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pochemuha
3 years ago
15

Before sending track and field athletes to the Olympics, the U.S. Holds a qualifying meet. The box plots below show the distance

s (in meters) achieved in the final round by the top 111111 women's discus throwers at the 201220122012 Olympic games and the top 121212 women's discus throwers at the U.S. Qualifying meet. Which pieces of information can be gathered from these box plots?
Mathematics
2 answers:
34kurt3 years ago
8 0

Answer:A

Step-by-step explanation:

sleet_krkn [62]3 years ago
7 0

Question:

The options are;

A. The distances in the Olympic final were farther on average.

B. The distances in the Olympic final varied noticeably more than the US qualifier distances

C. The distances in the Olympic final were all greater than the US qualifier distances

D. none of the above

Answer:

The correct option is;

A. The distances in the Olympic final were farther on average.

Step-by-step explanation:

From the options given, we have

A. The distances in the Olympic final were farther on average.

This is true as the sum of the 5 points divided by 5 is more in the Olympic final

B. The distances in the Olympic final varied noticeably more than the US qualifier distances

This is not correct as the difference between the upper and lower quartile in the Olympic final is lesser than in the qualifier

C. The distances in the Olympic final were all greater than the US qualifier distances

This is not correct as the max of the qualifier is more than the lower quartile in the Olympic final

D. none of the above

We have seen a possible correct option in option A

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Answer:

a) The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

b)

The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c) They are respected, as the upper bound of both intervals is below the new FAA recommendations.

Step-by-step explanation:

We have the standard deviation for the sample, which means that the t-distribution is used to solve these questions.

Question a:

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 100 - 1 = 99

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 99 degrees of freedom(y-axis) and a confidence level of 1 - \frac{1 - 0.95}{2} = 0.975. So we have T = 1.9842

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.9842\frac{20}{\sqrt{100}} = 4

In which s is the standard deviation of the sample and n is the size of the sample.

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The upper end of the interval is the sample mean added to M. So it is 183 + 4 = 187 pounds.

The 95% confidence interval for the mean summer weight (including carry-on luggage) of Frontier Airlines passengers is between 179 and 187 pounds. This means that we are 95% sure that the mean summer weight of all Frontier Airlines passengers is between these two values.

Question b:

Critical value is the same(same sample size and confidence level).

The margin of error is:

M = T\frac{s}{\sqrt{n}} = 1.9842\frac{23}{\sqrt{100}} = 4.6

The lower end of the interval is the sample mean subtracted by M. So it is 190 - 4.6 = 185.4 pounds.

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The 95% confidence interval for the mean winter weight (including carry-on luggage) of Frontier Airlines passengers is between 185.4 pounds and 194.6 pounds. This means that we are 95% sure that the mean winter weight of all Frontier Airlines passengers is between these two values.

c. The new FAA recommendations are 190 pounds for summer and 195 pounds for winter. Comment on these recommendations in light of the confidence interval estimates from Parts (a) and (b).

They are respected, as the upper bound of both intervals is below the new FAA recommendations.

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