Exam 2: Significance: How Strong Is the Evidence

If the sample size increases, the standard deviation of the null distribution of sample proportions will also increase.

An environmental science teacher at a high school with a large population of students was curious whether the majority (more than half) of students at the school regularly recycle plastic bottles. The teacher selected a random sample of 146 students at the school to interview, then asked each student: "Do you recycle plastic bottles more often than you throw them in the trash?" (Yes/No). Suppose that 89 of the students answered "Yes". -The sample proportion of students who said "Yes" was 0.75 instead of 0.61.

If an observed statistic is NOT statistically significant, then the chance model is plausible.

Match each standardized statistic value with its corresponding p-value: - _______

A survey on 1,500 high school seniors who took the SAT and who completed an optional web survey shows that 55% of high school seniors are fairly certain that they will participate in a study abroad program in college. Does this survey provide convincing evidence that the majority (more than 50%) of all high school seniors who take the SAT are fairly certain they will participate in a study abroad program in college? -Fill in the blanks with the correct values to simulate another survey of 1,500 high school seniors who took the SAT in which the long-run proportion of all high school seniors who take the SAT that are fairly certain they will participate in a study abroad program in college is 0.50. Create a spinner with ______ percent shaded red, and _____ percent shaded black. Spin the spinner _____ times. Record the _____ of times the spinner lands on red.

A study conducted by the National Center for Health Statistics as part of the Center for Disease Control and Prevention (CDC) found that, as of 2015-2016, 39.6% of Americans over the age of 20 fit the medical definition of being obese (BMI of 30 or higher). A city known for its plentiful outdoor opportunities believes that number is lower among its residents. A representative sample of 80 city residents is collected and the BMI calculated for each (based on reported height and weight). The variable of interest is whether the resident fit the medical definition of obese. The study found 22 people in the sample fit the medical definition of obese. -Identify which of the following is the null hypothesis.

Match the parts of the real study corresponding to the physical (coin-flipping) simulation: -Chance of heads = _______

Match the parts of the real study corresponding to the physical (coin-flipping) simulation: -One repetition = _______

A study conducted by the National Center for Health Statistics as part of the Center for Disease Control and Prevention (CDC) found that, as of 2015-2016, 39.6% of Americans over the age of 20 fit the medical definition of being obese (BMI of 30 or higher). A city known for its plentiful outdoor opportunities believes that number is lower among its residents. A representative sample of 80 city residents is collected and the BMI calculated for each (based on reported height and weight). The variable of interest is whether the resident fit the medical definition of obese. The study found 22 people in the sample fit the medical definition of obese. -The standardized statistic is equal to -2.213. Interpret this value in the context of the problem.

Do red uniform wearers tend to win more often than those wearing blue uniforms in Taekwondo matches where competitors are randomly assigned to wear either a red or blue uniform? In a sample of 80 Taekwondo matches, there were 45 matches where the red uni-form wearer won. -What is the statistic for this study?

The standardized statistic represents the number of standard deviations the observed statistic is above or below the hypothesized null value.

The first iPhone became available for public purchase in 2007. By 2010, approximately 30% of smartphone users in the US owned an iPhone. Several new companies have entered the smartphone market since then and the folks at Apple want to know how they are stacking up against their competition. In 2019, a representative sample of 529 smartphone users in the US showed that 47.4% use an Apple iOS device. Does it appear that Apple's share of the US smartphone market has increased since 2010? -Which of the following strength of evidence statements are correct, based on the standardized statistic in 29? Select all that apply. (If you didn't report a standardized statistic in 29, then use for this question.)

Match the parts of the real study corresponding to the physical (coin-flipping) simulation: -Coin flip = _______

A survey on 1,500 high school seniors who took the SAT and who completed an optional web survey shows that 55% of high school seniors are fairly certain that they will participate in a study abroad program in college. Does this survey provide convincing evidence that the majority (more than 50%) of all high school seniors who take the SAT are fairly certain they will participate in a study abroad program in college? -The p-value for this study is less than 0.001. Interpret this value in the context of the problem.

When President Trump took office in 2016, a Gallup poll reported that 55% of Americans supported stricter laws covering the sale of firearms. In 2020, the same poll was conducted on a representative sample of 943 Americans, and 64% of those surveyed supported stricter laws covering the sale of firearms. Has the percent of Americans supporting stricter laws covering the sale of firearms increased from 2016? -Which hypothesis testing method is appropriate for this study?

A study conducted by the National Center for Health Statistics as part of the Center for Disease Control and Prevention (CDC) found that, as of 2015-2016, 39.6% of Americans over the age of 20 fit the medical definition of being obese (BMI of 30 or higher). A city known for its plentiful outdoor opportunities believes that number is lower among its residents. A representative sample of 80 city residents is collected and the BMI calculated for each (based on reported height and weight). The variable of interest is whether the resident fit the medical definition of obese. The study found 22 people in the sample fit the medical definition of obese. -Identify the correct alternative hypothesis.

An environmental science teacher at a high school with a large population of students was curious whether the majority (more than half) of students at the school regularly recycle plastic bottles. The teacher selected a random sample of 146 students at the school to interview, then asked each student: "Do you recycle plastic bottles more often than you throw them in the trash?" (Yes/No). Suppose that 89 of the students answered "Yes". -What is the parameter of interest for this study?

A survey on 1,500 high school seniors who took the SAT and who completed an optional web survey shows that 55% of high school seniors are fairly certain that they will participate in a study abroad program in college. Does this survey provide convincing evidence that the majority (more than 50%) of all high school seniors who take the SAT are fairly certain they will participate in a study abroad program in college? -Using a count as the statistic, where would you expect the null distribution to be centered?

Research done in the mid 1980s indicated that 80% of grizzly bears in the greater ecosystem of Yellowstone National Park entered their den for hibernation by the last day of November. This has come into question as of late. Researchers have hypothesized that climate change has postponed bears entering hibernation until later in the season; that is, researchers believe that a smaller percentage of bears are entering their den for hibernation by the last day of November. Sixty-two Yellowstone grizzly bears were tracked via radio monitors, which allow scientists to pinpoint when the bears enter their dens with a high degree of accuracy. Of the sixty-two Yellowstone grizzly bears being tracked, forty-two entered their den for hibernation by the last day of November. -A distribution of simulated "Number of successes," assuming the null hypothesis is true, is shown below. Circle the portion of the plot below that you would count to calculate the p-value.

The official four-year graduation rate among US colleges and universities is 57.6%. Suppose a researcher takes a random sample of 100 college students and tracks their progress through school to determine whether each student graduates in four years or not. Which of the following do you know to be true? Select all that apply.