classify the possible responses to the question "How much time do you use the Blu-ray player every week on the average?."
continuous numerical variable
An alcohol awareness task force at a major university sampled 200 students after the midterm to ask them whether they went bar hopping the weekend before the midterm or spent the weekend studying, and whether they did well or poorly on the midterm. The accompanying result was obtained. What describes the events "Did Well on Midterm" and "Studying for Exam"?
dependent
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. Classify the possible responses to the question "In which year were you born?."
discrete numerical variable
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. Classify the possible responses to the question "Out of a 100-point score with 100 being the highest and 0 being the lowest, what is your satisfaction level on the videocassette recorder that you purchased?."
discrete numerical variable
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. Classify the possible responses to the question "What is your annual income rounded to the nearest thousands?."
discrete numerical variable
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. Classify the possible responses to the question "How many people are there in your household?."
discrete numerical variable
The manager of the customer service division of a major consumer electronics company is interested in determining whether the customers who have purchased a Blu-ray player made by the company over the past 12 months are satisfied with their products. The possible responses to the question "How many Blu-ray players made by other manufacturers have you used?" are values from what type of variable?
discrete variable
