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liq [111]
2 years ago
15

Sample Response: You would graph the equation f(x) = –x + 3 for input values less than 2. There would be an open circle at the p

oint (2, 1) since the domain for the first piece does not include 2. You would then graph a horizontal line at f(x) = 3 for input values between 2 and 4. There would be a closed circle at (2, 3) and an open circle at (4, 3). Last, you would graph f(x) = 4 – 2x for input values greater than or equal to 4. There would be a closed circle at the point (4, –4) since 4 is in the domain of the third piece.
What did you include in your response? Check all that apply.

There would be an open circle at (2, 1).
There would be a closed circle at (2, 3).
There would be an open circle at (4, 3).
There would be a closed circle at (4, −4).
Endpoints that are not included in the domain of a particular piece of a function are represented by an open circle.
Mathematics
1 answer:
fgiga [73]2 years ago
7 0

Answer:

Step-by-step explanation:

What did you include in your response? Check all that apply.

There would be an open circle at (2, 1).  <u>Yes</u>

There would be a closed circle at (2, 3).  <u>Yes</u>

There would be an open circle at (4, 3).  <u>Yes</u>

There would be a closed circle at (4, −4).  <u>Yes</u>

Endpoints that are not included in the domain of a particular piece of a function are represented by an open circle.  <u>Yes</u>

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3 years ago
A statistician is testing the null hypothesis that exactly half of all engineers will still be in the profession 10 years after
lana [24]

Answer:

95% confidence interval estimate for the proportion of engineers remaining in the profession is [0.486 , 0.624].

(a) Lower Limit = 0.486

(b) Upper Limit = 0.624

Step-by-step explanation:

We are given that a statistician is testing the null hypothesis that exactly half of all engineers will still be in the profession 10 years after receiving their bachelor's.

She took a random sample of 200 graduates from the class of 1979 and determined their occupations in 1989. She found that 111 persons were still employed primarily as engineers.

Firstly, the pivotal quantity for 95% 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)

where, \hat p = sample proportion of persons who were still employed primarily as engineers  = \frac{111}{200} = 0.555

           n = sample of graduates = 200

           p = population proportion of engineers

<em>Here for constructing 95% confidence interval we have used One-sample z proportion test statistics.</em>

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95  {As the critical value of z at 2.5% level of

                                                 significance are -1.96 & 1.96}  

P(-1.96 < \frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } } < 1.96) = 0.95

P( -1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < {\hat p-p} < 1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

P( \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } < p < \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ) = 0.95

<u>95% confidence interval for p</u> = [ \hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } , \hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } } ]

 = [ 0.555-1.96 \times {\sqrt{\frac{0.555(1-0.555)}{200} } } , 0.555+1.96 \times {\sqrt{\frac{0.555(1-0.555)}{200} } } ]

 = [0.486 , 0.624]

Therefore, 95% confidence interval for the estimate for the proportion of engineers remaining in the profession is [0.486 , 0.624].

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