Researchers collected samples of water from streams in a mountain range to investigate the effects of acid rain. They measured the pH​ (acidity) of the water and classified the streams with respect to the kind of substrate​ (type of rock over which they​ flow). A lower pH means the water is more acidic. The plot to the right shows the pH of the streams by substrate​ (limestone, mixed, or​ shale). Selected parts of a software analysis comparing pH of streams with mixed and shale substrates are shown below. Complete parts a through c.   ​2-Sample t-test of μ1−μ2=​0, Difference Between Means=0.195 t-Statistic=5.30 ​w/125 ​df,  P≤0.0001

A chemistry experiment is performed measuring the solubility of potassium chloride (KCl) in water at different temperatures. The goal was to determine if there is a linear relationship between the temperature of the water and how much KCl can dissolve, measured as grams per 100 milliliter (g/100mL). After the experiments were performed, the following data was collected with temperature being the independent x-variable and solubility being the dependent y-variable: Temperature (°C) x Solubility (g/100mL) y 10 31 20 33 30 37 40 41 50 42 Based on the data given for temperature and solubility of KCl and without doing any math yet, which of the following do you predict would best describe the relationship between these variables?     A positive linear relationship (r close to 1)     A positive linear relationship (r close to -1)     A negative linear relationship (r close to 1)     A negative linear relationship (r close to -1)…

The mtcars data set contains data on 32 cars from the 1974 Motor Trend US magazine. The data set has 11 variables that measure different aspects of the cars, such as miles per gallon (mpg), horsepower (hp), weight (wt), and number of cylinders (cyl). The data set can be used to study the relationship between fuel consumption and car performance, as well as other factors that affect the efficiency and design of the cars. What is the maximum and minimum number of the range regarding the explanatory variable for which the regression model can make valid predictions?

The cost of fuel is the largest component of cost of ownership for most vehicles. Fuel cost is​ (almost) inversely proportional to gas​ mileage; higher gas mileage means lower fuel cost and​ vice-versa. If you keep track of the number of miles driven on each tank of gas as well as how much gas is​ purchased, it is easy to calculate gas​ mileage; many cell phone apps exist to track this. The data in the following table is the gas mileage for Mr.​ Hebert's 2015 Jeep Wrangler Unlimited.     12.85 14.98 15.36 17.09 18.86 13.28 15.11 15.62 17.50 19.07 13.48 15.12 15.65 17.66 20.91 14.65 15.13 16.41 18.17 21.17 14.71 15.14 16.80 18.27 22.11 c. Find the five number summary. enter your response here​, enter your response here​, enter your response here​, enter your response here​, enter your response here

Suppose a researcher collects data on the air pollution levels, measured in milligrams per cubic meter, for both urban and rural areas in 35 states. The data is plotted with urban air pollution levels on the horizontal axis and rural air pollution levels on the vertical axis. Nevada is an outlier in the ?x‑direction. What must be true about this state? The urban air pollution levels for this state are much higher or lower than the rest of the states in the data set. The rural air pollution levels for this state are much higher or much lower than the rest of the states in the data set. This state is an influential observation. The rural air pollution levels for this state are much higher or lower than other states in the data set that have similar urban air pollution levels. The absolute value of the residual of this state is large.

A financial website reported the beta value for a certain company was 0.86. Betas for individual stocks are determined by simple linear regression. The dependent variable is the total return for the stock, and the independent variable is the total return for the stock market, such as the return of a market index. The slope of this regression equation is referred to as the stock's beta. Many financial analysts prefer to measure the risk of a stock by computing the stock's beta value.   Suppose the following data show the monthly percentage returns for the market index and the company for a recent year. Month Market Index% Return Company% Return August -3 4 September 8 7 October 0 1 November -2 1 December -5 0 January 0 0 February 7 7 March 0 -2 April 2 0 May -5 -1 a. Develop the least squares estimated regression equation. (Let x = Market Index % Return (as a %), and let y = Company % Return (as a %). Round your numerical values to four decimal places.)

Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days 75 79 35 91 203 y km/100 14.2 19.1 5.8 11.2 35.4 (a) Verify that  Σx = 483,   Σy = 85.7,   Σx2 = 62,581,   Σy2 = 1978.69,   Σxy = 10982.3,  and  r ≈ 0.94895. Σx   Σy   Σx2   Σy2   Σxy   r   (b) Use a 1% level of significance to test the claim  ρ > 0.  (Use 2 decimal places.) t   critical t     (c) Verify that  Se ≈ 4.1118,   a ≈ 0.7378,  and  b ≈ 0.1698. Se   a   b