Questions and Answers of Statistics Informed Decisions Using Data

Construct a 95% confidence interval for the predicted mean total cholesterol of all 42-ear-old females using statistical software. Construct a $95 \%$ prediction interval for the predicted total
A family doctor wishes to further examine the variables that affect his female patients' total cholesterol. He randomly selects 14 of his female patients and asks them to determine their average
Test $H_{0}: \beta_{1}=\beta_{2}=0$ versus $H_{1}$ : at least one $\beta_{i} eq 0$ for the regression model found in Example 2.Approach To perform this inference, we need to determine whether
For our model presented in Example 2, test the hypotheseswhere $\beta_{1}$ is the slope coefficient for the explanatory variable age, and $\beta_{2}$ is the slope coefficient for the explanatory
Suppose a multiple regression model is given by $\hat{y}=3.64 x_{1}-7.99 x_{2}+30.89$. An interpretation of the coefficient of $x_{1}$ would be, "if $x_{1}$ decreases by 1 unit, then the
Suppose that a multiple regression has $k=7$ explanatory variables. The coefficient of determination, $R^{2}$, is found to be 0.829 based on a sample of $n=20$ observations.(a) Compute the
What does it mean when we say that the explanatory variables have an additive effect or do not interact?
What does it mean when we say that $t$-test statistics are marginal?
Fill in the blank. If there is __________ between $x_{1}$ and $x_{2}$ in a least-squares regression model, we would build a model of the form \(\hat{y}_{i}=\beta_{0}+\beta_{1} x_{1 i}+\beta_{2}
Fill in the blank. $\mathrm{A}(\mathrm{n})$ ___________ or ____________ variable is a qualitative explanatory variable in a multiple regression model that takes on the value 0 or 1 .
Use the stepwise regression procedure to find the best model to describe miles per gallon for the data in Table 10. Use a level of significance of $\alpha=0.15$ as the criteria for an explanatory
For the data set below, use a partial $F$-test to determine whether the variables $x_{4}$ and $x_{5}$ do not significantly help to predict the response variable, $y$. Use the $\alpha=0.10$
First-Year College GPA Researchers at the College Board wanted to build a model that describes one's first-year college GPA. The researchers obtained the following model:\[\hat{y}=0.06 x_{1}+0.07
A nutritionist wants to develop a model that describes the relation between the calories, total fat content, protein, sugar, and carbohydrates in cheeseburgers at fast-food restaurants. She obtains
Suppose we record the gender of the 15 students enrolled in an introductory statistics course as they enter the classroom. The males are denoted by a blue M and the females are denoted by a red
Find the upper and lower critical values at the $\alpha=0.05$ level of significance from Table XI if $n_{1}=10$ and $n_{2}=5$.Approach Determine the intersection of the row corresponding to
The data in Table 2 represent the monthly rates of return of the Standard and Poor's Index of 500 Stocks from January 2012 through March 2015. Test the randomness of positive monthly rates of return
A sequence is given:F F M M F M M F M F F M M F(a) Identify the values of n, $n_{1}, n_{2}$, and $r$.(b) Determine the critical values at the $\alpha=0.05$ level of significance.(c) Conduct a
A sequence is given:YN Y YN Y Y YN N N N N N N N Y Y (a) Identify the values of n, $n_{1}, n_{2}$, and $r$.(b) Determine the critical values at the $\alpha=0.05$ level of significance.(c)
In a least-squares regression model, the residuals are assumed to be random. The following data represent the life expectancy of a female born in the given year.The least-squares regression equation
Using statistical software or a graphing calculator with advanced statistical features, randomly generate a sequence of 20 integer values, each either 0 or 1 . Conduct a runs test at the
A recent General Social Survey asked the following two questions of a random sample of 1492 adult Americans under the hypothetical scenario that the government suspected that a terrorist act was
In fiscal year (FY) 2013-2014 (July 2013-June 2014), the Florida Lottery generated $\$ 5.37$ billion in total sales. Over that period, the state spent $\$ 37.5$ million on advertising to promote
Problem Compute the $F$-test statistic for the data in Table 2(a). The data are presented again for convenience.Approach Follow Steps 1 through 6. Table 2 x1 12 x3 31 32 4 7 10 14 10 6 5 8 10 2 3
Verify the normality requirement for the data analyzed in Example 1.Approach Compute the mean value for each level of the factor and subtract the result from each observation to obtain the residuals.
Find the critical value from the Studentized range distribution with $u=7$ degrees of freedom and $k=3$ degrees of freedom, with a familywise error rate $\alpha=0.05$.Approach Look in Table
(a) $\alpha=0.05, u=12$, and $k=17$.(b) $\alpha=0.01, u=30$, and $k=19$.(c) $\alpha=0.05, u=8$, and $k=14$.(d) $H_{0}: \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}=\mu_{5}$, with $n=20$ at
(a) $\alpha=0.05, u=11$, and $k=16$.(b) $\alpha=0.01, u=12$, and $k=17$.(c) $\alpha=0.05, u=30$, and $k=19$.(d) $H_{0}: \mu_{1}=\mu_{2}=\mu_{3}=\mu_{4}=\mu_{5}$, with $n=22$ at
A researcher is interested in the effect of four diets on the weight gain of newborn rats. The researcher randomly assigns rats from the same mother to each treatment so that a set of four rats
Verify the normality requirement for the data analyzed in Example 2.Approach Obtain the residuals and draw the normal probability plot.Data from Example 2A researcher is interested in the effect of
Use Tukey's test to determine which pairwise means differ for the data in Example 2, with a familywise error rate of $\alpha=0.05$, using Minitab.Approach The steps for conducting Tukey's test
We presented data for an experimental drug that was meant to increase HDL cholesterol. The data are represented in Table 13 for convenience.(a) HDL cholesterol levels are known to have a distribution
Verify the normality requirement for the HDL data analyzed in Example 3. Approach We will use Minitab to obtain the residuals and draw the normal probability plot.Data from Example 3We presented data
Draw an interaction plot for the data from Example 3.By-Hand Approach Follow Steps 1 and 2.Technology Approach Use Minitab or StatCrunch to draw the interaction plot. The steps to follow are given in
An educational psychologist conducts an experiment to determine whether varying the conditions in which learning and testing take place affects test results. She randomly selects 20 students who are
Use statistical software to perform Tukey's test to determine which pairwise means differ for the data presented in Example 3 using a familywise error rate of $\alpha=0.05$.Approach We will use
If factor A has 4 levels and factor B has 3 levels in a two-way ANOVA, we have a a ___x_____factorial design
Is there a relationship between marital status and happiness? The data in Table 4 show the marital status and happiness of individuals who participated in the General Social Survey. Compute the
Does one's happiness depend on one's marital status? We present the data from Table 4 in Example 1 again in Table 9 to answer this question. Use the $\alpha=0.05$ level of significance.Data from
Find the conditional distribution of happiness by marital status for the data in Table 9. Then draw a bar graph that represents the conditional distribution of happiness by marital status.Approach
One growing concern regarding the U.S. economy is the inequality in the distribution of income. The data in Table 1 represent the distribution of household income for various levels of income in
One growing concern regarding the U.S. economy is the inequality in the distribution of income. An economist wants to know if the distribution of income is changing, so she randomly selects 1500
An obstetrician wants to know whether the proportion of children born on each day of the week is the same. She randomly selects 500 birth records and obtains the data shown in Table 3 (based on data
Test whether \(\mu_{1}
If $n_{1}=31, s_{1}=12, n_{2}=51$, and $s_{2}=10$, test whether $\sigma_{1}>\sigma_{2}$ at the $\alpha=0.05$ level of significance.Perform the appropriate hypothesis test.
(a) Test the hypothesis that $\mu_{1} eq \mu_{2}$ at the $\alpha=0.1$ level of significance for the given sample data.(b) Construct a $90 \%$ confidence interval for $\mu_{1}-\mu_{2}$.(c)
(a) Test the hypothesis that $\mu_{1} eq \mu_{2}$ at the $\alpha=0.1$ level of significance for the given sample data.(b) Construct a 95\% confidence interval for $\mu_{1}-\mu_{2}$.(c) Test the
(a) Test the hypothesis that $\mu_{1}(b) Test the hypothesis that \(\sigma_{1} eq \sigma_{2}$ at the $\alpha=0.05$ level of significance for the given sample data.Assume that the populations are
Using the data from Problem 7, test whether the standard deviation of acidity in the rain near Houston, Texas, is different from that near Chicago, Illinois, at the $\alpha=0.05$ level of
Dr. Penelope Nicholls is interested in exploring a possible connection between high plasma homocysteine (a toxic amino acid created by the body as it metabolizes protein) levels and cardiac
According to the U.S. Census Bureau, $7.1 \%$ of all babies born are of low birth weight ( \(
(a) Test whether \(\mu_{1}
Test whether $\mu_{1}>\mu_{2}$ at the $\alpha=0.05$ level of significance for the given sample data.Assume that the populations are normally distributed.
Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. The students in group 1 were asked to spend 5 minutes thinking about what
Kids and Leisure A random sample of 40 adults with no children under the age of 18 years results in a mean daily leisure time of 5.25 hours, with a standard deviation of 2.36 hours. A random sample
Comparing Step Pulses A physical therapist wanted to know whether the mean step pulse of men was less than the mean step pulse of women. She randomly selected 60 men and 77 women to participate in
Right-tailed test with $\alpha=0.01$, degrees of freedom in the numerator $=12$, degrees of freedom in the denominator $=25$.Find the critical value( $s$ ) for $\alpha$.
Right-tailed test with $\alpha=0.025$, degrees of freedom in the numerator $=15$, degrees of freedom in the denominator $=50$.Find the critical value( $s$ ) for $\alpha$.
Two-tailed test with $\alpha=0.05$, degrees of freedom in the numerator $=12$, degrees of freedom in the denominator $=20$.Find the critical value( $s$ ) for $\alpha$.
Two-tailed test with $\alpha=0.10$, degrees of freedom in the numerator $=12$, degrees of freedom in the denominator $=20$.Find the critical value( $s$ ) for $\alpha$.
Left-tailed test with $\alpha=0.01$, degrees of freedom in the numerator $=20$, degrees of freedom in the denominator $=25$.Find the critical value( $s$ ) for $\alpha$.
Left-tailed test with $\alpha=0.05$, degrees of freedom in the numerator $=25$, degrees of freedom in the denominator $=15$.Find the critical value( $s$ ) for $\alpha$.
$\sigma_{1} eq \sigma_{2}$ at the $\alpha=0.1$ level of significanceAssume that the populations are normally distributed. Test the given hypothesis.
$\sigma_{1}>\sigma_{2}$ at the $\alpha=0.01$ level of significanceAssume that the populations are normally distributed. Test the given hypothesis.
\(\sigma_{1}
\(\sigma_{1}
$\sigma_{1}>\sigma_{2}$ at the $\alpha=0.05$ level of significanceAssume that the populations are normally distributed. Test the given hypothesis.
Clifford Adelman, a researcher with the Department of Education, followed a cohort of students who graduated from high school in 1992, monitoring the progress the students made toward completing a
In Example 2 from Section 10.3, the quality-control engineer for M\&MMars tested whether the mean weight of fun-size Snickers was 20.1 grams. Suppose that the standard deviation of the weight of
(a) Determine the critical values for a right-tailed test of a standard population deviation with 18 degrees of freedom at $\alpha=0.1$ level of significance.(b) Determine the critical values for a
(a) Determine the critical values for a right-tailed test of a standard population deviation with 15 degrees of freedom at $\alpha=0.1$ level of significance.(b) Determine the critical values for a
To test $H_{0}: \sigma=50$ versus \(H_{1}: \sigma
To test $H_{0}: \sigma=0.35$ versus \(H_{1}: \sigma
A simple random sample of size $n=200$ drivers were asked if they drive a car manufactured in a certain country. Of the 200 drivers surveyed, 109 responded that they did. Determine if more than
A simple random sample of size $n=20$ is drawn from a population that is normally distributed. The sample variance is found to be 49.3. Determine whether the population variance is less than 95 at
We tested $H_{0}: p=0.5$ versus \(H_{1}: p
Compute the power of the test for the situation in Example 1.Approach The power of the test is $1-\beta$. In Example 1, we found that $\beta$ is 0.7764 when the true population proportion is 0.48
$H_{0}: p=0.6$ versus $H_{1}: p>0.6$$n=250 ; x=165$Test the hypothesis at the $\alpha=0.05$ level of significance, using(a) the classical approach(b) the P-value approach. Be sure to verify
The mean height of American males is 69.5 inches. The heights of the 43 male U.S. presidents* (Washington through Obama) have a mean 70.78 inches and a standard deviation of 2.77 inches. Treating the
The "fun size" of a Snickers bar is supposed to weigh 20 grams. Because the penalty for selling candy bars under their advertised weight is severe, the manufacturer calibrates the machine so the mean
According to the American Community Survey, the mean travel time to work in Collin County, Texas, in 2013 was 27.5 minutes. The Department of Transportation reprogrammed all the traffic lights in
(a) Determine the critical value(s) for a right-tailed test of a population mean at the $\alpha=0.01$ level of significance with 15 degrees of freedom.(b) Determine the critical value(s) for a
To test $H_{0}: \mu=50$ versus \(H_{1}: \mu
To test $H_{0}: \mu=80$ versus \(H_{1}: \mu
To test $H_{0}: \mu=20$ versus \(H_{1}: \mu
One year, the mean age of inmates on death row was 40.6 years. A sociologist wondered whether the mean age of a death row inmate has changed since then. She randomly selects 32 death row inmates and
$H_{0}: p=0.6$ versus \(H_{1}: p
$H_{0}: p=0.45$ versus \(H_{1}: p
$H_{0}: p=0.25$ versus \(H_{1}: p
According to a certain government agency for a large country, the proportion of fatal traffic accidents in the country in which the driver had a positive blood alcohol concentration (BAC) is 0.37 .
In a previous poll, $29 \%$ of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Suppose that, in a more recent poll, 318 of 1157 adults
Taught Enough Math? In $1994,52 \%$ of parents with children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey
Several years ago, $39 \%$ of parents who had children in grades $\mathrm{K}-12$ were satisfied with the quality of education the students receive. A recent poll asked 1,065 parents who have
Political Philosophy According to Gallup, $21 \%$ of adult Americans consider themselves to be liberal. Respondents of the Sullivan Statistics Survey I were asked to disclose their political
Problem Decide whether the sampling method is independent or dependent. Then determine whether the response variable is qualitative or quantitative.(a) Joliet Junior College decided to implement a
In the Spacelab Life Sciences 2 payload, 14 male rats were sent to space. Upon their return, the red blood cell mass (in milliliters) of the rats was determined. A control group of 14 male rats was
Using the data from Table 2, construct a $95 \%$ confidence interval estimate of the mean difference, $\mu_{d}$.By Hand ApproachStep 1 Compute the differenced data. Because the sample size is
In clinical trials of Nasonex, 3774 adult and adolescent allergy patients (patients 12 years and older) were randomly divided into two groups. The patients in group 1 (experimental group) received
Construct a 95% confidence interval for $\mu_{1}-\mu_{2}$ using the data presented in Table 3.Approach The normal probability plots and boxplot (Figure 10) indicate that the data are approximately
The Gallup organization surveyed 1100 adult Americans on May 6- 9, 2002, and conducted an independent survey of 1100 adult Americans on May 8- 11, 2014. In both surveys they asked the following:

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