stats chapter 9

A film distribution manager calculates that 9%9% of the films released are flops. If the manager is right, what is the probability that the proportion of flops in a sample of 457457 released films would differ from the population proportion by greater than 4%4%? Round your answer to four decimal places.

0.0028

A researcher believes that 8%8% of pet dogs in Europe are Labradors. If the researcher is right, what is the probability that the proportion of Labradors in a sample of 694694 pet dogs would differ from the population proportion by greater than 3%3%? Round your answer to four decimal places.

0.0036

A racing car consumes a mean of 114114 gallons of gas per race with a variance of 4949. If 3333 racing cars are randomly selected, what is the probability that the sample mean would be greater than 117.2117.2 gallons? Round your answer to four decimal places.

0.0044

The mean life of a television set is 141141 months with a variance of 256256. If a sample of 7171 televisions is randomly selected, what is the probability that the sample mean would be less than 136.3136.3 months? Round your answer to four decimal places.

0.0067

Suppose 44%44% of politicians are lawyers. If a random sample of size 853853 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 40%40%? Round your answer to four decimal places.

0.0093

A hotel manager believes that 17%17% of the hotel rooms are booked. If the manager is right, what is the probability that the proportion of rooms booked in a sample of 859859 rooms would be less than 14%14%? Round your answer to four decimal places.

0.0096

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 139139 millimeters, and a variance of 4949. If a random sample of 3636 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 2.92.9 millimeters? Round your answer to four decimal places.

0.0129

Suppose 51%51% of the children in a school are girls. If a sample of 493493 children is selected, what is the probability that the sample proportion of girls will be greater than 56%56%? Round your answer to four decimal places.

0.0132

A researcher believes that 8%8% of pet dogs in Europe are Labradors. If the researcher is right, what is the probability that the proportion of Labradors in a sample of 446446 pet dogs would differ from the population proportion by more than 3%3%? Round your answer to four decimal places.

0.0192

A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true proportion is 0.040.04. If 217217 are sampled, what is the probability that the sample proportion will differ from the population proportion by greater than 0.030.03? Round your answer to four decimal places.

0.0238

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 149149 millimeters, and a standard deviation of 55 millimeters. If a random sample of 4949 steel bolts is selected, what is the probability that the sample mean would be greater than 150.4150.4 millimeters? Round your answer to four decimal places.

0.0250

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 145145 millimeters, and a variance of 4949. If a random sample of 3434 steel bolts is selected, what is the probability that the sample mean would differ from the population mean by more than 2.62.6 millimeters? Round your answer to four decimal places.

0.0301

A film distribution manager calculates that 9%9% of the films released are flops. If the manager is accurate, what is the probability that the proportion of flops in a sample of 424424 released films would differ from the population proportion by more than 3%3%? Round your answer to four decimal places.

0.0309

Suppose 47%47% of the population has a college degree. If a random sample of size 460460 is selected, what is the probability that the proportion of persons with a college degree will differ from the population proportion by greater than 5%5%? Round your answer to four decimal places.

0.0316

A hotel manager assumes that 18%18% of the hotel rooms are booked. If the manager is correct, what is the probability that the proportion of rooms booked in a sample of 480480 rooms would be less than 15%15%? Round your answer to four decimal places.

0.0436

Suppose 40%40% of the students in a university are baseball players. If a sample of 781781 students is selected, what is the probability that the sample proportion of baseball players will be greater than 43%43%? Round your answer to four decimal places.

0.0436

Suppose babies born in a large hospital have a mean weight of 40884088 grams, and a variance of 55,69655,696. If 128128 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by more than 4141 grams? Round your answer to four decimal places.

0.0488

The mean number of words per minute (WPM) read by sixth graders is 8989 with a variance of 625625. If 9696 sixth graders are randomly selected, what is the probability that the sample mean would be greater than 93.0293.02 WPM? Round your answer to four decimal places.

0.0576

The mean life of a television set is 135135 months with a standard deviation of 1818 months. If a sample of 9898 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by greater than 3.43.4 months? Round your answer to four decimal places.

0.0615

A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true proportion is 0.050.05. If 300300 are sampled, what is the probability that the sample proportion will differ from the population proportion by more than 0.030.03? Round your answer to four decimal places.

0.0714

The quality control manager at a computer manufacturing company believes that the mean life of a computer is 120120 months, with a variance of 6464. If he is correct, what is the probability that the mean of a sample of 8989 computers would be less than 118.81118.81 months? Round your answer to four decimal places

0.0803

A scientist claims that 4%4% of viruses are airborne. If the scientist is accurate, what is the probability that the proportion of airborne viruses in a sample of 553553 viruses would be greater than 5%5%? Round your answer to four decimal places.

0.1151

A film distribution manager calculates that 4%4% of the films released are flops. If the manager is right, what is the probability that the proportion of flops in a sample of 463463 released films would be greater than 5%5%? Round your answer to four decimal places.

0.1361

A film distribution manager calculates that 6%6% of the films released are flops. If the manager is right, what is the probability that the proportion of flops in a sample of 575575 released films would be greater than 7%7%? Round your answer to four decimal places.

0.1562

The mean number of words per minute (WPM) read by sixth graders is 9090 with a standard deviation of 1919 WPM. If 7070 sixth graders are randomly selected, what is the probability that the sample mean would differ from the population mean by more than 3.073.07 WPM? Round your answer to four decimal places.

0.1770

A researcher believes that 6%6% of pet dogs in Europe are Labradors. If the researcher is right, what is the probability that the proportion of Labradors in a sample of 462462 pet dogs would be greater than 7%7%? Round your answer to four decimal places.

0.1814

Suppose 41%41% of the doctors in America are dentists. If a random sample of size 826826 is selected, what is the probability that the proportion of doctors who are dentists will be less than 40%40%? Round your answer to four decimal places

0.2810

The mean per capita consumption of milk per year is 126126 liters with a variance of 676676. If a sample of 9494 people is randomly selected, what is the probability that the sample mean would differ from the true mean by greater than 2.242.24 liters? Round your answer to four decimal places.

0.4010

The operation manager at a tire manufacturing company believes that the mean mileage of a tire is 36,30936,309 miles, with a standard deviation of 46934693 miles. What is the probability that the sample mean would differ from the population mean by less than 170170 miles in a sample of 211211 tires if the manager is correct? Round your answer to four decimal places.

0.4038

The head of maintenance at XYZ Rent-A-Car believes that the mean number of miles between services is 39813981 miles, with a standard deviation of 443443 miles. If he is correct, what is the probability that the mean of a sample of 3535 cars would differ from the population mean by less than 4747 miles? Round your answer to four decimal places.

0.4714

Suppose 52%52% of politicians are lawyers. If a random sample of size 416416 is selected, what is the probability that the proportion of politicians who are lawyers will be less than 53%53%? Round your answer to four decimal places.

0.6591

The mean number of words per minute (WPM) typed by a speed typist is 7373 with a variance of 144144. What is the probability that the sample mean would differ from the population mean by greater than 0.60.6 WPM if 7777 speed typists are randomly selected? Round your answer to four decimal places.

0.6600

Suppose babies born in a large hospital have a mean weight of 33663366 grams, and a variance of 244,036244,036. If 118118 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by less than 4545 grams? Round your answer to four decimal places.

0.6778

The cost of 55 gallons of ice cream has a variance of 4949 with a mean of 3030 dollars during the summer. What is the probability that the sample mean would differ from the true mean by less than 0.60.6 dollars if a sample of 145145 5-gallon pails is randomly selected? Round your answer to four decimal places.

0.6980

Suppose a large consignment of cell phones contained 22%22% defectives. If a sample of size 215215 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 3%3%? Round your answer to four decimal places.

0.7108

Suppose a batch of steel rods produced at a steel plant have a mean length of 151151 millimeters, and a variance of 6464. If 116116 rods are sampled at random from the batch, what is the probability that the mean length of the sample rods would differ from the population mean by less than 0.810.81 millimeters? Round your answer to four decimal places.

0.7242

A quality control expert at LIFE batteries wants to test their new batteries. The design engineer claims they have a standard deviation of 7777 minutes with a mean life of 551551 minutes. If the claim is true, in a sample of 135135 batteries, what is the probability that the mean battery life would be greater than 545.6545.6 minutes? Round your answer to four decimal places.

0.791

The mean life of a television set is 119119 months with a standard deviation of 1313 months. If a sample of 6767 televisions is randomly selected, what is the probability that the sample mean would differ from the true mean by less than 22 months? Round your answer to four decimal places.

0.7923

An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean output of 451451 watts with a variance of 144144. What is the probability that the mean amplifier output would be greater than 449.8449.8 watts in a sample of 7676 amplifiers if the claim is true? Round your answer to four decimal places.

0.8078

The standard deviation of the scores on a skill evaluation test is 421421 points with a mean of 17281728 points. If 309309 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 3636 points? Round your answer to four decimal places.

0.8664

Suppose 52%52% of the population has a retirement account. If a random sample of size 471471 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 4%4%? Round your answer to four decimal places.

0.9181

A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.050.05. If 212212 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.030.03? Round your answer to four decimal places.

0.9550

The standard deviation of the scores on a skill evaluation test is 260260 points with a mean of 16121612 points. If 344344 tests are sampled, what is the probability that the mean of the sample would differ from the population mean by less than 3030 points? Round your answer to four decimal places.

0.9676

The director of the library believes that 19%19% of the library's collection is checked out. If the director is right, what is the probability that the proportion of books checked out in a sample of 818818 books would differ from the population proportion by less than 3%3%? Round your answer to four decimal places.

0.9714

A bottle maker believes that 23%23% of his bottles are defective. If the bottle maker is accurate, what is the probability that the proportion of defective bottles in a sample of 602602 bottles would differ from the population proportion by less than 4%4%? Round your answer to four decimal places.

0.9802

Suppose 54%54% of the population has a retirement account. If a random sample of size 555555 is selected, what is the probability that the proportion of persons with a retirement account will differ from the population proportion by less than 5%5%? Round your answer to four decimal places.

0.9818

Suppose a large shipment of laser printers contained 22%22% defectives. If a sample of size 276276 is selected, what is the probability that the sample proportion will differ from the population proportion by less than 6%6%? Round your answer to four decimal places.

0.9840

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 137 millimeters, and a standard deviation of 8 millimeters. If a random sample of 31 steel bolts is selected, what is the probability that the sample mean would be greater than 133.5 millimeters? Round your answer to four decimal places.

0.9926

Thompson and Thompson is a steel bolts manufacturing company. Their current steel bolts have a mean diameter of 137137 millimeters, and a standard deviation of 88 millimeters. If a random sample of 3131 steel bolts is selected, what is the probability that the sample mean would be greater than 133.5133.5 millimeters? Round your answer to four decimal places.

0.9926

The mean per capita income is 24,65324,653 dollars per annum with a standard deviation of 778778 dollars per annum. What is the probability that the sample mean would be less than 2474524745 dollars if a sample of 441441 persons is randomly selected? Round your answer to four decimal places.

0.9935

A courier service company wishes to estimate the proportion of people in various states that will use its services. Suppose the true proportion is 0.060.06. If 305305 are sampled, what is the probability that the sample proportion will differ from the population proportion by less than 0.040.04? Round your answer to four decimal places.

0.9967

Judgment Sample

A sample in which the observations are selected by an expert in the field and not picked at random

systematic sample

A sample in which you choose a starting point and then every kth member of the population is included in the sample.

convienece sampling

A sample of observations that are easily obtained and not random

enable an analyst to determine the probable errors that an estimator might generate. Essentially, they allow the analyst a known degree of confidence in their estimation.

Probability samples

random number tables

Random number tables are composed of random digits, arranged in groups of 4 or 5 to improve readability. To use the random number table, randomly pick a row and column in the table as a starting point and select the appropriate number of digits. The appropriate number of digits is based on the size of the sampling frame. If the size of the sampling frame is from 1 to 99, then two digits should be selected. If the size of the sampling frame is from 100 to 999, then three digits should be selected.

sampling distribution of the sample mean.

The probability distribution which describes the distribution of the sample means

Which of the following is a good point estimator for the population mean?

__ x

Select the scenario which is an example of voluntary sampling.

a magazine wants to write a story bout its readers eating habits and asks readers to send in their response to the question " how often do you eat fast food"

Select the scenario which is an example of simple random sampling.

a mobil network operator wants to determine the mean age of its most active subscribers. a random sample of subscribers with the number of text exceeding 30 a day was selected

Select the scenario which is an example of simple random sampling

a random sample of hotel guest were chosen to fill out a email servey

Non-probability samples

are convenient means of obtaining sample data. If data from a non-probability sample is used to estimate a population parameter, there is no statistical theory that helps define the potential error of the estimate, and hence no statement about an estimate's reliability can be made.

Identify the sampling technique used for the following study. Poll each member of the entire population.

census

Identify the sampling technique used for the following study. For administrative purposes, a secretary needs to know the average length of tenure of instructors at their school

census

Identify the sampling technique used for the following study. For budget purposes, a financial advisor needs to know the average length of tenure of instructors at their college.

census

Identify the sampling technique used for the following study. Select each member of the population.

census

Identify the sampling technique used for the following study. A random number generator is used to choose twenty-five districts. Then a college student collects data from each person in these districts

cluster sample

Identify the sampling technique used for the following study. A school administrator interviews each member from each of the ten randomly chosen zoning districts in a town.

cluster sample

Identify the sampling technique used for the following study. A market researcher interviews each member from each of the fifteen randomly chosen neighborhoods throughout a city.

cluster sampling

Identify the sampling technique used for the following study. A random number generator is used to choose fifty cities. Then a biologist collects data from each person in these cities

cluster sampling

simple random sample

from a finite population is one in which every possible sample of the same size n has the same probability of being selected.

Select the scenario which is an example of voluntary sampling.

hotel admins want to get feedback on hotel services so they leave a questioner in every room

biased

if it over represents or under represents some segment(s) of the population

voluntary sampling

individuals are self-selected by responding to an incentive

cluster sampling

involves dividing the population into clusters, and randomly selecting a sample of clusters to represent the population. Cluster sampling is used when "natural" groupings are evident in the population

sampling frame

is a list which identifies all members of the population.

point estimator

is a single-valued estimate, calculated from the sample data, which is intended to be close to the true population value

sample

is a subset of the population. Data are collected from the sample in order to gain insight about the population

central limit theorem

is a very important theorem that summarizes the distribution of the sample mean. The distribution of the sample mean becomes closer to a normal distribution as the sample size becomes larger, regardless of the shape of the population from which the sample is drawn.

sampling distribution of a statistic

is the probability distribution of all values of the statistic when all possible samples of size n are taken from a population.

For a quantitative variable in a particular population, how many different sample means are there?

many

Suppose babies born in a large hospital have a mean weight of 32253225 grams, and a standard deviation of 535535 grams. If 106106 babies are sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by more than 5353 grams? Round your answer to four decimal places.

more than 53 grams is 0.3078 less than 53 grams is 0.6992

Which of the following is a good point estimator for the population standard deviation

s

Identify the sampling technique used for the following study. A pollster chooses fifty people at random from each neighborhood.

stratified sampling

Identify the sampling technique used for the following study. First, the population is subdivided by city. Then a political strategist uses a random number generator to select fifty members from each city to study.

stratified sampling

Identify the sampling technique used for the following study. A market researcher chooses thirty members of the sampling frame at random from each neighborhood.

stratified sampling

Identify the sampling technique used for the following study. First, the population is subdivided by region. Then a political strategist uses a random number generator to select twenty-five members from each region to study.

stratified sampling

Stratified Sampling

the population is divided into strata, which are subpopulations. A strata can be any identifiable characteristic that can be used to classify the population. If the population consists of people, then strata could be sex, income, political party, religion, education, race, or location

Select the scenario which is an example of simple random sampling

to determine the gpa of the school a simple random sample was taken

Select the scenario which is an example of simple random sampling.

to obtain feedback on the hotel service, a random sample of guests were chosen to fill out a questioner via email

Which of the following is a good point estimator for the population variance?

u

standard error of the mean

which is the standard deviation of a point estimator. We will use the standard error of the mean to indicate how far the sample mean is from the population mean. Suppose, for example, you were drawing a sample from a population whose variance is 0.000610.00061. The variance of the sample means for samples of size n=2n=2 would be