Download Days to recover from cold Treated with multivitamin

A random selection of volunteers at a research institute have been exposed
to a typical cold virus. After they started to have cold symptoms, 15 of them
were given multivitamin tablets daily which contain 1 gram of vitamin C and
various other vitamins and minerals. The remaining 15 volunteers were
given tablets only containing 4 grams of vitamin C. For each individual, the
length of time taken to recover from cold is recorded. At the end of the
experiment the following data are obtained:
Days to recover from cold
Treated with multivitamin 7.4, 4.6, 5.9, 8.1, 2.1, 7.6, 6.8, 5.3, 8.3, 6.9,
4.0, 6.4, 7.4, 2.6, 4.8.
Treated with Vitamin C 6.4, 3.5, 5.1, 4.7, 4.3, 4.2, 3.1, 4.1, 5.4, 2.2, 5.0,
3.9, 3.6, 2.4, 4.0.
It is known that the population standard deviation of recovery time from cold
is 18 days when treated with multivitamin, and the population standard
deviation of recovery time from cold is1.5 days when treated with
vitamin C tablets. It is also known that both populations are approximately
normally distributed. The researchers claim that the mean recovery
time, μ1 ,of the patients treated with multivitamin is less than or
equal to the mean
recovery time , μ 2, of the patients who are treated with vitamin C
tablets. At the 0.05 level of significance, is there enough evidence to reject
this claim? Perform a one-tailed test. Then answer the questions below.
Carry your intermediate computations to at least three decimal
places and round your answers as specified in the
questions.
1. The null hypothesis:
H0
:
2.The alternative hypothesis:
H1
:
3. The type of test statistic:
a. Z
b. t
c. Chi-Square
d. F
4. The value of the test statistic:
(Round to at least three decimal places.)
5. The critical value at the 0.05 level of significance:
(Round to at least three decimal places.)
6. Can we reject the researchers' claim that the mean recovery
time when treated with multivitamin is less than or equal to the
mean recovery time when treated with vitamin C only?
a. Yes b. No
A random selection of volunteers at a research institute have
been exposed to a typical cold virus. After they started to have
cold symptoms, 10 of them were given multivitamin tablets daily
which contain 3 grams of vitamin C and various other vitamins
and minerals. The remaining 10 volunteers were given placebo
tablets. For each individual, the length of time taken to recover
from cold is recorded. At the end of the experiment following data
are obtained:
Days to recover from cold
Treated with multivitamin 5.7, 3.2, 6.2, 5.7, 3.5, 2.5, 5.0,
4.2, 7.7, 3.8.
Treated with placebo 3.6, 6.1, 7.5, 4.9, 5.2, 2.6, 4.3, 2.8, 4.6,
3.9.
It is known that the population standard deviation of recovery
time from cold is 1.8 days when treated with
multivitamin, and the population standard deviation of recovery
time from cold is 1.5 days when treated with
placebo tablets. It is also known that both populations are
approximately normally distributed. The researchers
claim that the mean recovery time, population (u1) , of the
patients treated with multivitamin is not equal to the mean
recovery time , population (u2), of the patients who are
treated with placebo tablets. At the 0.1 level of significance, is
there enough evidence to support this claim? Perform a two-tailed
test. Then answer the questions below.
Carry your intermediate computations to at least three decimal
places and round your answers as specified in the
questions.
1. The null hypothesis:
H0
2. The alternative hypothesis:
H1
3. The type of test statistic:
a. Z
b. t
c. Chi-Square
d. F
4.The value of the test statistic:
(Round to at least three decimal places.)
5.The p-value:
(Round to at least three decimal places.)
6.Can we support the researchers' claim that the mean recovery
time when treated with multivitamin is not
equal to the mean recovery time when treated with placebo?
a. Yes b. No
3. Much is still to be learned about the relationship between
sound frequency and loudness. One way to study the
relationship between sound frequency and loudness is to have
listeners perform loudness judgments for tones of
different frequencies. For each listener, the output of these
judgments is a number, measured in sones, that gives
the loudness of the tone relative to the loudness of a reference
tone. Suppose that you have in front of you data from an
experimental study in which listeners were asked to perform
such loudness judgments for tones of various intensities and
frequencies. The listeners were divided into
non-overlapping groups according to their hearing ability
("normal, unaided hearing," "some hearing loss at certain
frequencies," "normal, aided hearing," etc.). The data give the
sone measurements for each listener for a 50 dB
SPL, 500 -Hz tone. You perform a one-way, independent-samples
ANOVA test of the hypothesis that the mean sone measurement
are equal for the different populations of listeners represented in
the study. This ANOVA test is summarized in the ANOVA table
below. Fill in the missing value of this ANOVA table (round your
answer to at least two decimal places), and then answer the
questions below the table.
Source of Variation
Degrees of
Freedom Sum of Squares
Mean Square F statistic
Treatments
(Between Groups)
5
1.73
0.35
Error
(Within Groups)
90
19.65
0.22
Total
95
21.38
1. How many groups of listeners were tested in the experiment?
3. Using the 0.01 level of significance, what is the critical value of
the F statistic for the ANOVA test? Round your answer to at least
two decimal places.
4. Using the 0.01 level of significance, do you conclude that there
are differences in the mean sone values for this tone for the three
populations of listeners? (a) Yes (b) No
4. Jointsoft is a great over-the-counter arthritis medication, but
who will ever know about it? Unfortunately, many people with
arthritis tend to be elderly and rather immobile, so advertisers of
arthritis medications face limitations in ways to get their
messages across. Currently, their best modes of advertisement
are commercials on daytime TV, advertisements in select
magazines, fliers in convalescent homes, and (believe it or not)
advertisements on certain Web pages. Marketing managers for
Jointsoft are investigating these four modes of advertisement in
four small communities(with a different mode of advertisement in
each community). The marketing managers have selected 36
days at random and are looking at the daily sales (in dollars) in
each of the communities on each of these days. Here is what they
have to work with:
Suppose that the marketing managers perform a one-way,
independent-samples ANOVA test to decide if there are
differences in the mean daily sales arising from the four modes of
advertisement. (So, they're assuming that the only difference
among the four communities is the mode of advertisement used
in it.) Such a test uses the statistic
F=
Variation between the samples.
Variation within the samples
For the information in the chart above,
1. Give the numerator degrees of freedom of this F statistic.
2. Give the denominator degrees of freedom of this F statistic.
3.Using the 0.01 level of significance, can the marketing
managers conclude that the mean daily sales arising from at least
one of the modes of advertisement differs from the others?
(a) Yes (b) No
5. Bivariate data for the quantitative variables X and Y are
given in the table below. These data are plotted in the
scatter plot shown next to the table. In the scatter plot, sketch an
approximation of the least-squares regression line for the data.
6. Below are four bivariate data sets and the scatter plot for
each. (Note that each scatter plot is displayed on the
same scale.) Each data set is made up of sample values drawn
from a population.
Figure 1
Figure 2
Figure 3
Figure 4
Answer the following questions. The same response may be the
correct answer for more than one question.
1. Which data set indicates a perfect positive linear relationship
between its two variables?
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set
e. none of the data sets
2. Which data set has an apparent negative, but not perfect,
linear relationship between its two variables?
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set
e. none of the data sets
3. In which data set is there evidence of a strong nonlinear
relationship between the two variables?
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set
e. none of the data sets
4. Which data set indicates the strongest negative linear
relationship between its two variables?
a. the x, y data set
b. the u, v data set
c. the w, t data set
d. the m, n data set
7. An advertising firm wishes to demonstrate to its clients the
effectiveness of the advertising campaigns it has conducted. The
following bivariate data on fifteen recent campaigns, including the
cost of each campaign (in millions of dollars) and the resulting
percentage increase in sales following the campaign, were
presented by the firm. Based on these data, we would compute
the least-squares regression line to be , Y=6.13+0.20x with x
representing campaign cost and y representing the resulting
percentage increase in sales. (This line is shown in Figure 1,
along with a scatter plot of the data.)
Answer the following:
1. Fill in the blank: For these data, values for percentage
increase in sales that are greater than the mean of the
values for percentage increase in sales tend to be paired
with values for campaign cost that are _____ the mean of
the values for campaign cost.
a. greater than b. less than
2. Fill in the blank: According to the regression equation, for an
increase of one million dollars in advertising campaign cost,
there is a corresponding _____ of 0.20 percent in sales.
a. increase b. decrease
3. From the regression equation, what is the predicted
percentage increase in sales when the advertising campaign
cost is 1.43 million dollars? (Round your answer to at least
two decimal places.)
4..What was the observed percentage increase in sales when
the advertising campaign cost was 1.43 million dollars?
.
8. A financial analyst is examining the relationship between stock
prices and earnings per share. She chooses fifteen,
publicly traded companies at random and records for each the
company's current stock price and the company's
earnings per share reported for the past 12 months. Her data are
given below, with x denoting the earnings per share from the
previous year and y denoting the current stock price (both in
dollars). A scatter plot of her data is shown in Figure 1.
The value of the sample correlation coefficient y for these data is
approximately 0.879.
Answer the following. Carry your intermediate computations to at
least four decimal places, and round your answers
as specified below.
What is the value of the slope of the least-squares regression line
for these data? Round your answer to at least three decimal
places.
What is the value of the y-intercept of the least-squares
regression line for these data? Round your answer to at least
three decimal places.
9. Using 23 observations on each variable, a computer program
generated the following multiple regression model:
If the standard errors of the coefficients of the independent
variables are, respectively, 1.22 and 1.27
can you conclude that the independent variable x2 is needed in
the regression model?
Let B1 and B2 denote the coefficients of the 2 variables in this
model, and use a two-sided hypothesis test and significance level
of 0.01 to determine your answer.
Carry your intermediate computations to at least three decimal
places and round your answers as specified.
1.The null hypothesis:
H0
2.The alternative hypothesis:
H1
3. The type of test statistic:
a. Z
b. t
c. Chi-Square
d. F
4. The value of the test statistic:
(Round to at least two decimal places.)
5. The two critical values at the 0.01 level of significance:
(Round to at least two decimal places.)
1. Can you conclude that the independent variable x2 is needed
in the regression model?
a. Yes b. No
Two popular drugs used for the treatment of depression are
Resithan and Exemor. A random sample of 437depressed
individuals is selected and treated with Resithan, and 143 find
relief from their depression. A random sample of 567 depressed
individuals is independently selected from the first sample and
treated with Exemor, And 191 find relief from their depression.
Can we conclude, at the 0.1 level of significance, that the
proportion p1 of depressed individuals taking Resithan who find
relief from depression is less than the proportion p2 of all
depressed individuals taking Exemor who find relief from
depression?
Perform a one-tailed test. Then answer the questions below.
Carry your intermediate computations to at least three decimal
places and round your answers as specified in the
questions.
1. The null hypothesis:
H0
2. The alternative hypothesis:
H1
3. The type of test statistic:
a. Z
b. t
c. Chi-Square
d. F
4.The value of the test statistic:
(Round to at least three decimal places.)
5. The critical value at the 0.1 level of significance:
(Round to at least three decimal places.)
6.Can we conclude that the proportion of depressed individuals
taking Resithan who find relief is less than the proportion taking
Exemor who find relief?
a. Yes b. No
11. A coin-operated drink machine was designed to discharge a
mean of 9 ounces of coffee per cup. Suppose that
we want to carry out a hypothesis test to see if the true mean
discharge differs from 9. State the null hypothesis H0
and the alternative hypothesis H1 that we would use for this test.
H0
H1
12. The following time series data represent the yearly amounts
spent on advertising (in millions of dollars) by a large toy
company:
7.5, 9.9, 8.5, 9.5, 11.6, 10.8, 10.4, 13.9, 13.9, 13.4
This series of data begins in year 1993 (i.e., time period t = 1
corresponds to 1993 ). Using regression
analysis, a linear trend line of the form
was fit to
the data. Using this information, generate a forecast for the total
yearly amount of money that will be spent on advertising in
2010.
We want to predict the selling price of a house in Newburg Park,
Florida, based on the distance the house lies from the beach.
Suppose that we're given the data in the table below. These data
detail the distance from the beach (x, in miles) and the selling
price ( y, in thousands of dollars) for each of a sample of fifteen
homes sold in Newburg Park in the past year. The data are
plotted in the scatter plot in Figure 1. Also given are the products
of the distances from the beach and house prices for each of the
fifteen houses. (These products, written in the column labelled
"xy ," may aid in calculations.)
Figure 1
Answer the following. Carry your intermediate computations to at
least four decimal places, and round your answer as specified
below.
What is the value of the sample correlation coefficient for these
data? Round your answer to at least three decimal
places.