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Marina86 [1]
3 years ago
9

In a sample of 1000 randomly, selected consumers who had opportunities to send in a rebate claim form after purchasing a product

, 250 of these people said they never did so. Reasons cited for their behavior included too many steps in the process, amount too small, missed deadline, fear of being placed on a mailing list, lost receipt, and doubts about receiving the money. Calculate a 95% confidence Interval for the true proportion of such consumers who never apply for a rebate.
Mathematics
1 answer:
Alexxx [7]3 years ago
8 0

Answer: =(0.2232,0.2768)

Step-by-step explanation:

The confidence interval for population proportion is given by :-

p\ \pm z_{\alpha/2}\sqrt{\dfrac{p(1-p)}{n}}

Given : Sample size : n=1000

The proportion of people selected consumers who had opportunities to send in a rebate claim form after purchasing a product said they never did so =\dfrac{250}{1000}=0.25

Significance level : 1-0.95=0.05

Critical value : z_{\alpha/2}=1.96

Now, the 95% confidence Interval for the true proportion of such consumers who never apply for a rebate will be :-

0.25\ \pm (1.96)\sqrt{\dfrac{0.25(1-0.25)}{1000}}\\\\\approx0.25\pm0.0268\\\\=(0.2232,\ 0.2768)

Hence, a confidence Interval for the true proportion of such consumers who never apply for a rebate .

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Philip made a total of 9 bracelets and necklaces from 120 inches of cord. He used 8 inches of cord for each bracelet and 20 inch
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Step-by-step explanation:

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Also, we have 8 inches of cord for each bracelet and 20 inches of cord for each necklace, then the total length for the bracelet is 8x and that for the necklace is 20y.

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Writing equations (1) and (3) in matrix form, we have

\left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}9\\30\end{array}\right]

Using Cramer's rule to solve for x and y,

x = det \left[\begin{array}{ccc}9&1\\30&5\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\

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y = det \left[\begin{array}{ccc}1&9\\2&30\end{array}\right] /det \left[\begin{array}{ccc}1&1\\2&5\end{array}\right] \\

y = (30 × 1 - 9 × 2) ÷ (1 × 5 - 1 × 2)

y = (30 - 18) ÷ (5 - 2)

y = 12 ÷ 3

y = 4

So Philip made 5 bracelets and 4 necklaces.

3 0
3 years ago
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