A binomial experiment must have all of the following:
a) A fixed number of trials.
b) The result of each trial is not affected by the results of the other trials (independence).
c) The probability of a 'success' is the same for each trial.
d) Each trial has only two possible outcomes, which are usually called 'success' and 'failure'.
Using the above criteria, the only choice of answer that qualifies as a binomial experiment is c) "flipping a coin 10 times and recording if it comes up heads."
Answer:
Note: The full question is attached as picture below
a) Hо : p = 0.71
Ha : p ≠ 0.71
<em>p </em>= x / n
<em>p </em>= 91/110
<em>p </em>= 0.83.
1 - Pо = 1 - 0.71 = 0.29.
b) Test statistic = z
= <em>p </em>- Pо / [√Pо * (1 - Pо ) / n]
= 0.83 - 0.71 / [√(0.71 * 0.29) / 110]
= 0.12 / 0.043265
= 2.77360453
Test statistic = 2.77
c) P-value
P(z > 2.77) = 2 * [1 - P(z < 2.77)] = 2 * 0.0028
P-value = 0.0056
∝ = 0.01
P-value < ∝
Reject the null hypothesis. There is sufficient evidence to support the researchers claim at the 1% significance level.
Answer:
≈ 20.11 m²
Step-by-step explanation:
Area of lawn covered by one full rotation:
- Ch = πdw, where
- C= circumference of the roller,
- w = width of the roller,
- d = diameter of the roller
<u>Area covered by 20 rotations of the roller:</u>
- 20*πdw = 20π*0.4*0.8 ≈ 20.11 m²