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Bombin1118
10.03.2021 •
Mathematics
Consider the line y=8x - 4.
What is the slope of a line parallel to this line?
What is the slope of a line perpendicular to this line?
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Ответ:
Parallel - 8
Perpendicular - -1/8
Step-by-step explanation:
If a line is parallel to another then they have the same slope
If a line is perpendicular to another line then the slope is just flipped and so is the sign
Ответ:
a)
b) 34%
c) practically 0
d) Reject the null hypothesis.
Step-by-step explanation:
a)
Since an individual aged 18 to 32 either continues to be dependent on their parents or not, this situation follows a Binomial Distribution and, according to the previous research, the probability p of “success” (depend on their parents) is 0.3 (30%) and the probability of failure q = 0.7
According to the sample, p seems to be 0.34 and q=0.66
To see if we can approximate this distribution with a Normal one, we must check that is not too skewed; this can be done by checking that np ≥ 5 and nq ≥ 5, where n is the sample size (400), which is evident.
We can then, approximate our Binomial with a Normal with mean
and standard deviation
Since in the current research 136 out of 400 individuals (34%) showed to be continuing dependent on their parents:
So, this is a right-tailed hypothesis testing.
b)
According to the sample the proportion of "millennials" that are continuing to be dependent on their parents is 0.34 or 34%
c)
Our level of significance is 0.05, so we are looking for a value
such that the area under the Normal curve to the right of
is ≤ 0.05
This value can be found by using a table or the computer and is
= 1.645
Applying the continuity correction factor (this should be done because we are approximating a discrete distribution (Binomial) with a continuous one (Normal)), we simply add 0.5 to this value and
Now we compute the z-score corresponding to the sample
where
s = standard deviation of the sample
n = size of the sample
The sample z-score is then
The p-value provided by the sample data would be the area under the Normal curve to the left of 33.7759 which can be considered zero.
d)
Since the z-score provided by the sample falls far to the left of
we should reject the null hypothesis and propose a new mean of 34%.