Questions and Answers of Statistics Informed Decisions Using Data

A nutritionist wants to estimate the difference between the proportion of males and females who consume the USDA's recommended daily intake of calcium. What sample size should be obtained if she
A researcher wishes to compare IQ scores of patients with and without cysts. She obtains a random sample of 708 patients of each category who take an IQ test and determines each patient's
(a) Determine $d_{i}=X_{i}-Y_{i}$ for each pair of data.(b) Compute $\bar{d}$ and $s_{d}$.(c) Test if \(\mu_{d}
A researcher wishes to compare academic aptitudes of married mathematicians and their spouses. She obtains a random sample of 287 such couples who take an academic aptitude test and determines each
Test whether $p_{1}>p_{2}$. Sample data: $x_{1}=127, n_{1}=255$, $x_{2}=133, n_{2}=309$, where $\alpha=0.05$.Conduct each test at the $\alpha$ level of significance by determining(a) the
Test whether $p_{1} > p_{2}$. Sample data: $x_{1}=28, n_{1}=254$, $x_{2}=36, n_{2}=302$, where $\alpha=0.010$.Conduct each test at the $\alpha$ level of significance by determining(a)
Test whether $p_{1} > p_{2}$. Sample data: $x_{1}=28, n_{1}=254$, $x_{2}=36, n_{2}=301$, where $\alpha=0.05$.Conduct each test at the $\alpha$ level of significance by determining(a) the
Test whether $p_{1}>p_{2}$. Sample data: $x_{1}=120, n_{1}=248$, $x_{2}=139, n_{2}=313$, where $\alpha=0.010$.Conduct each test at the $\alpha$ level of significance by determining(a) the
$x_{1}=357, n_{1}=514, x_{2}=426, n_{2}=566,90 \%$ confidence Construct a confidence interval for $p_{1}-p_{2}$ at the given level of confidence.
$x_{1}=371, n_{1}=509, x_{2}=434, n_{2}=579,95 \%$ confidence Construct a confidence interval for $p_{1}-p_{2}$ at the given level of confidence.
$x_{1}=30, n_{1}=257, x_{2}=34, n_{2}=318,99 \%$ confidence Construct a confidence interval for $p_{1}-p_{2}$ at the given level of confidence.
$x_{1}=30, n_{1}=225, x_{2}=40, n_{2}=317,95 \%$ confidence Construct a confidence interval for $p_{1}-p_{2}$ at the given level of confidence.
In 1948, an organization surveyed 1100 adults and asked, "Are you a total abstainer from, or do you on occasion consume, alcoholic beverages?" Of the 1100 adults surveyed, 374 indicated that they
A survey asked, "How many tattoos do you currently have on your body?" Of the 1248 males surveyed, 176 responded that they had at least one tattoo. Of the 1026 females surveyed, 147 responded that
A physical therapist wants to determine the difference in the proportion of men and women who participate in regular sustained physical activity. What sample size should be obtained if she wishes the
The two major college entrance exams that a majority of colleges accept for admission are the SAT and ACT. ACT looked at historical records and established 22 as the minimum ACT math score for a
What do you think is more important- to protect the right of Americans to own guns or to control gun ownership? When asked this question, $46 \%$ of all Americans said protecting the right to own
A 2009 study by Princeton Survey Research Associates International found that $34 \%$ of teenagers text while driving. Does a recent survey conducted by Consumer Reports, which found that 353 of
According to the U.S. Department of Agriculture (USDA), $48.9 \%$ of males aged 20 to 39 years consume the recommended daily requirement of calcium. After an aggressive "Got Milk" advertising
The website fueleconomy.gov allows drivers to report the miles per gallon of their vehicle. The data in Table 7 shows the reported miles per gallon of 2011 Ford Focus automobiles for 16 different
Use StatCrunch to estimate a 95\% confidence interval for the mean and median miles per gallon of a 2011 Ford Focus based on the sample data in Table 7.Approach The steps for constructing confidence
Suppose the following data represent the heights (in inches) of a random sample of males: $63,67,68,69,73,74$. Which of the following could be a possible bootstrap sample?(a)
Suppose the following data represent the heights (in inches) of a random sample of males: $63,66,67,70,73,75$. Below are three bootstraps samples. For each bootstrap sample, determine the bootstrap
IQ scores are known to be approximately normally distributed with mean 100 and standard deviation 15 .(a) Simulate obtaining a random sample of 12 IQ scores from this population.(b) Use the data from
The exponential probability distribution can be used to model waiting time in line or the lifetime of electronic components. Its density function is skewed right. Suppose the wait-time in a line can
Certain statistics are difficult to bootstrap. One such statistic is the median. Consider the following to see why.(a) Simulate obtaining a random sample of 12 IQ scores. Recall IQ scores are
A friend of yours wants to play a simple coin-flipping game. If the coin comes up heads, you win; if it comes up tails, your friend wins. Suppose the outcome of five plays of the game is
Determine the null and alternative hypotheses. State whether the test is two tailed, left-tailed, or right-tailed.(a) The Medco pharmaceutical company has just developed a new antibiotic for
Problem The Medco pharmaceutical company has just developed a new antibiotic. Two percent of children taking competing antibiotics experience headaches as a side effect. A researcher for the Food and
The Medco pharmaceutical company has just developed a new antibiotic. Two percent of children taking competing antibiotics experience a headache as a side effect. A researcher for the Food and Drug
$H_{0}: \sigma=9$The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested?
$H_{0}: \mu=7$$H_{1}: \sigma7$The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being tested?
$H_{0}: \mu=110$\(H_{1}: \mu
$H_{0}: \sigma=7.8$$H_{1}: \sigma eq 7.8$The null and alternative hypotheses are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed. What parameter is being
For students who first enrolled in two year public institutions in a recent semester, the proportion who earned a bachelor's degree within six years was 0.386 . The president of a certain college
Single-Family Home Price Three years ago, the mean price of an existing single-family home was $\$ 243,787$. A real estate broker believes that existing home prices in her neighborhood are
According to a report, the standard deviation of monthly cell phone bills was $\$ 49.11$ three years ago. A researcher suspects that the standard deviation of monthly cell phone bills is different
For the hypotheses in Problem 15, the null hypothesis is rejected.Data from Problem 15Complete College For students who first enrolled in two year public institutions in a recent semester, the
Popcorn Consumption According to a food website, the mean consumption of popcorn annually by Americans is 59 quarts. The marketing division of the food website unleashes an aggressive campaign
E-Cigs According to the Centers for Disease Control and Prevention, $9.8 \%$ of high school students currently use electronic cigarettes. A high school counselor is concerned the use of e-cigs at
84%Determine the critical value zα/2 that corresponds to the given level of confidence.
91%Determine the critical value zα/2 that corresponds to the given level of confidence.
82%Determine the critical value zα/2 that corresponds to the given level of confidence.
97%Determine the critical value zα/2 that corresponds to the given level of confidence.
Lower bound = 0.229, upper bound = 0.771, n = 1200 Determine the point estimate of the population proportion, the margin of error for each confidence interval, and the number of individuals in the
Lower bound = 0.102, upper bound = 0.348, n = 1000 Determine the point estimate of the population proportion, the margin of error for each confidence interval, and the number of individuals in the
Lower bound = 0.257, upper bound = 0.513, n = 1200 Determine the point estimate of the population proportion, the margin of error for each confidence interval, and the number of individuals in the
Lower bound = 0.114, upper bound = 0.606, n = 1200 Determine the point estimate of the population proportion, the margin of error for each confidence interval, and the number of individuals in the
x = 105, n = 150, 90% confidence Construct a confidence interval of the population proportion at the given level of confidence.
x = 45, n = 150, 99% confidence Construct a confidence interval of the population proportion at the given level of confidence.
x = 80, n = 200, 95% confidence Construct a confidence interval of the population proportion at the given level of confidence.
x = 120, n = 1200, 94% confidence Construct a confidence interval of the population proportion at the given level of confidence.
In a survey of 2065 adults in a certain country conducted during a period of economic uncertainty, 54% thought that wages paid to workers in industry were too low. The margin of error was 9
A national survey of 1000 adult citizens of a nation found that 25% dreaded Valentine’s Day. The margin of error for the survey was 5.6 percentage points with 85% confidence. Explain what this
A researcher wishes to estimate the proportion of adults who have high-speed Internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 99% confidence
A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 3 percentage points with 99%
A television sports commentator wants to estimate the proportion of Americans who follow professional football. What sample size should be obtained if he wants to be within 3 percentage points with
In a poll, 37% of the people polled answered yes to the question: “Are you in favor of the death penalty for a person convicted of murder?” The margin of error in the poll was 3%, and the
A group conducted a poll of 2049 likely voters just prior to an election. The results of the survey indicated that candidate A would receive 48% of the popular vote and candidate B would receive 46%
Explain what “98% confidence” means in a 98% confidence interval.
By how many times does the sample size have to be increased to decrease the margin of error by a factor of 1/3?
The website fueleconomy.gov allows drivers to report the miles per gallon of their vehicle. The data in Table 2 show the reported miles per gallon of 2011 Ford Focus automobiles for 16 different
(a) Use statistical software such as Minitab or StatCrunch to obtain 1500 simple random samples of size n = 5 from a normal population with μ = 50 and σ = 10. Calculate the sample mean and sample
Find the t-value such that the area under the t-distribution to the right of the t-value is 0.10, assuming 15 degrees of freedom (df). That is, find t0.10 with 15 degrees of freedom.ApproachStep 1
The website fueleconomy.gov allows drivers to report the miles per gallon of their vehicle. The data in Table 3 show the reported miles per gallon of 2011 Ford Focus automobiles for 16 different
We again consider the problem of estimating the miles per gallon of a 2011 Ford Focus. How large a sample is required to estimate the mean miles per gallon within 0.5 mile per gallon with 95%
$n=12$; Correlation $=0.987$A simple random sample of size \(n
$n=15$; Correlation $=0.893$A simple random sample of size \(n
$n=13 ;$ Correlation $=0.966$A simple random sample of size \(n
$n=9$; Correlation $=0.997$A simple random sample of size \(n
Lower bound: 20 , upper bound: 26 Determine the point estimate of the population mean and margin of error for each confidence interval.
Lower bound: 16 , upper bound: 26 Determine the point estimate of the population mean and margin of error for each confidence interval.
Lower bound: 19 , upper bound: 27 Determine the point estimate of the population mean and margin of error for each confidence interval.
Lower bound: 21 , upper bound: 29 Determine the point estimate of the population mean and margin of error for each confidence interval.
In a survey, 700 adults in a certain country were asked how many hours they worked in the previous week. Based on the results, a $95 \%$ confidence interval for mean number of hours worked was
A trade magazine routinely checks the drive-through service times of fast-food restaurants. A 95% confidence interval that results from examining 602 customers in one fast-food chain's drivethrough
For the "Hours Worked" survey conducted by Gallup in Problem 21, provide two recommendations for increasing the precision of the interval.Data from Problem 21In a survey, 700 adults in a certain
A doctor wants to estimate the mean HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean HDL cholesterol within 2 points with $99 \%$ confidence
People were polled on how many books they read the previous year. Initial survey results indicate that $s=18.8$ books.(a) How many subjects are needed to estimate the mean number of books read the
Find the critical values that separate the middle $90 \%$ of the chi-square distribution from the 5% area in each tail, assuming 15 degrees of freedom.Approach Perform the following steps to obtain
Table 4 shows the sale price of 12 randomly selected 6-year-old Chevy Corvettes. Construct a $90 \%$ confidence interval for the population variance and standard deviation of the price of a 6-
$90 \%$ confidence, $n=25$Find the critical values $\chi_{1-\alpha / 2}^{2}$ and $\chi_{\alpha / 2}^{2}$ for the given level of confidence and sample size.
$80 \%$ confidence, $n=15$Find the critical values $\chi_{1-\alpha / 2}^{2}$ and $\chi_{\alpha / 2}^{2}$ for the given level of confidence and sample size.
$98 \%$ confidence, $n=30$Find the critical values $\chi_{1-\alpha / 2}^{2}$ and $\chi_{\alpha / 2}^{2}$ for the given level of confidence and sample size.
$98 \%$ confidence, $n=10$Find the critical values $\chi_{1-\alpha / 2}^{2}$ and $\chi_{\alpha / 2}^{2}$ for the given level of confidence and sample size.
A simple random sample of size $n$ is drawn from a population that is known to be normally distributed. The sample variance, $s^{2}$, is determined to be 12.4.(a) Construct a $90 \%$ confidence
A simple random sample of size $n$ is drawn from a population that is known to be normally distributed. The sample variance, $s^{2}$, is determined to be 19.8 .(a) Construct a $95 \%$
The following data represent the $\mathrm{pH}$ of rain for a random sample of 12 rain dates in a particular region. A normal probability plot suggests the data could come from a population that is
Robert wishes to estimate the mean number of miles that his Buick Lacrosse can be driven on a full tank of gas. He fills up his car with regular unleaded gasoline from the same gas station 10 times
A simple random sample of size $n=450$ individuals who are currently employed is asked if they work at home at least once per week. Of the 450 employed individuals surveyed, 42 responded that they
A simple random sample of size $n=23$ is drawn from a population that is normally distributed. The sample mean is found to be $\bar{x}=67$, and the sample standard deviation is found to be
A simple random sample of size $n=40$ is drawn from a population. The sample mean is found to be $\bar{x}=120.8$, and the sample standard deviation is found to be $s=12.3$. Construct a \(99
A simple random sample of size 20 is drawn from a population that is known to be normally distributed. The sample variance, $s^{2}$, is determined to be 12.8 . Construct a $90 \%$ confidence
A simple random sample of size $n=25$ is drawn from a population that is normally distributed. The sample variance is found to be $s^{2}=3.97$. Construct a $95 \%$ confidence interval for the
Estate Tax Returns In a random sample of 100 audited estate tax returns, it was determined that the mean amount of additional tax owed was $\$ 3481$ with a standard deviation of $\$ 2588$.
The Gallup Organization conducted a poll in which a simple random sample of 1016 Americans 18 and older were asked, “Do you consider the amount of federal income tax you have to pay is fair?” Of
When the Gallup Organization conducted the poll introduced in Example 1, 54.9% of those surveyed considered the amount of federal income tax they have to pay as fair. Gallup reported its “survey
In the Parent–Teen Cell Phone Survey conducted by Princeton Survey Research Associates International, 800 randomly sampled 16-to 17-year-olds living in the United States were asked whether they
For the problem of estimating the proportion of 16- to 17- year-old teenagers who text while driving, determine the effect on the margin of error by increasing the level of confidence from 95% to
An economist wants to know if the proportion of the U.S. population who commutes to work via carpooling is on the rise. What size sample should be obtained if the economist wants an estimate within 2

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