Pew Research, in November 2011, polled a random sample of 799 U.S. teens about Internet use. 49% of those teens reported that they had misrepresented their age online to gain access to websites and online services. If we only need to be 90% confident, will the margin of error be larger or smaller? Explain.

Pew Research, in November 2011, polled a random sample of 799 U.S. teens about Internet use. 49% of those teens reported that they had misrepresented their age online to gain access to websites and online services. Find the margin of error for this poll if we want 95% confidence in our estimate of the percent of American teens who have misrepresented their age online.

The Pew Research Center surveyed a random sample of U.S. teens and adults about their use of social media. The following pictograph displays some results. Explain how this graph is misleading.

Pew Research, in 2015, polled a random sample of 1060 U.S. teens (ages 13-17) about Internet use. 56% of those teens reported going online several times a day-a fact of great interest to advertisers.

a) Explain the meaning of $\hat{p}$ = 0.56 in the context of this situation.

b) Calculate the standard error of $\hat{p}$.

c) Explain what this standard error means in the context of this situation.

Find the value of $k$ so that the given differential equation is exact.

$$\left( 6 x y ^ { 3 } + \cos y \right) d x + \left( 2 k x ^ { 2 } y ^ { 2 } - x \sin y \right) d y = 0$$

The Pew Research Center recently conducted a survey of a random sample of 200 teens and concluded that 43% of all teens who take their cell phones to school text in class on a daily basis. How accurately did their random sample represent all teens?

Solve each of the following inequalities. a. $x^{3}+54>-2 x^{2}+57 x$ b. $\frac{x^{2}+x}{x+9} \leq 1$

In a national poll taken in February 2008, Gallup asked 1006 adults whether they were baseball fans; 43% said they were. Two months previously, in December 2007, 40% of a similar-size sample had reported being baseball fans. Find the margin of error for the 2008 poll if we want 90% confidence in our estimate of the percent of national adults who are baseball fans.

Base your answer on the text below. In the early 20th century, astronomers did not know that they would find huge groups of stars far beyond the familiar stars in the night skies. At that time, the world's largest telescope was on Mt. Wilson in California. There, Edwin Hubble observed dim, fuzzy objects called "nebulae" Nebula is the Latin word for cloud. He discovered that many nebulae are huge collections of stars and star systems. Hubble realized that these fuzzy shapes are distant galaxies, similar to our Milky Way. He developed a classification system based on the shapes of the galaxies. He hoped that he could use his classification system to understand how galaxies change through time. Another classification of stars, the H-R diagram, had been devised about a decade earlier. The H-R diagram proved very useful in tracing the evolution of individual stars. Since Hubble published his classification scheme in 1926, astronomers have not been able to use it to show a regular evolution of galaxies with age, as Hubble had hoped. However, his system of classification of galaxies based on their shapes is still used today. The Milky Way is classified as what type of galaxy. (1) elliptical (2) lenticular (3) spiral (4) irregular

You roll a die, winning nothing if the number of spots is odd, $1 for a 2 or a 4, and$10 for a 6. a) Find the expected value and standard deviation of your prospective winnings. b) You play twice. Find the mean and standard deviation of your total winnings. c) You play 40 times. What’s the probability that you win at least $100?

When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that in fact 8% of the apples on the truck do not meet the desired standard. What’s the probability that the shipment will be accepted anyway?

In a national poll taken in February 2008, Gallup asked 1006 adults whether they were baseball fans; 43% said they were. Two months previously, in December 2007, 40% of a similar-size sample had reported being baseball fans. If we wanted to be 99% confident, would the margin of error be larger or smaller? Explain.

In a national poll taken in February 2008, Gallup asked 1006 adults whether they were baseball fans; 43% said they were. Two months previously, in December 2007, 40% of a similar-size sample had reported being baseball fans. Explain what that margin of error means.

In a national poll taken in February 2008, Gallup asked 1006 adults whether they were baseball fans; 43% said they were. Two months previously, in December 2007, 40% of a similar-size sample had reported being baseball fans. Find that margin of error.