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At a wedding, guests will be asked what type of meal they want. Let V be the event that a guest will select the vegetarian dinner and C be the event that the guest will select the chicken dinner. Let $$P(V) = 0.3$$, $$P(C) = 0.7$$, and $$P(V \cup C) = 1.0$$. Which of the following statements must be true?

For which of the following distributions is the mean clearly greater than the median?

The scatterplots for five different sets of bivariate quantitative data are shown. The correlation coefficients for two of the scatterplots are $$r = -0.656$$ and $$r = 0.907$$.

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Which of the following matches the graph with the correct correlation coefficient?

A number cube has six sides, each with equal probability of landing face-up when rolled, which is also known as a fair number cube. A statistics teacher is trying to create a six-sided number cube where each side does not have an equal probability of landing face-up when rolled. A claim is made that after baking a fair number cube for 10 minutes at 175 degrees Fahrenheit (°F), each face will no longer have an equal probability of landing face-up when the number cube is rolled. Thus, the distribution of the number landing face-up will not be uniform. To test this claim, the statistics teacher baked a fair number cube for 10 minutes at 175°F and recorded the results of 200 number cube rolls, shown in the following table.
Results from 200 Rolls of Baked Number Cube
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All conditions for inference were met, and the test statistic and $$p$$-value for the appropriate hypothesis test were 7.66 and 0.176, respectively. Which of the following statements is the best interpretation of the $$p$$-value?

A large regional sports league wants all teams to use the same airline company when they travel on Fridays to a particular city for games. The league wants to ensure the teams arrive on time as often as possible. The league records all arrivals (both on-time and late) for six airline companies on all Fridays for the past year to that city. The bar chart displays the number of on-time arrivals for the six companies.

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Based on the bar chart, which airline company should the league select so that the teams are more likely to arrive on time?

At a grocery store, there are three self-checkout stations for customers to complete their purchases. Let $$X =$$ the number of self-checkout stations being used by customers at any given time. The probability distribution of $$X$$ is given in the following table.
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The mean of $$X$$ is 2. Which of the following is closest to the standard deviation of $$X$$?

There is a certain compound found in the cacao plant that can affect blood pressure. A researcher is studying whether adding a capsule that contains this compound along with regular medication will aid in reducing blood pressure. The researcher recruited 22 volunteer patients who had approximately the same blood pressure and were taking the same brand of blood pressure medicine. The researcher randomly assigned 11 of the volunteers to take the compound capsule along with their current medication and the other 11 of the volunteers to take a placebo capsule along with their current medication. After one month, the systolic blood pressure, in millimeters of mercury (mmHg), was taken for the volunteers and recorded. The table displays summary statistics for the systolic blood pressure for each group of volunteers.

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Assuming all conditions for inference are met, which of the following is a 95 percent confidence interval for the difference between the means of the systolic blood pressure (compound minus placebo), in mmHg, for all patients similar to those in the study?

A strong, heat-resistant synthetic fiber currently used in manufacturing has a mean strength of 1.62 gigapascals (GPa). Scientists believe that spider silk, a natural material, is stronger on average than the currently used fiber. A scientist randomly selected 10 strands of spider silk and determined the strength of each strand. The sample mean strength was 1.87 GPa with a sample standard deviation of 0.26 GPa. The scientist conducted an appropriate test of significance for the following hypotheses.
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Assuming all conditions for inference are met, what are the values of the appropriate test statistic and associated $$p$$-value?

Farmer Jones and Farmer O'Grady grow avocados in two different states. The farmers want to estimate the difference in the proportion of avocados from their large farms that cannot be sold because they are rotten. Which of the following combinations of sample sizes and proportions of rotten avocados for each of the two farms would not allow the farmers to assume the sampling distribution of the difference in sample proportions of rotten avocados will have an approximately normal distribution?

A wildlife sanctuary is a place where wild animals are kept safe. A researcher at a certain sanctuary is interested in the relationship between weight and average daily amount of water consumed by lions in the sanctuary. To investigate this relationship, the researcher selected a random sample of 20 lions from the sanctuary. The weight, in pounds, and the average daily amount of water consumed, in ounces, was recorded for each lion for a period of 5 days. From the data, a least-squares regression model was constructed using weight as the explanatory variable and average daily amount of water consumed as the response variable. A computer summary of the least-squares regression model is shown in the following table.

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The researcher will use the regression results to test the hypotheses $$H_0$$: There is not a linear relationship between weight and average daily amount of water consumed by all lions in the sanctuary versus $$H_a$$: There is a linear relationship between weight and average daily amount of water consumed by all lions in the sanctuary.
Assuming the conditions for inference were met, which of the following statements is true at the 0.05 significance level?

According to an association of dentists, half of all adults over the age of 30 suffer from some form of gum disease. One indicator of the health of gums is the gap between the pocket of the gum and the nearby tooth, measured in millimeters (mm). These gap measurements range from 0 to 7 mm, with 0 indicating no gum disease and 7 indicating the most severe gum disease.
A group of dentists claims that improving tooth-brushing techniques will decrease the greatest gap measurement, on average, of patients in their large practice. The dentists randomly select 32 patients from the approximately 1,500 patients in their dental practice and measure the greatest gap at the beginning and then again at the end of a three-year period of improved tooth-brushing techniques. Summary statistics of the measurements are displayed in the table.

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Assuming all conditions for inference are met, which of the following is the correct value of the test statistic and $$p$$-value to test the dentists' claim?

An aerial view of a large suburban area shows that 40 percent of the residences have gardens and 30 percent of the residences have solar panels. Among the residences with gardens, 50 percent have solar panels. If a residence is selected at random, what is the probability that the residence has a garden, solar panels, or both?

According to a recent survey, 40 percent of all households in a certain country have newspapers delivered to their homes. Holly, a local city manager, is investigating whether the percentage of households in her city that have newspapers delivered is different from the national percentage reported in the survey. The hypotheses for her investigation are $$H_0: p = 0.40$$ versus $$H_a: p \neq 0.40$$, where $$p$$ is the proportion of all households in the city that have newspapers delivered. To test these hypotheses at the significance level of $$\alpha = 0.05$$, Holly selected a simple random sample of 85 households. Among the households sampled, 42 reported having newspapers delivered. Assuming the conditions for inference are met, which of the following is the correct inference decision?

Ms. Sato, a president of a large university, is interested in estimating the proportion of students from the university who are fluent in more than one language. She takes a random sample of 2,200 students from the university. The 95 percent confidence interval she calculates to estimate the population proportion of students from the university who are fluent in more than one language is (0.274, 0.312). Assuming all conditions for inference have been met, which of the following is the best interpretation of the 95 percent confidence interval?

A study was conducted to investigate the association between temperature and length of the wings of butterflies. A random sample of butterflies of a certain species was collected across a continent. On the day each butterfly was collected, the day's mean temperature at that location, in degrees Celsius (°C), and the butterfly's forewing length, in millimeters (mm), were recorded. From these data, a least-squares regression line was calculated to predict forewing length (mm) from mean temperature (°C). The equation of the least-squares regression line is $$\hat{y} = 22.550 + 0.262x$$, where $$x$$ is the mean temperature on the day each butterfly was collected and $$y$$ is the forewing length of the butterfly. On the day one butterfly in the sample was collected, the mean temperature was $$20.80^\circ C$$ and the forewing length of the butterfly was $$27.15$$ mm. Using the least-squares regression line, which of the following is closest to the residual for this butterfly?

According to a report, only 18 percent of all drivers can drive a car with a manual transmission. Mr. Jerry, a morning radio show host in a certain city, was curious to know whether the proportion of the show's listeners who can drive a car with a manual transmission is different from 0.18. He requested that listeners call the show and report whether they can drive a car with a manual transmission. Mr. Jerry did not have time to talk to everyone who called, so he took a random sample of the callers by rolling a die. Because the die landed on 5, the fifth call was answered and then every fifth call after that one was answered until there were 40 responses from the 200 listeners who called. Of the callers who were selected, 25 percent stated that they can drive a car with a manual transmission. Which of the following is true about the results of the survey conducted by the radio host?

In some years at a certain beach, loud concerts are held every weekend during the summer. In other years, there are no concerts held during the summer. A bird lover is concerned that the concerts affect the number of eggs a certain type of bird lays on the beach. The bird lover took a random sample of years with concerts and another random sample of years without concerts. Using available records, the bird lover recorded the number of eggs birds of the specified type laid on the beach each year. A two-sample $$t$$-test for the difference in population means was conducted, and the bird lover concluded the mean number of eggs the birds laid each year is significantly less in the years when there were summer concerts. Assuming the conditions for inference were met, which of the following is a correct statement about the conclusion that can be made from the study?

In a certain large city, a recycling bin is considered to be used correctly if it does not contain any food or other biological waste (such as used tissues or diapers). In the city, 65 percent of all households with recycling bins use the bins correctly.
In a random sample of 600 households in the city, what are the mean, $$\mu$$, and standard deviation, $$\sigma$$, of the number of households with recycling bins that use them correctly?

A company with many grocery stores buys grapefruit from two regions, X and Y. A produce buyer at the company believes that grapefruit grown in region X weigh more, on average, than grapefruit grown in region Y. The buyer randomly selects and weighs 125 grapefruits from each region. Let $$\mu_{X}$$ be the mean weight of all grapefruit from region X and let $$\mu_{Y}$$ be the mean weight of all grapefruit from region Y. The buyer uses the data to conduct a two-sample t-test to test the following hypotheses.
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The assumptions for inference are met, and the buyer makes a decision based on the data collected and the results of the inference test.
Which of the following describes a Type II error for this test?

For competition play, the mass of a tennis ball must be between 56.0 grams and 59.4 grams. The distribution of the mass of tennis balls manufactured by a certain company is approximately normal with a mean of 57.7 grams. If 96 percent of all tennis balls made by the company meet the mass requirement for competition play, which of the following expressions is closest to the standard deviation of the distribution of the mass of tennis balls made by the company?

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