1. A worldwide organization of academics claims that the mean IQ score of its members is
. A randomly selected group of
, with a standard deviation of
members of this organization is tested, and the results reveal that the mean IQ score in
this sample is
. If the organization's claim is correct, what is the probability of having a sample mean of
for a random sample of this size?
or less
2. A minority representation group accuses a major bank of racial discrimination in its recent hires for financial analysts. Exactly
of all applications were from minority members, and exactly
the minority.
a. Find the mean of , where
from all applications.
of the
open positions were filled by members of
is the proportion of minority member applications in a random sample of
b. Find the standard deviation of
that is drawn
.
Compute an approximation for
, which is the probability that there will be
applications in a random sample of
or fewer minority member
drawn from all applications. Round your answer to four decimal places.
3. Suppose that we want to estimate the mean PCB (Polychlorinated biphenyl) level in white croaker fish from the San Francisco
Bay. The sample we select has a mean of
parts per million and a standard deviation of
parts per million. For each of
the following sampling scenarios, determine which test statistic is appropriate to use when making inference statements about the
population mean.
(In the table,
refers to a variable having a standard normal distribution, and
refers to a variable having a t distribution.)
4. The lifetime of a certain brand of electric light bulb is known to have a standard deviation of
hours. Suppose that a random
sample of
bulbs of this brand has a mean lifetime of
hours. Find a
confidence interval for the true mean
lifetime of all light bulbs of this brand. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place.
What is the lower limit of the 90% confidence interval and upper limit of the 90% confidence interval/.
5. A researcher collected sample data for
(measured in mg/100 mL) of
women ages
to
, with a standard deviation of
. The sample had a mean serum cholesterol level
. Assuming that serum cholesterol levels for women ages
to
are normally distributed, find a
confidence interval for the mean serum cholesterol level of all women in this
age group. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to one decimal place. What is the lower
limit of the confidence interval and upper limit?
6.
A random sample of
individuals working in a large city indicated that
are dissatisfied with their working conditions.
Based upon this, compute a
confidence interval for the proportion of all individuals in this city who are dissatisfied with
their working conditions. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places.
What is the lower limit of the 90% confidence interval and upper limit of the 90% confidence interval?
7. For a new study conducted by a fitness magazine,
females were randomly selected. For each, the mean daily calorie
consumption was calculated for a September-February period. A second sample of
females was chosen independently of the
first. For each of them, the mean daily calorie consumption was calculated for a March-August period. During the SeptemberFebruary period, participants consumed a mean of
calories daily with a standard deviation of
. During the
March-August period, participants consumed a mean of
calories daily with a standard deviation of
. The
population standard deviations of daily calories consumed for females in the two periods can be estimated using the sample
standard deviations, as the samples that were used to compute them were quite large. Construct a
, the difference between the mean daily calorie consumption
daily calorie consumption
confidence interval for
of females in September-February and the mean
of females in March-August. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your answers to at least two decimal places. (If
necessary, consult a list of formulas.)
What is the lower and upper limit of the 99% confidence interval?
8.
The university data center has two main computers. The center wants to examine whether computer
tasks that require processing times comparable to those of computer
computer
showed a mean of
processing times from computer
seconds with a standard deviation of
. A random sample of
seconds with a standard deviation of
computer
(chosen independently of those for computer
) showed a mean of
seconds. Assume that the populations of processing times are normally
between the mean processing time of computer
,
processing times from
seconds, while a random sample of
distributed for each of the two computers and that the variances are equal. Construct a
the difference
is receiving
,
confidence interval for
, and the mean processing time of
. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your responses to at least two decimal
places. (If necessary, consult a list of formulas.)
What is the lower limit of the 90% confidence interval and upper limit of the 90% confidence interval/.
9. A random sample of
random sample of
bolts from machine A contained
bolts from machine B contained
defective bolts, while an independently chosen,
defective bolts. Let
population of all bolts from machine A that are defective, and let
be the proportion of the
be the proportion of the population of all bolts
from machine B that are defective. Find a
confidence interval for
. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Round your responses to at least three decimal places. (If necessary,
consult a list of formulas.) What is the lower and upper limit of the 99% confidence interval?
10. An examination in communications has been taken by communications majors and also by some students from other majors. It is widely
believed that the scores for both groups are normally distributed. A random sample of
majors and an independent random sample of
examinations completed by students from other majors are selected. Among sampled
students, the communications majors scored a mean of
scored a mean of
examinations completed by communications
points with a variance of
points with a variance of
. Construct a
, and the students from other majors
confidence interval for
, the ratio of the
variance of all scores of communications majors to the variance of all scores of other majors. Then complete the table below.
Carry your intermediate computations to at least three decimal places. Write your final responses to at least two
decimal places. (If necessary, consult a list of formulas.) What is the lower limit of the 90% confidence interval and
upper limit of the 90% confidence interval/.
11. To
inspect manufacturing processes, companies typically examine samples of parts for
deficiencies. One company that manufactures ballpoint pens selected samples of
pens on
each of
days. The company recorded, for each sample of
, the number of defective pens
in the sample. Here are their data: 8, 21, 2, 3, 29, 11, 4, 9 What is the mean the median and how
many modes does the data set have?
12. BIG Corporation produces just about everything but is currently interested in the lifetimes of
its batteries, hoping to obtain its share of a market boosted by the popularity of portable CD and
MP3 players. To investigate its new line of Ultra batteries, BIG randomly selects
Ultra
batteries and finds that they have a mean lifetime of
hours, with a standard deviation of
hours. Suppose that this mean and standard deviation apply to the population of all Ultra
batteries. Complete the following statements about the distribution of lifetimes of all Ultra
batteries.
1According to Chebs theorem at least % of the lifetimes lie between 616 hours and 984 hrs?
2.
%
662
938 hrs?
3. Suppose that the distribution is bell, shape. According to the empirical rule, apprx % of the
lifetimes lie between 616 hours to 984 hours?
Suppose that the distribution is bell shape. According to the hempirical rule, approx. 99.7 of the
lifetimes lie between _____hours and ______hours/