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DanielleElmas [232]
3 years ago
10

A random sample of 400 items from a population shows that 160 of the sample items possess a given characteristic. A random sampl

e of 400 items from a second population resulted in 110 of the sample items possessing the characteristic. Using this data, a 99% confidence interval is constructed to estimate the difference in population proportions which possess the given characteristic. The resulting confidence interval is _______.
Mathematics
1 answer:
Free_Kalibri [48]3 years ago
3 0

Answer: (0.04,\ 0.21)

Step-by-step explanation:

The confidence interval for population proportion is given by :-

p_1-p_2\pm z_{\alpha/2}\sqrt{\dfrac{p_1(1-p_1)}{n_1}+\dfrac{p_2(1-p_2)}{n_2}}

Given : Significance level : \alpha=1-0.99=0.01

Critical value : z_{\alpha/2}=2.576

n_1=400 ;\ p_1=\dfrac{160}{400}=0.4

n_2=400 ;\ p_2=\dfrac{110}{400}=0.275

Then a 99% confidence interval is constructed to estimate the difference in population proportions which possess the given characteristic will be :-

0.4-0.275\pm (2.576)\sqrt{\dfrac{0.4(1-0.4)}{400}+\dfrac{0.275(1-0.275)}{400}}\\\\\approx0.125\pm0.085=(0.125-0.085,0.125+0.085)=(0.04,\ 0.21)

Hence, the resulting confidence interval is (0.04,\ 0.21) .

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Complete Question

Carmen and Matt are conducting different chemistry experiments in school. In both experiments, each student starts with an initial amount of water in a flask. They combine two chemicals which react to produce more water. Carmen's experiment starts with 30 milliliters of water in a flask, and the water increases in volume by 8.5 milliliters per second. Matt's experiment starts with 10 milliliters of water and increases in volume by 28% each second. The graph represents the volume of water in the two flasks in relation to time. Which two conclusions can be made if f represents the volume of water in Carmen's flask and g represents the volume of water in Matt's flask? a) The volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval [0, 2].

b) The volume of water in Carmen's flask is increasing at a faster rate than the volume of water in Matt's flask over the interval [6, 8].

c) The volume of water in Carmen's flask will always be greater than the volume of water in Matt's flask.

d) The volume of water in Matt's flask will eventually be greater than the volume of water in Carmen's flask.

e) The volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval [4, 6].

Answer:

c) The volume of water in Carmen's flask will always be greater than the volume of water in Matt's flask.

e) The volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval [4, 6].

Step-by-step explanation:

Looking at the graph, the average rate of change is given as [0,2], [4,6], and [6,8].

From the graph and question, we can tell that Matt's experiment starts with 10 milliliters of water and increases in volume by 28% each second

Which would gives us:

28% of 10 milliliter of water = 2.8 millimeters per second.

For Carmen , his experiment starts with 30 milliliters of water in a flask, and the water increases in volume by 8.5 milliliters per second,

Because, Carmen starts with 30 milliliters of water in his flask, the volume of water in Carmen's flask will always be greater than the volume of water in Matt's flask.

Secondly, comparing the quantity as which the volume of the flask increases per second, at the interval of [4, 6], the volume of water in Carmen's flask is increasing at a slower rate than the volume of water in Matt's flask over the interval

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