If a point is chosen inside the large circle, what is the probability that it will also be inside the small circle?
1 answer:
If a point is randomly selected within the larger circle, the chance that it also lies within the smaller circle is 0.25. Step-by-step explanation: i) The area of the smaller circle is calculated as 
= 
. ii) The area of the larger circle is given by
. iii) The likelihood that a randomly selected point from the larger circle also resides in the smaller circle is expressed as
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Response:
It is inferred that the authors of the sonnets belong to a certain poet from the Elizabethan era.
Step-by-step breakdown:
The details provided in the question are as follows:
Population mean, μ = 8.9
Sample mean, = 10.2
Sample size, n = 6
Alpha, α = 0.05
Population standard deviation, σ = 2.5
Initially, we formulate the null hypothesis and the alternative hypothesis
To conduct this test, we utilize the One-tailed z test.
a) Equation:
By substituting in all relevant values, we determine:
Next,
b) The p-value is computed using the z-table.
P-value = 0.1003
The p-value surpasses the alpha of 0.05
c) Because the p-value exceeds the alpha threshold, there is insufficient evidence to dismiss the null hypothesis, thereby supporting the null hypothesis.
Consequently, it is concluded that the authorship of the sonnets belongs to a particular Elizabethan poet.