1)Suppose a random sample of n = 16 observations is selected from a population t
ID: 3361512 • Letter: 1
Question
1)Suppose a random sample of n = 16 observations is selected from a population that is normally distributed with mean equal to 101 and standard deviation equal to 12.
(a) Give the mean and the standard deviation of the sampling distribution of the sample mean x(with a line above). (Enter your standard deviation to two decimal places.)
mean =
standard deviation =
(b) Find the probability that x(line above it) exceeds 107. (Round your answer to four decimal places.)
Answer:
(c) Find the probability that the sample mean deviates from the population mean = 101 by no more than 4. (Round your answer to four decimal places.)
Answer:
2)Find a 90% confidence interval for a population mean for these values. (Round your answers to three decimal places.)
(a) n = 115, x = 0.85, s2 = 0.082
_______ to________
(b) n = 40, x = 27.4, s2 = 3.77
_______ to ________
(c) Interpret the intervals found in parts (a) and (b).
a) There is a 90% chance that an individual sample proportion will fall within the interval.
b)In repeated sampling, 10% of all intervals constructed in this manner will enclose the population proportion.
c)There is a 10% chance that an individual sample proportion will fall within the interval.
d)In repeated sampling, 90% of all intervals constructed in this manner will enclose the population mean.
e) 90% of all values will fall within the interval.
3)A) A random sample of n = 400 observations from a binomial population produced x = 366 successes. Find a 90% confidence interval for p. (Round your answers to three decimal places.)
_______ to ______
B)Interpret the interval.
a)90% of all values will fall within the interval.
b)There is a 10% chance that an individual sample proportion will fall within the interval.
c)There is a 90% chance that an individual sample proportion will fall within the interval.
d)In repeated sampling, 10% of all intervals constructed in this manner will enclose the population proportion.
e)In repeated sampling, 90% of all intervals constructed in this manner will enclose the population proportion.
4. A random sample of n measurements is selected from a population with unknown mean and known standard deviation = 9.Calculate the width of a 95% confidence interval for for these values of n. (Round your answers to two decimal places.)
(a) n = 81
_______
(b) n = 300
_________
(c) n = 900
_________
5) Acid rain, caused by the reaction of certain air pollutants with rainwater, is a growing problem in the United States. Pure rain falling through clean air registers a pH value of 5.7 (pH is a measure of acidity: 0 is acid; 14 is alkaline). Suppose water samples from 90 rainfalls are analyzed for pH, and x and s are equal to 3.2 and 0.5, respectively. Find a 99% confidence interval for the mean pH in rainfall. (Round your answers to three decimal places.)
______ to _______
A)Interpret the interval.
a)In repeated sampling, 1% of all intervals constructed in this manner will enclose the population mean.
b)In repeated sampling, 99% of all intervals constructed in this manner will enclose the population mean.
c)There is a 99% chance that an individual sample mean will fall within the interval.
d)There is a 1% chance that an individual sample mean will fall within the interval.
e)99% of all values will fall within the interval.
B)What assumption must be made for the confidence interval to be valid?
a)The standard deviation must be less than 10.
b)The sample must be random.
c)The sample mean must be greater than 5.
d)The sampling distribution must be symmetrical.
e)There must be at least 100 samples.
Explanation / Answer
1)
a)
mean = 101
standard deviation = 12/sqrt(16) = 12/4 = 3
b)
P(X >107) = P(Z > 107-101/3)
= P(Z > 2)
= 0.0228
c)
P(97<X<105) = P(X < 105) - P(X < 97)
= P(Z < 105-101/3) - P(Z < 97-101/3)
= P(Z < 1.3333) - P(Z < -1.333)
= 0.1824
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