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sashaice [31]
3 years ago
11

A U.S. Travel Data Center survey of 500 adults found that 195 said they would take more vacations this year than last year. Cons

truct a 95% confidence interval for the true proportion of adults who said that they will travel more this year.
Mathematics
1 answer:
Lelechka [254]3 years ago
5 0

Using the z-distribution, it is found that the 95% confidence interval for the true proportion of adults who said that they will travel more this year is (0.347, 0.433).

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

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

In which z is the z-score that has a p-value of \frac{1+\alpha}{2}.

195 out of 500 people said they would take more vacations this year than last year, hence:

n = 500, \pi = \frac{195}{500} = 0.39

95% confidence level, hence\alpha = 0.95, z is the value of Z that has a p-value of \frac{1+0.95}{2} = 0.975, so z = 1.96.

The lower limit of this interval is:

\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.39 - 1.96\sqrt{\frac{0.39(0.61)}{500}} = 0.347

The upper limit of this interval is:

\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.39 + 1.96\sqrt{\frac{0.39(0.61)}{500}} = 0.433

The 95% confidence interval for the true proportion of adults who said that they will travel more this year is (0.347, 0.433).

A similar problem is given at brainly.com/question/15850972

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Given that:

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n           r

1        30.00

2       33.60

3       37.63

4       42.15

5       47.21

6       52.87

7       59.21

8       66.32

9       74.28

10      83.19

11       93.18

12      104.36

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if each rabbit consume 10 lbs of rabbit food each year

n           r                food consumed(lbs)

1        30.00               300

2       33.60               336

3       37.63                376

4       42.15                422

5       47.21                472

6       52.87               529

7       59.21                592

8       66.32               663

9       74.28               743

10      83.19                832

total                          5265

Therefore, the rabbit food consumed during the 10th year is approximately 832 pounds

And the rabbit food consumed in total for the 1st through 10th years is approximately 5265 pounds

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