Consider the following figure.
1 answer:
Answer:
80 units.
Step-by-step explanation:
The rectangle ABCD is drawn and attached in the image below. The diagonal BD measures 100 units, the side BC measures 60 units. We need to find the measure of side DC which is represented by x in the figure.
Note that a Right Angled Triangle DCB is being formed with BD as the hypotenuse and sides BC and DC as its two legs. The Pythagoras Theorem relates the length of hypotenuse and the two legs of the Right Angled Triangle as:
c is the length of hypotenuse = 100
a is the length of one leg = 60
b is the length of second leg = x
Using these values, we get:
Therefore, measure of the side DC is 80 units
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Answer:
a) The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.
b) Wider
Step-by-step explanation:
Question a:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the z-score that has a p-value of .
In a survey of randomly selected 3,900 family-owned businesses with revenues exceeding $1 million a year, it was found that 1,911 of them had no strategic business plan.
This means that
90% confidence level
So , z is the value of Z that has a p-value of
, so
.
The lower limit of this interval is:
The upper limit of this interval is:
The 90% confidence interval to estimate the proportion of family-owned businesses without strategic business plans is (0.4768, 0.5032). This means that we are 90% sure that the true proportion of all family-owned businesses without strategic business plans is between these two values.
Question b:
The margin of error is:
The higher the confidence level, the higher the value of z, thus the higher the margin of error and the interval is wider. Thus, a 99% confidence interval is wider than a 90% confidence interval.