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aniked [119]
3 years ago
11

Write an inequality that expresses the range in the volume of acceptable tennis balls.

Mathematics
1 answer:
Rudik [331]3 years ago
4 0

Answer:

the smallest number is the lower bound and the largest number is the upper bound, your inequality would be

8.2 ≤ x ≤ 9.5, where x represents the volume of tennis balls.

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A magazine provided results from a poll of 500500 adults who were asked to identify their favorite pie. Among the 500500 ​respon
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Answer:

99% confidence interval is wider as compared to the 80% confidence interval.

Step-by-step explanation:

We are given that a magazine provided results from a poll of 500 adults who were asked to identify their favorite pie.

Among the 500 respondents, 14​% chose chocolate​ pie, and the margin of error was given as plus or minus ±3 percentage points. 

The pivotal quantity for the confidence interval for the population proportion is given by;

                            P.Q.  =  \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }  ~ N(0,1)

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            n = sample of adults = 500

            p = true proportion

Now, the 99% confidence interval for p =  \hat p \pm Z_(_\frac{\alpha}{2}_)  \times \sqrt{\frac{\hat p(1-\hat p)}{n} }

Here, \alpha = 1% so  (\frac{\alpha}{2}) = 0.5%. So, the critical value of z at 0.5% significance level is 2.5758.

Also, Margin of error = Z_(_\frac{\alpha}{2}_)  \times \sqrt{\frac{\hat p(1-\hat p)}{n} }  = 0.03 for 99% interval.

<u>So, 99% confidence interval for p</u>  =  0.14 \pm2.5758  \times \sqrt{\frac{0.14(1-0.14)}{500} }

                                                        = [0.14 - 0.03 , 0.14 + 0.03]

                                                        = [0.11 , 0.17]

Similarly, <u>80% confidence interval for p</u>  =  0.14 \pm 1.2816  \times \sqrt{\frac{0.14(1-0.14)}{500} }

Here, \alpha = 20% so  (\frac{\alpha}{2}) = 10%. So, the critical value of z at 10% significance level is 1.2816.

Also, Margin of error = Z_(_\frac{\alpha}{2}_)  \times \sqrt{\frac{\hat p(1-\hat p)}{n} }  = 0.02 for 80% interval.

So, <u>80% confidence interval for p</u>  =  [0.14 - 0.02 , 0.14 + 0.02]

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Now, as we can clearly see that 99% confidence interval is wider as compared to 80% confidence interval. This is because more the confidence level wider is the confidence interval and we are more confident about true population parameter.

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