[DATA] CEO Performance [See Problem 19 in Section 12.3] The following data represent the total compensation for 12 randomly selected chief executive officers (CEOs) and the company’s stock performance in 2017.

b. Suppose a researcher wanted to determine if there is a linear relation between compensation and stock return. What would be the null and alternative hypotheses?

[DATA] Height versus Head Circumference [See Problem 13 in Section 12.3] A pediatrician wants to determine the relation that may exist between a child’s height and head circumference. She randomly selects 11 children from her practice, measures their heights and head circumferences, and obtains the following data:

d. State your conclusion to the hypotheses from part (b).

[DATA] Hurricanes [See Problem 14 in Section 12.3] The following data represent the maximum wind speed (in knots) and atmospheric pressure (in millibars) for a random sample of hurricanes that originated in the Atlantic Ocean.

c. Use the “Randomization test for slope” applet in StatCrunch to build the null model to generate at least 2000 repetitions of this study to obtain a P-value. Interpret the P-value.

[DATA] Concrete [See Problem 15 in Section 12.3] As concrete cures, it gains strength. The following data represent the 7-day and 28-day strength (in pounds per square inch) of a certain type of concrete:

b. Suppose a researcher wanted to determine if there is a linear relation between 7-day strength and 28-day strength. What would be the null and alternative hypotheses?

[DATA] Concrete [See Problem 15 in Section 12.3] As concrete cures, it gains strength. The following data represent the 7-day and 28-day strength (in pounds per square inch) of a certain type of concrete:

d. State your conclusion to the hypotheses from part (b).

[DATA] Bear Markets [See Problem 20 in Section 12.3] A bear market is a market condition in which the price of the security falls. A bear market in the stock market is defined as a condition in which market declines by 20% or more over the course of at least two months. The following data represent the number of months and percentage change in the S&P500 (a group of 500 stocks).

b. Suppose a researcher wanted to determine if there is a linear relation between months and percent change. What would be the null and alternative hypotheses?

[DATA] Home Runs (Refer to Problem 31, Section 4.2) The following data represent the speed at which a ball was hit (in miles per hour) and the distance it traveled (in feet) for a random sample of home runs in a Major League baseball game in 2018.

a. Treating speed at which the ball was hit as the explanatory variable and distance the ball traveled as the response variable, determine estimates for β0 and β1.

In Problems 5–10, use the results of Problems 7–12, respectively, from Section 4.2 to answer the following questions:

c. Determine s_{b₁}.

In Problems 5–10, use the results of Problems 7–12, respectively, from Section 4.2 to answer the following questions:

d. Assuming the residuals are normally distributed, test H₀: β₁ = 0 versus H₁: β₁ ≠ 0 at the α = 0.05 level of significance.