Question

Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 43 male firefighters are tested and that they have a plasma volume sample mean of x = 37.5 ml/kg (milliliters plasma per kilogram body weight). Assume that σ = 7.70 ml/kg for the distribution of blood plasma.

(b) What conditions are necessary for your calculations? (Select all that apply.)

σ is known

the distribution of weights is uniform

*n* is large

σ is unknown

the distribution of weights is normal

Do you want to own your own candy store? Wow! With some interest
in running your own business and a decent credit rating, you can
probably get a bank loan on startup costs for franchises such as
Candy Express, The Fudge Company, Karmel Corn, and Rocky Mountain
Chocolate Factory. Startup costs (in thousands of dollars) for a
random sample of candy stores are given below. Assume that the
population of *x* values has an approximately normal
distribution.

90 | 175 | 131 | 100 | 75 | 94 | 116 | 100 | 85 |

(a) Use a calculator with mean and sample standard deviation
keys to find the sample mean startup cost *x* and sample
standard deviation *s*. (Round your answers to one decimal
place.)

x = |
thousand dollars |

s = |
thousand dollars |

(b) Find a 90% confidence interval for the population average
startup costs *μ* for candy store franchises. (Round your
answers to one decimal place.)

lower limit | thousand dollars |

upper limit | thousand dollars |

How much do wild mountain lions weigh? Adult wild mountain lions (18 months or older) captured and released for the first time in the San Andres Mountains gave the following weights (pounds):

66 | 107 | 129 | 126 | 60 | 64 |

Assume that the population of *x* values has an
approximately normal distribution.

(b) Find a 75% confidence interval for the population average weight μ of all adult mountain lions in the specified region. (Round your answers to one decimal place.)

lower limit | lb |

upper limit | lb |

What is the minimal sample size needed for a 95% confidence interval to have a maximal margin of error of 0.1 in the following scenarios? (Round your answers up the nearest whole number.)

(a) a preliminary estimate for *p* is 0.17

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

A random sample of 5,320 permanent dwellings on an entire reservation showed that 1,662 were traditional hogans.

(a)

Let *p* be the proportion of all permanent dwellings on
the entire reservation that are traditional hogans. Find a point
estimate for *p*. (Round your answer to four decimal
places.)

(b)

Find a 99% confidence interval for *p*. (Round your
answer to three decimal places.)

lower limitupper limit

Give a brief interpretation of the confidence interval.

1% of all confidence intervals would include the true proportion of traditional hogans.1% of the confidence intervals created using this method would include the true proportion of traditional hogans. 99% of the confidence intervals created using this method would include the true proportion of traditional hogans.99% of all confidence intervals would include the true proportion of traditional hogans.

(c)

Do you think that *np* > 5 and *nq* > 5 are
satisfied for this problem? Explain why this would be an important
consideration.

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

A random sample of medical files is used to estimate the proportion
*p* of all people who have blood type B.

(a) If you have no preliminary estimate for *p*, how many
medical files should you include in a random sample in order to be
85% sure that the point estimate *p̂* will be within a
distance of 0.06 from *p*? (Round your answer up to the
nearest whole number.)

(b) Answer part (a) if you use the preliminary estimate that about 9 out of 90 people have blood type B.

Answer #1

Que.1

Necessary condition

n is large

the distribution of weights is normal.

Que.2 Candy store example

I used R software to solve this question.

> x=c(90,175,131,100,75,94,116,100,85)

> mean(x)

[1] 107.3333

> sd(x)

[1] 30.29851

> t.test(x,conf.level=0.90)

One Sample t-test

data: x

t = 10.628, df = 8, p-value = 5.379e-06

alternative hypothesis: true mean is not equal to 0

90 percent confidence interval:

88.55282 126.11385

sample estimates:

mean of x

107.3333

Mean od start up cost is 107.3 (1000$) and standard deviation is 30.3 (1000$)

90% confidence interval is

Lower limit = 88.6 thousands dollars

Upper limit = 126.1 thousands dollars

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to rounding. A
random sample of 5120 permanent dwellings on an entire reservation
showed that 1697 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings on the
entire reservation that are traditional hogans. Find a point
estimate for p. (Round your answer to four decimal places.)
(b) Find a 99% confidence interval for p. (Round your answer...

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(b) Find a 99% confidence interval for p. (Round your
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estimate for p. (Round your answer to four decimal
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(b) Find a 99% confidence interval for p. (Round your
answer...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
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reservation showed that 1683 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings
on the entire reservation that are traditional hogans. Find a point
estimate for p. (Round your answer to four decimal
places.)
(b) Find a 99% confidence interval for p. (Round your
answer...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
A random sample of 5020 permanent dwellings on an entire
reservation showed that 1683 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings
on the entire reservation that are traditional hogans. Find a point
estimate for p. (Round your answer to four decimal
places.)
(b) Find a 99% confidence interval for p. (Round your
answer...

For this problem, carry at least four digits after the decimal
in your calculations. Answers may vary slightly due to
rounding.
A random sample of 5380 permanent dwellings on an entire
reservation showed that 1676 were traditional hogans.
(a) Let p be the proportion of all permanent dwellings
on the entire reservation that are traditional hogans. Find a point
estimate for p. (Round your answer to four decimal
places.)
(b) Find a 99% confidence interval for p. (Round your
answer...

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in your calculations. Answers may vary slightly due to
rounding.
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(b) Find a 99% confidence interval for p. (Round
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