Exam 2: Significance: How Strong Is the Evidence

A parameter is a number summarizing the results in the sample.

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? -Let X represent the value of your standardized statistic in 29. Select the best contextual interpretation of the value X.

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 uniform wearer won. Given below is the simulated null distribution of proportion of "red wins" that could happen by chance alone in a sample of 80 matches. Also, given are the mean and SD for this null distribution. -Is there evidence that in Taekwondo matches, red uniform wearers tend to win more often than those wearing blue uniforms than would be expected by chance alone?

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? -Fill in the appropriate inputs to the Theory-Based Inference applet to conduct a theory-based test for this scenario. n: _______ count: _______ _______

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". -We want to know if less than half of all students at the school would have said "Yes" rather than greater than half.

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

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 62 Yellowstone grizzly bears being tracked, 42 entered their den for hibernation by the last day of November. For each of the following sample results, circle whether the p-value would increase, decrease, or remain the same if we were to track another sample of Yellowstone grizzly bears. -21 of 31 bears had entered their den for hibernation by the last day of November.

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 can we conclude from the results of this study? Select all that apply.

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. -Identify which of the following is the null hypothesis, and which is the alternative hypothesis: _____The sample proportion of 62 Yellowstone grizzly bears that enter their den for hibernation by the last day of November is 0.80. _____The long-run proportion of Yellowstone grizzly bears that enter their den for hibernation by the last day of November is 0.80. _____ The long-run proportion of Yellowstone grizzly bears that enter their den for hibernation by the last day of November is less than 0.80. _____ The long-run proportion of Yellowstone grizzly bears that enter their den for hibernation by the last day of November is greater than 0.80.

The World Health Organization reports that the SARS (Severe Acute Respiratory Syndrome) outbreak in 2003 resulted in 8098 probable cases reported, 774 of which were fatalities. A student who is planning to travel to Vietnam is concerned about another virus outbreak and would like to use data on how Vietnam handled SARS cases as a gauge for how well its health care system would handle another virus outbreak. The student plans to test if the fatality rate in Vietnam from SARS is different from the global fatality rate. Of the 89 SARS cases reported in Vietnam in 2003, 5 people died. The student analyzes these data in two ways: Method 1: The theory-based p-value was calculated to be 0.2061. Method 2: The simulation-based p-value was calculated to be 0.2797. Which p-value is most valid?

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? -Fill in the blanks to enter the appropriate hypotheses into the Theory-Based Inference applet. H₀:? = ______ (B1) H_S:? ______ (DD) ______ (B3) Drop-down (DD) options: • ? • < • >

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. -Let 'A' represent your answer from 60. Which of the following displays the correct method of calculating the standardized statistic?

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. -Once more, let 'A' represent your answer from 60. How should the p-value be calculated for this test? Select all that apply.

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

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 62 Yellowstone grizzly bears being tracked, 42 entered their den for hibernation by the last day of November. For each of the following sample results, circle whether the p-value would increase, decrease, or remain the same if we were to track another sample of Yellowstone grizzly bears. -45 of 62 bears had entered their den for hibernation by the last day of November.