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Stella [2.4K]
3 years ago
8

Some students were asked what kinds of animals they have at home.

Mathematics
1 answer:
Nataly_w [17]3 years ago
8 0

(a) Animals by popularity; Dogs, Cats, Others, Horses.

(b) If 250 students were interviewed, 20 students have other pets.

(c) No, it was incorrect.

Step-by-step explanation:

Step 1; We arrange the different pets in chronological order, from the highest percent to the lowest percent;

1. Dogs - 67%,

2. Cats - 20%

3. Others - 8%,

4. Horses - 1%.

None is not included in this list.

Step 2; If 250 students were interviewed, 8% of those have other pets. So we need to calculate how much 8% of 250 is.

8% of 250 = \frac{8}{100} × 250 = 0.08 × 250 = 20.

So 20 students had other pets.

Step 3; 20% of the interviewed students had cats. If 75 students had cats, we need to equate 20% to the 75 and find out how many students were actually interviewed.

20% × x = 75, 0.2 × x = 75,

x = \frac{75}{0.2} = 375.

So if 375 students were interviewed, 75 students would have cats. So the estimate of 250 students being interviewed is incorrect.

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Answer:

\hat p = \frac{0.244+0.326}{2}=0.285

ME = \frac{0.326-0.244}{2}=0.041

0.285 \pm 0.041

Step-by-step explanation:

For this case we have a confidence interval given as a percent:

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We know that the confidence interval for the true proportion is given by:

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We can estimate the estimated proportion like this:

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And the margin of error can be estimaed using the fact that the confidence interval is symmetrical

ME = \frac{0.326-0.244}{2}=0.041

And then the confidence interval in the form desired is:

0.285 \pm 0.041

7 0
3 years ago
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