Aerodynamics Scientists used the Transonic Tunnel at NASA Langley Research Center, Virginia, to study the dynamics of air flow. The elliptical opening of the Transonic Tunnel is 82 ft wide and 58 ft high. What is an equation of the ellipse? Plan How can a drawing help you solve this problem?

Solve the given problems
A medical research lab is growing a virus for a vaccine that grows at a rate of $2.3\%$ per hour. If there are $500.0$ units of the virus originally, the amount present after t hours is given by $N = 500.0(1.023)^{t} .$ How many units of the virus are present after two days?

Which of the following is true of multiple regression?

A. There is a limit to the number of predictors that can be statistically significant.
B. It can control for all third variables, including those that are not measured.
C. Adding more predictors means research is controlling for more variables.
D. There is a limit to the number of predictors that can be included in a regression.

Research an endangered or threatened species in your state. Gather information on its population for several years. Make a scatter plot using the data you gather. Is there a positive or negative correlation? Explain. Draw a trend line and make a prediction about the species population over the next 5 years.

Refer to the Development Psychology (Mar. 2003) study of the behavior of elementary school children. The researchers used a quadratic equation to model the level (y) of aggressive fantasies experienced by a child as. a function of the child's age (x). [Note: Level y was measured as an average of responses to six questions (e.g., "Do you sometimes have daydreams about hitting or hurting someone you don't like?"). Responses were measured on a scale ranging from 1 (never) to 5 (always).] a. Write the equation of the hypothesized model for E(y). b. Research psychologists theorized that a child's aggressive fantasies increase with age but at a slower rate of acceleration in older children. Sketch the curve hypothesized by the researchers. c. Set up $H_0$ and $H_a$ for testing the researchers' theory. d. The model was fitted to data collected for over 11,000 elementary school children, with the following results: $\hat{y}=1.926+.097 x-.003 x^{2}$, standard error of $\hat{\beta}_{2}=.001$. Compute the test statistic for the test you set up in part c. e. Use the result you found in part d to make the appropriate conclusion. Take $\alpha=.05$.

A 2016 Pew Research poll reported that 80 percent of Americans shop online. Assume the percentage is accurate.

a. If two Americans are randomly selected, what is the probability that both shop online?

b. If the two Americans selected are a married couple, explain why they would not be considered independent with regard to online shopping.

The CEO of a company that owns five resort hotels wants to evaluate and compare satisfaction with the five hotels. The company's research department randomly sampled 125 people who had stayed at any of the hotels during the past month and asked them to rate their expectations of the hotel before their stay and to rate the quality of the actual stay at the hotel. Both observations used a rating scale of 0-10, with 0 = very poor and 10 = excellent. The researchers compared the hotels on the gap between prior expectation and actual quality, using the difference score, y = performance gap = ( prior expectation score - actual quality score).

Identify the response variable, the factor, and the categories that form the groups.

A study claims that all adults spend an average of 14 hours or more on chores during a weekend. A researcher wanted to check if this claim is true. This researcher's random sample of 200 adults revealed that these adults put in an average of $14.65$ per hour on housework over the course of a weekend. The $3.00$ hour population standard deviation is well known. a. The alternative hypothesis is that all adults spend more than 14 hours on housework on the weekends. Calculate the $p$-value for the hypothesis test with this alternative hypothesis. At $\alpha=.01$, will you reject the null hypothesis? b. Test the hypothesis of part a using the critical-value approach and $\alpha=.01$.

Amyloid Fibers in Disease Several small aromatic molecules, such as phenol red (used as a nontoxic drug model), have been shown to inhibit the formation of amyloid in laboratory model systems. A goal of the research on these small aromatic compounds is to find a drug that would efficiently inhibit the formation of amyloid in the brain in people with incipient Alzheimer's disease.
(a) Suggest why molecules with aromatic substituents would disrupt the formation of amyloid.
(b) Some researchers have suggested that a drug used to treat Alzheimer's disease may also be effective in treating type 2 (non-insulin-dependent) diabetes mellitus. Why might a single drug be effective in treating these two different conditions?

An investment opportunity boasts that the chance of doubling your money in 3 years is 95%. However, when you research the details of the investment, you estimate that there is a 3% chance that you could lose the entire investment. Based on this information, are you certain to make money on this investment? Are there risks in this investment opportunity?

Many people think that living in an unfriendly atmosphere is bad for them. Researchers conducted a series of tests to see if experiencing rudeness and disrespect had an impact on task performance. 11 In one study, 34 participants met in small groups and saw the group leader treating a "participant" impolitely when the "participant" arrived late for the group meeting. Following the discussion, each participant completed a 5-minute solo brainstorming assignment in which they had to come up with as many uses for a brick as they could. The average cost per use was 7.88, with a 2.35 standard deviation. (a) Suppose that prior research has shown that the average number of uses a person can produce in 5 minutes under normal conditions is 10 . Given that the researchers hypothesize that witnessing this rudeness will decrease performance, state the appropriate null and alternative hypotheses. (b) Carry out the significance test using a significance level of $0.05$. Give the $P$-value and state your conclusion.

You and a friend are each typing your research papers on computers. The function y = 1400 - 50x models the number y of words you have left to type after x minutes. For your friend, y = 1200 - 50x models the number y of words left to type after x minutes. Who will finish first? Explain.

For each of the following research questions, would it make more sense to collect paired data or independent samples? Explain. What is the mean difference in height for the male and female in fraternal twin pairs in which there is one of each sex? What is the difference in mean heights for males and females in the adult population?

Suppose you want to move to a European city with a warm, moist climate. (a) Use maps and the information to identify a suitable city. (b) Explain why you think the climate of that city or town is warm and moist (c) Use the Internet to research the climate of that city or town. Was your prediction correct? Explain.