Mathematics, 29.07.2020 23:01 milonirishovnsez

Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower. Obtain and interpret a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus using Agresti and Coull's method. Construct and interpret the 95% confidence interval. Select the correct choice below and fill in the answer boxes within your choice.
(Round to three decimal places as needed.)
A. The proportion of students who eat cauliflower on Jane's campus is between_ and 95% of the time.
B. There is a 95% chance that the proportion of students who eat cauliflower in Jane's sample is between and .
C. There is a 95% chance that the proportion of students who eat cauliflower on Jane's campus is between and.
D. One is 95% confident that the proportion of students who eat cauliflower on Jane's campus is between and .

Answers: 3

Show answers

Answers

Answer from: lilymessina94

A 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus is [0.012, 0.270].

Step-by-step explanation:

We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower.

Firstly, the pivotal quantity for finding 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)

where, $\hat p$ = sample proportion of students who eat cauliflower

n = sample of students

p = population proportion of students who eat cauliflower

Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.

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

Now, in Agresti and Coull's method; the sample size and the sample proportion is calculated as;

$n = n + Z^{2}__(\frac{_\alpha}{2})$

n = $24 + 1.96^{2}$ = 27.842

$\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}$ = $\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}$ = 0.141

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

= [ $0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }$ , $0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }$ ]

= [0.012, 0.270]

Therefore, a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus [0.012, 0.270].

The interpretation of the above confidence interval is that we are 95% confident that the proportion of students who eat cauliflower on Jane's campus is between 0.012 and 0.270.

Answer from: Quest

location: point 0

step-by-step explanation:

well, -8 to 10 on a number line is 18 spaces.

1/9 of 18 is 2.

so, 4/9 of 18 must be 8.

8 spaces from -8 (a) is 0.

so, 4/9 of the way from -8 to 10 is 0!

Answer from: Quest

step-by-step explanation:

to find if any function is an inverse of the other, put the first equation in as x in the next one. then simplify and solve. if at the end you get the statement y = x, then it is an inverse. if you get anything else, it is not.

Another question on Mathematics

Mathematics, 21.06.2019 23:40

Binh says the point of intersections is (0,-3) which statements identify the errors binh made , check all that apply

Answers: 2

Answer

Mathematics, 22.06.2019 00:30

You borrow $25,000 to buy a boat. the simple interest rate is 4%. you pay the loan off after 10 years. what is the total amount you paid for the loan?

Answers: 1

Answer

Mathematics, 22.06.2019 01:30

Need asap i will give brainliest and 98 points classify each pair of numbered angles corresponding, alternate interior, alternate exterior or none o these

Answers: 2

Answer

Mathematics, 22.06.2019 02:30

Carlos by 24 mi and ran 6 miles what is the ratio of the distance carlos ran to the distance he biked

Answers: 1

Answer

You know the right answer?

Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying...

Questions