First, you want to get x by itself on one side. We write the equation as

. Since 14 is being subtracted from

, we add it to both sides to cancel it out,

or

.
Your answer would be D.
Answer:
(25.53, 37.87): 95% CI
(23.59, 39.81): 99% CI
Step-by-step explanation:
The margin of error of a confidence interval is given by:

In which
is the standard deviation of the population and n is the size of the sample.
z is related to the confidence level. The higher the confidence level, the higher the values of z, and thus, we wider the confidence interval is.
In this question:
The narrower C.I. is the 95%, and the wider is the 99%. So
(25.53, 37.87): 95% CI
(23.59, 39.81): 99% CI
Answer:
The fourth line will have 15 marbles
Step-by-step explanation:
The third line has 7 marbles. So, you double that and add one in order to find the number of marbles in the fourth line.
7*2=14
14+1=15
Answer:
try the calculator best thing to use
Answer:
a) 0.0853
b) 0.0000
Step-by-step explanation:
Parameters given stated that;
H₀ : <em>p = </em>0.6
H₁ : <em>p = </em>0.6, this explains the acceptance region as;
p° ≤
=0.63 and the region region as p°>0.63 (where p° is known as the sample proportion)
a).
the probability of type I error if exactly 60% is calculated as :
∝ = P (Reject H₀ | H₀ is true)
= P (p°>0.63 | p=0.6)
where p° is represented as <em>pI</em><em> </em>in the subsequent calculated steps below
= P ![[\frac{p°-p}{\sqrt{\frac{p(1-p)}{n}}} >\frac{0.63-p}{\sqrt{\frac{p(1-p)}{n}}} |p=0.6]](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bp%C2%B0-p%7D%7B%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%20%3E%5Cfrac%7B0.63-p%7D%7B%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%7D%7D%20%7Cp%3D0.6%5D)
= P ![[\frac{p°-0.6}{\sqrt{\frac{0.6(1-0.6)}{500}}} >\frac{0.63-0.6}{\sqrt{\frac{0.6(1-0.6)}{500}}} ]](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bp%C2%B0-0.6%7D%7B%5Csqrt%7B%5Cfrac%7B0.6%281-0.6%29%7D%7B500%7D%7D%7D%20%3E%5Cfrac%7B0.63-0.6%7D%7B%5Csqrt%7B%5Cfrac%7B0.6%281-0.6%29%7D%7B500%7D%7D%7D%20%5D)
= P ![[Z>\frac{0.63-0.6}{\sqrt{\frac{0.6(1-0.6)}{500} } } ]](https://tex.z-dn.net/?f=%5BZ%3E%5Cfrac%7B0.63-0.6%7D%7B%5Csqrt%7B%5Cfrac%7B0.6%281-0.6%29%7D%7B500%7D%20%7D%20%7D%20%5D)
= P [Z > 1.37]
= 1 - P [Z ≤ 1.37]
= 1 - Ф (1.37)
= 1 - 0.914657 ( from Cumulative Standard Normal Distribution Table)
≅ 0.0853
b)
The probability of Type II error β is stated as:
β = P (Accept H₀ | H₁ is true)
= P [p° ≤ 0.63 | p = 0.75]
where p° is represented as <em>pI</em><em> </em>in the subsequent calculated steps below
= P ![[\frac{p°-p} \sqrt{\frac{p(1-p)}{n} } }\leq \frac{0.63-p}{\sqrt{\frac{p(1-p)}{n} } } | p=0.75]](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bp%C2%B0-p%7D%20%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%20%7D%20%7D%5Cleq%20%5Cfrac%7B0.63-p%7D%7B%5Csqrt%7B%5Cfrac%7Bp%281-p%29%7D%7Bn%7D%20%7D%20%7D%20%7C%20p%3D0.75%5D)
= P ![[\frac{p°-0.6} \sqrt{\frac{0.75(1-0.75)}{500} } }\leq \frac{0.63-0.75}{\sqrt{\frac{0.75(1-0.75)}{500} } } ]](https://tex.z-dn.net/?f=%5B%5Cfrac%7Bp%C2%B0-0.6%7D%20%5Csqrt%7B%5Cfrac%7B0.75%281-0.75%29%7D%7B500%7D%20%7D%20%7D%5Cleq%20%5Cfrac%7B0.63-0.75%7D%7B%5Csqrt%7B%5Cfrac%7B0.75%281-0.75%29%7D%7B500%7D%20%7D%20%7D%20%5D)
= P![[Z\leq\frac{0.63-0.75}{\sqrt{\frac{0.75(1-0.75)}{500} } } ]](https://tex.z-dn.net/?f=%5BZ%5Cleq%5Cfrac%7B0.63-0.75%7D%7B%5Csqrt%7B%5Cfrac%7B0.75%281-0.75%29%7D%7B500%7D%20%7D%20%7D%20%5D)
= P [Z ≤ -6.20]
= Ф (-6.20)
≅ 0.0000 (from Cumulative Standard Normal Distribution Table).