Question

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.

In a random sample of 69 professional actors, it was found that 36
were extroverts.

(a) Let *p* represent the proportion of all actors who
are extroverts. Find a point estimate for *p*. (Round your
answer to four decimal places.)

(b) Find a 95% confidence interval for *p*. (Round your
answers to two decimal places.)

lower limit | |

upper limit |

Give a brief interpretation of the meaning of the confidence
interval you have found.

We are 5% confident that the true proportion of actors who are extroverts falls within this interval.We are 95% confident that the true proportion of actors who are extroverts falls within this interval. We are 5% confident that the true proportion of actors who are extroverts falls above this interval.We are 95% confident that the true proportion of actors who are extroverts falls outside this interval.

(c) Do you think the conditions *np* > 5 and *nq*
> 5 are satisfied in this problem? Explain why this would be an
important consideration.

Yes, the conditions are satisfied. This is important because it
allows us to say that *p̂* is approximately binomial.No, the
conditions are not satisfied. This is important because it allows
us to say that *p̂* is approximately
normal. Yes, the conditions are satisfied.
This is important because it allows us to say that *p̂* is
approximately normal.No, the conditions are not satisfied. This is
important because it allows us to say that *p̂* is
approximately binomial.

Answer #1

solution:-

given that sample n = 69 , x = 36

(a)point estimate for p = x/n = 36/69

** = 0.5217**

(b)95% confidence values for z is 1.96

confidence interval formula for proportion

=> p +/- z * sqrt(p*(1-p)/n)

=> 0.5217 +/- 1.96 * sqrt(0.5217*(1-0.5217)/69)

=> 0.5217 +/- 0.1179

=> (0.40 , 0.64)

**lower limit = 0.40**

**upper limit = 0.64**

Give a brief interpretation of the meaning of the confidence
interval you have found

**=> We are 95% confident that the true proportion of
actors who are extroverts falls within this interval**

(c) Do you think the conditions np > 5 and nq > 5 are
satisfied in this problem? Explain why this would be an important
consideration.

**=> Yes, the conditions are satisfied. This is important
because it allows us to say that p̂ is approximately
normal**

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
In a random sample of 63 professional actors, it was found that 40
were extroverts.
(a) Let p represent the proportion of all actors who
are extroverts. Find a point estimate for p. (Round your
answer to four decimal places.)
(b) Find a 95% confidence interval for p. (Round your
answers to two decimal places.)
lower limit
upper limit ...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
In a random sample of 67 professional actors, it was found that 43
were extroverts.
(a)
Let p represent the proportion of all actors who are
extroverts. Find a point estimate for p. (Round your
answer to four decimal places.)
(b)
Find a 95% confidence interval for p. (Round your
answers to two decimal places.)
lower
limit
upper
limit ...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
In a random sample of 61 professional actors, it was found that 41
were extroverts.
(a) Let p represent the proportion of all actors who
are extroverts. Find a point estimate for p. (Round your
answer to four decimal places.)
(b) Find a 95% confidence interval for p. (Round your
answers to two decimal places.)
lower limit?
upper...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to rounding. In
a random sample of 66 professional actors, it was found that 44
were extroverts.
(a) Let p represent the proportion of all actors who are
extroverts. Find a point estimate for p. (Round your answer to four
decimal places.)
(b) Find a 95% confidence interval for p. (Round your answers to
two decimal places.)
lower limit
upper limit...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
In a random sample of 63 professional actors, it was found that 39
were extroverts.
(a) Let p represent the proportion of all actors who
are extroverts. Find a point estimate for p. (Round your
answer to four decimal places.)
(b) Find a 95% confidence interval for p. (Round your
answers to two decimal places.)
lower
limit
upper
limit ...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
In a random sample of 70 professional actors, it was found that 37
were extroverts.
(a) Let p represent the proportion of all actors who
are extroverts. Find a point estimate for p. (Round your
answer to four decimal places.)
(b) Find a 95% confidence interval for p. (Round your
answers to two decimal places.)
lower
limit
upper
limit ...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
In a random sample of 66 professional actors, it was found that 39
were extroverts.
(a) Let p represent the proportion of all actors who
are extroverts. Find a point estimate for p. (Round your
answer to four decimal places.)
(b) Find a 95% confidence interval for p. (Round your
answers to two decimal places.)
lower limit
upper limit ...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to rounding. In
a random sample of 61 professional actors, it was found that 45
were extroverts. (a) Let p represent the proportion of all actors
who are extroverts. Find a point estimate for p. (Round your answer
to four decimal places.) (b) Find a 95% confidence interval for p.
(Round your answers to two decimal places.) lower limit upper limit...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to rounding. In
a random sample of 69 professional actors, it was found that 43
were extroverts. (a) Let p represent the proportion of all actors
who are extroverts. Find a point estimate for p. (Round your answer
to four decimal places.) (b) Find a 95% confidence interval for p.
(Round your answers to two decimal places.) lower limit upper limit...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to rounding. In
a random sample of 66 professional actors, it was found that 42
were extroverts. (a) Let p represent the proportion of all actors
who are extroverts. Find a point estimate for p. (Round your answer
to four decimal places.) Incorrect: Your answer is incorrect. (b)
Find a 95% confidence interval for p. (Round your answers to two
decimal...

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