Answer:
The sample proportion shows a statistically significant divergence from 50%
Step-by-step explanation:
Null hypothesis: The sample proportion equals 50%
Alternative hypothesis: The sample proportion does not equal 50%
z = (p' - p) ÷ sqrt[p(1 - p) ÷ n]
p' is the sample proportion = 289/400 = 0.7225
p is the population proportion = 50% = 0.5
n is the number of students surveyed = 400
z = (0.7225 - 0.5) ÷ sqrt[0.5(1 - 0.5) ÷ 400] = 0.2225 ÷ 0.025 = 8.9
The analysis is two-tailed. At a significance level of 0.01, the critical value is 2.576. The acceptance region for the null hypothesis is between -2.576 and 2.576.
Conclusion:
Reject the null hypothesis since the calculated z-score of 8.9 is beyond the bounds established by the critical values of -2.576 and 2.576.
There is compelling evidence to support the assertion that the sample proportion signifies a meaningful difference from 50%.
Answer:
The rectangular prism has dimensions of 5 inches by 7 inches by 8 inches. The volume can be calculated as follows:
Length of base multiplied by width of base multiplied by height.
Volume = 5 × 7 × 8 = 280 cubic inches
A golf ball is spherical. The volume formula for a sphere is:
Volume of a sphere = 4/3πr^3
Given a golf ball's diameter of 1.7 inches, the radius is 1.7/2 = 0.85 inches.
Thus, the volume for each golf ball is calculated as follows:
Volume of each golf ball = 4/3 × 3.14 × 0.85^3
= 2.57 cubic inches
The number of golf balls fitting into the compartment calculates to:
Volume of compartment divided by volume of each golf ball, resulting in
280/2.57 equals 109 golf balls.
Step-by-step explanation:
Sample Answer: No, Ingrid's statement is incorrect. In this situation, the starting point is at 170 feet, which denotes the y-intercept. The reduction of 4 feet per year symbolizes the rate of change, or slope. In the slope-intercept equation format, y = mx + b, with 'm' denoting the slope and 'b' signifying the y-intercept, the accurate equation would be y = −4x + 170.
Answer:
A biconditional statement integrates a conditional statement alongside its converse in an if and only if format. Two line segments are congruent if and only if their lengths are identical... A biconditional is deemed true only when both conditional statements are true. there??
Step-by-step explanation:
Answer: x ≥ 3.2 OR x ≤ -0.75
Here's how to solve the compound inequality step-by-step: start by separating it into two inequalities. For the first one, 5x - 4 ≥ 12, add 4 to both sides to remove the constant, leaving 5x ≥ 16. Then divide both sides by 5 to isolate x, resulting in x ≥ 3.2.
Now for the second part, 12x + 5 ≤ -4, subtract 5 from both sides to obtain 12x ≤ -9. Dividing both sides by 12 gives x ≤ -9/12, which simplifies to x ≤ -0.75. So, combining both, the solution is x ≥ 3.2 OR x ≤ -0.75.
