Exam 2: Significance: How Strong Is the Evidence

If the sample size increases, the mean of the null distribution of sample proportions will decrease.

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? -The following simulated null distribution of proportion of "Apple iOS users" that could happen by chance alone in a sample of 529 smartphone users was created with the One Proportion applet. Also, given are the mean and SD for this null distribution. Calculate and report the standardized statistic.

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". -Use the One Proportion applet to calculate a p-value 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. -Select the appropriate method of calculating the standard deviation of the sample proportions under the null hypothesis.

Suppose you are testing to see if your dog, Hope, understands pointing towards an object. You place two objects about 2.5 meters away, then you point towards one of the objects. In 20 trials, Hope goes to the correct object 13 times (or 65%). -Given below is the resulting simulation distribution from the One Proportion applet. Based on this simulation, do we have convincing evidence against the observed study results happening by chance alone?

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? -What is the value of the statistic and its proper notation in this study?

For each of the following scenarios, determine whether the alternative hypothesis would be one-sided or two-sided. -In 2010, it was believed that 18% of American cell phone owners do their browsing on their phone rather than a computer or other device. A recent survey conducted on a representative sample of 621 American cell phone owners showed 22% now do their browsing on their mobile device. Do these data provide evidence that the proportion of American cell phone owners who do their browsing on their phones rather than their computers or other devices has changed in the last 10 years?

A simulated distribution of sample proportions will always be approximately normal.

A standardized statistic that is closer to zero provides stronger evidence against the null hypothesis.

A result that is unlikely to occur just by chance alone is called statistically significant.

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. -Is a theory-based method appropriate for these data?

Suppose you are testing to see if your dog, Hope, understands pointing towards an object. You place two objects about 2.5 meters away, then you point towards one of the objects. In 20 trials, Hope goes to the correct object 13 times (or 65%). -Which of the following is NOT a step in the 3S Strategy for measuring strength of evidence?

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

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. -How could we use coins, a spinner, or cards to simulate one of the samples in the above simulation? Select all that apply.

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 teacher sampled 300 students instead of 146.

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? -State the null and alternative hypotheses in proper notation.

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? -Under the null hypothesis, what is the value of the parameter of interest and its proper notation in this study?

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 are the null and alternative hypotheses in appropriate notation?

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. -126 of 186 bears had entered their den for hibernation by the last day of November.

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? -Use the Theory-Based Inference applet to compute the standardized statistic and p-value for this study. standardized statistic = ______ p-value = _____