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Flura [38]
3 years ago
15

If a manufacturer conducted a survey among randomly selected target market households and wanted to be 95​% confident that the d

ifference between the sample estimate and the actual market share for its new product was no more than 9​%, what sample size would be​ needed?
Mathematics
1 answer:
katen-ka-za [31]3 years ago
6 0

Answer:

We need a sample size of least 119

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of \pi, and a confidence level of 1-\alpha, we have the following confidence interval of proportions.

\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}

In which

z is the zscore that has a pvalue of 1 - \frac{\alpha}{2}.

The margin of error is:

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

95% confidence level

So \alpha = 0.05, z is the value of Z that has a pvalue of 1 - \frac{0.05}{2} = 0.975, so Z = 1.96.

Sample size needed

At least n, in which n is found when M = 0.09

We don't know the proportion, so we use \pi = 0.5, which is when we would need the largest sample size.

M = z\sqrt{\frac{\pi(1-\pi)}{n}}

0.09 = 1.96\sqrt{\frac{0.5*0.5}{n}}

0.09\sqrt{n} = 1.96*0.5

\sqrt{n} = \frac{1.96*0.5}{0.09}

(\sqrt{n})^{2} = (\frac{1.96*0.5}{0.09})^{2}

n = 118.6

Rounding up

We need a sample size of least 119

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ch4aika [34]
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3 years ago
The Moores paid $6 more for skate rentals than the Cotters did. Together, the two families paid $30 for skate rentals.How many p
iren2701 [21]

Answer:

Step-by-step explanation:

Consider Cotters paid "x" dollars:

According to given condition:

Moores paid "x+6" dollars.

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3 0
3 years ago
Read 2 more answers
A rectangular football field is 64 meters wide and 100 maters long. A player runs from one corner of the field in a diagonal lin
Dimas [21]

Answer:

119 or 118.726577

Step-by-step explanation:

We should use the Pythagorean Theorem to solve this problem.

a^2+ b^2=c^2

64^2+100^2=c^2

4096+10000=14096

c^2=14096

c=\sqrt{14096}14096

And the root of 14096 is 118.726577.

So the Answer is About 119 meters, or 118.726577

hope this helps!

3 0
2 years ago
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