# The Lower Limit of The Confidence Interval Statistics Questions

Description

Question 1
The population standard deviation in the sales of bikes per day of an
automobile company is known to be 3 bikes per day. A random sample
of 47 days has a mean sales of 5 bikes per day. Identify the distribution
that can be used to construct a confidence interval for the mean sales
per day:
A. The distribution that can be used in constructing a confidence
interval is the Chi-square distribution with (n-1) degrees of freedom
B. The distribution that can be used in constructing a confidence
interval is the normal distribution with mean and standard deviation > 0
C. The distribution that can be used in constructing a confidence
interval is the standard normal distribution
D. The distribution that can be used in constructing a confidence
interval is the t distribution with (n-1) degrees of freedom
E. The distribution that can be used in constructing a confidence
interval is the F distribution
Question 2
A random variable X takes on the following values and probabilities:
X
1
2
3
4
P(X=x)
0.07
0.22
0.09
0.62
Find the mean value of X.
If rounding is needed, round only once you have completed all
calculations (to two decimals, example answer: 1.23).
Question 3
Let X be the number of problems solved in a single day (along with their
associated probabilities).
X
1
6
11
18
21
P(X=x)
0.18
0.32
0.28
0.12
0.1
Calculate the variance and standard deviation for the random variable
X:
If rounding is needed, round only once you have completed all
calculations (to two decimals, example answer: 1.23).
Question 4
The duration of a cricket match is normally distributed with a mean of
182 minutes and a standard deviation of 9 minutes. Find the probability
that a cricket match is completed within 180 minutes
A. The probability that a cricket match is completed within 180 minutes
is 0.588
B. The probability that a cricket match is completed within 180 minutes
is 0.222
C. The probability that a cricket match is completed within 180 minutes
is 0.788
D. The probability that a cricket match is completed within 180 minutes
is 0.412
E. The probability that a cricket match is completed within 180 minutes
is 0.500
Question 5
A student claims that the average audience size of sports events is
significantly different from 190 in his school. He samples 30 sports
events, and the average audience size is 220. We already know the
standard deviation of audience size of sports events in his school is 25.
Test the student’s claim at 90% confidence level by using both the
confidence interval and hypothesis testing methods. What is the decision
in terms of the null hypothesis by both the methods?
A. The null hypothesis is rejected, and the student is correct in her claim
by using both the hypothesis and confidence interval methods.
B. The null hypothesis is rejected, and the student is not correct in her
claim by using both the hypothesis and confidence interval methods.
C. The null hypothesis is not rejected, and the student is correct in her
claim by using both the hypothesis and confidence interval methods.
D. The null hypothesis is not rejected, and the student is not correct in
her claim by using both the hypothesis and confidence interval methods.
Question 6
The average waiting time duration in a medical clinic is assumed to be 45
minutes with a standard deviation of 10 minutes. A researcher
conducted a hypothesis test to test whether the average waiting time is
more than 45 minutes. The test statistic value is found to be
1.907. Given an interpretation of the test at 0.01 (1%) level of
significance:
A. The null hypothesis is rejected and there is insufficient evidence to
conclude that the average waiting time duration in the medical clinic is
more than 45 minutes
B. The null hypothesis is rejected and there is sufficient evidence to
conclude that the average waiting time duration in the medical clinic is
more than 45 minutes
C. The null hypothesis is not rejected and there is insufficient evidence
to conclude that the average waiting time duration in the medical clinic is
more than 45 minutes
D. The null hypothesis is not rejected and there is sufficient evidence to
conclude that the average waiting time duration in the medical clinic is
more than 45 minutes
Question 7
To test H0:μ≥40,Ha:μ0.04
E. H0:p≤0.04Ha:p>0.04
F. H0:μ≤0.04Ha:μ>0.04
Question 10
In a private hospital, the director claimed that they provide all the
essentials to the nurses for their work (in terms of medical equipment,
travel facilities, etc.) and that exactly 90% (no more or less) of the nurses
are satisfied with the essentials provided by the hospital. 79 nurses were
sampled and asked whether they are satisfied with the essentials in the
hospital — 7 nurses said they were not. Find the appropriate test statistic
and p-value for this test.
A.
B.
C.
D.
The test statistic is 0.34 and the p-value is 0.7339
The test statistic is 0.34 and the p-value is 0.3669
The test statistic is 0.34 and the p-value is 0.633
The test statistic is 0.34 and the p-value is 0.367
Question 11
The 95% confidence interval for the proportion of students who work in
part time jobs is (0.0815, 0.1785). The sample proportion of students
who work in part time jobs is known to be 0.13. What sample size is used
to obtain the confidence interval: (Only round at the end of your
calculation to nearest whole number. Example answer: 137)
Question 12
A researcher claims that the proportion of athlete fatalities related to
alcohol is less than 24%. In a random sample of 35 athlete fatalities, it
was found that 17% of deaths were caused by alcohol. Test the claim at
alpha = 1%
B. There is not enough evidence to conclude that the proportion of
athlete fatalities related to alcohol is greater than 24%
C. There is sufficient evidence to conclude that the proportion of athlete
fatalities related to alcohol is greater than 24%
D. There is not enough evidence to conclude that the proportion of
athlete fatalities related to alcohol is less than 24%
E. There is sufficient evidence to conclude that the proportion of athlete
fatalities related to alcohol is less than 24%
Question 13
The upper limit of a 99% confidence interval for the mean is known to be
45.4 and the standard error is 3.7. If the population standard deviation is
known, find the lower limit of the given confidence interval:
A.
B.
C.
D.
The lower limit of the confidence interval is 26.35
The lower limit of the confidence interval is 35.87
The lower limit of the confidence interval is 36.79
The lower limit of the confidence interval is 28.19
Question 14
The 99% confidence interval for the mean number of road accidents per
day in a country is known as (14.3, 19.3). Is there sufficient evidence to
conclude that the mean number of accidents is 17.4 per day?
A. The null hypothesis is rejected and there is insufficient evidence to
conclude that the mean number of accidents is 17.4 per day
B. The null hypothesis is not rejected and there is insufficient evidence
to conclude that the mean number of accidents is 17.4 per day
C. The null hypothesis is not rejected and it’s possible that the mean
number of accidents is 17.4 per day
D. The null hypothesis is rejected and it’s possible that the mean
number of accidents is 17.4 per day
E. There is not enough information provided to make a decision for a
hypothesis test
Question 15
The 95% confidence interval for the proportion of people who support
the new budget scheme is (0.34 – 0.60). Find the margin of error and
standard error of this estimate.
A. The margin of error is 0.130 and the standard error of the estimate is
0.0663
B. The margin of error is 0.130 and the standard error of the estimate is
0.0790
C. The margin of error is 0.260 and the standard error of the estimate is
0.0663
D. The margin of error is 0.260 and the standard error of the estimate is
0.0790
Question 16
In a sample of 400 high school students, the proportion of students who
support a new teaching method is 0.25. Give an interpretation for a 99%
confidence interval for the proportion of students who support the new
teaching method.
A. There is 99% confidence that the sample proportion of students who
support the new teaching method lies between 0.1941 and 0.3059
B. There is 99% confidence that the population proportion of students
who support the new teaching method lies between 0.1941 and 0.3059
C. There is 99% confidence that the sample proportion of students who
support the new teaching method lies between 0.1996 and 0.3004
D. There is 99% confidence that the population proportion of students
who support the new teaching method lies between 0.1996 and 0.3004
Question 17
Which of the following is inversely proportional to the width of the
confidence interval for proportions?
A. Confidence level is inversely proportional to the width of the
confidence interval for proportions
B. Sample size is inversely proportional to the width of the confidence
interval for proportions
C. Standard Error is inversely proportional to the width of the
confidence interval for proportions
D. Sample proportion (00.04
F. H0:μ≤0.04Ha:μ>0.04
Question 10
In a private hospital, the director claimed that they provide all the
essentials to the nurses for their work (in terms of medical equipment,
travel facilities, etc.) and that exactly 90% (no more or less) of the nurses
are satisfied with the essentials provided by the hospital. 79 nurses were
sampled and asked whether they are satisfied with the essentials in the
hospital — 7 nurses said they were not. Find the appropriate test statistic
and p-value for this test.
A.
B.
C.
D.
The test statistic is 0.34 and the p-value is 0.7339
The test statistic is 0.34 and the p-value is 0.3669
The test statistic is 0.34 and the p-value is 0.633
The test statistic is 0.34 and the p-value is 0.367
Question 11
The 95% confidence interval for the proportion of students who work in
part time jobs is (0.0815, 0.1785). The sample proportion of students
who work in part time jobs is known to be 0.13. What sample size is used
to obtain the confidence interval: (Only round at the end of your
calculation to nearest whole number. Example answer: 137)
Question 12
A researcher claims that the proportion of athlete fatalities related to
alcohol is less than 24%. In a random sample of 35 athlete fatalities, it
was found that 17% of deaths were caused by alcohol. Test the claim at
alpha = 1%
B. There is not enough evidence to conclude that the proportion of
athlete fatalities related to alcohol is greater than 24%
C. There is sufficient evidence to conclude that the proportion of athlete
fatalities related to alcohol is greater than 24%
D. There is not enough evidence to conclude that the proportion of
athlete fatalities related to alcohol is less than 24%
E. There is sufficient evidence to conclude that the proportion of athlete
fatalities related to alcohol is less than 24%
Question 13
The upper limit of a 99% confidence interval for the mean is known to be
45.4 and the standard error is 3.7. If the population standard deviation is
known, find the lower limit of the given confidence interval:
A.
B.
C.
D.
The lower limit of the confidence interval is 26.35
The lower limit of the confidence interval is 35.87
The lower limit of the confidence interval is 36.79
The lower limit of the confidence interval is 28.19
Question 14
The 99% confidence interval for the mean number of road accidents per
day in a country is known as (14.3, 19.3). Is there sufficient evidence to
conclude that the mean number of accidents is 17.4 per day?
A. The null hypothesis is rejected and there is insufficient evidence to
conclude that the mean number of accidents is 17.4 per day
B. The null hypothesis is not rejected and there is insufficient evidence
to conclude that the mean number of accidents is 17.4 per day
C. The null hypothesis is not rejected and it’s possible that the mean
number of accidents is 17.4 per day
D. The null hypothesis is rejected and it’s possible that the mean
number of accidents is 17.4 per day
E. There is not enough information provided to make a decision for a
hypothesis test
Question 15
The 95% confidence interval for the proportion of people who support
the new budget scheme is (0.34 – 0.60). Find the margin of error and
standard error of this estimate.
A. The margin of error is 0.130 and the standard error of the estimate is
0.0663
B. The margin of error is 0.130 and the standard error of the estimate is
0.0790
C. The margin of error is 0.260 and the standard error of the estimate is
0.0663
D. The margin of error is 0.260 and the standard error of the estimate is
0.0790
Question 16
In a sample of 400 high school students, the proportion of students who
support a new teaching method is 0.25. Give an interpretation for a 99%
confidence interval for the proportion of students who support the new
teaching method.
A. There is 99% confidence that the sample proportion of students who
support the new teaching method lies between 0.1941 and 0.3059
B. There is 99% confidence that the population proportion of students
who support the new teaching method lies between 0.1941 and 0.3059
C. There is 99% confidence that the sample proportion of students who
support the new teaching method lies between 0.1996 and 0.3004
D. There is 99% confidence that the population proportion of students
who support the new teaching method lies between 0.1996 and 0.3004
Question 17
Which of the following is inversely proportional to the width of the
confidence interval for proportions?
A. Confidence level is inversely proportional to the width of the
confidence interval for proportions
B. Sample size is inversely proportional to the width of the confidence
interval for proportions
C. Standard Error is inversely proportional to the width of the
confidence interval for proportions
D. Sample proportion (00.04
F. H0:μ≤0.04Ha:μ>0.04
Question 10
In a private hospital, the director claimed that they provide all the
essentials to the nurses for their work (in terms of medical equipment,
travel facilities, etc.) and that exactly 90% (no more or less) of the nurses
are satisfied with the essentials provided by the hospital. 79 nurses were
sampled and asked whether they are satisfied with the essentials in the
hospital — 7 nurses said they were not. Find the appropriate test statistic
and p-value for this test.
A.
B.
C.
D.
The test statistic is 0.34 and the p-value is 0.7339
The test statistic is 0.34 and the p-value is 0.3669
The test statistic is 0.34 and the p-value is 0.633
The test statistic is 0.34 and the p-value is 0.367
Question 11
The 95% confidence interval for the proportion of students who work in
part time jobs is (0.0815, 0.1785). The sample proportion of students
who work in part time jobs is known to be 0.13. What sample size is used
to obtain the confidence interval: (Only round at the end of your
calculation to nearest whole number. Example answer: 137)
Question 12
A researcher claims that the proportion of athlete fatalities related to
alcohol is less than 24%. In a random sample of 35 athlete fatalities, it
was found that 17% of deaths were caused by alcohol. Test the claim at
alpha = 1%
B. There is not enough evidence to conclude that the proportion of
athlete fatalities related to alcohol is greater than 24%
C. There is sufficient evidence to conclude that the proportion of athlete
fatalities related to alcohol is greater than 24%
D. There is not enough evidence to conclude that the proportion of
athlete fatalities related to alcohol is less than 24%
E. There is sufficient evidence to conclude that the proportion of athlete
fatalities related to alcohol is less than 24%
Question 13
The upper limit of a 99% confidence interval for the mean is known to be
45.4 and the standard error is 3.7. If the population standard deviation is
known, find the lower limit of the given confidence interval:
A.
B.
C.
D.
The lower limit of the confidence interval is 26.35
The lower limit of the confidence interval is 35.87
The lower limit of the confidence interval is 36.79
The lower limit of the confidence interval is 28.19
Question 14
The 99% confidence interval for the mean number of road accidents per
day in a country is known as (14.3, 19.3). Is there sufficient evidence to
conclude that the mean number of accidents is 17.4 per day?
A. The null hypothesis is rejected and there is insufficient evidence to
conclude that the mean number of accidents is 17.4 per day
B. The null hypothesis is not rejected and there is insufficient evidence
to conclude that the mean number of accidents is 17.4 per day
C. The null hypothesis is not rejected and it’s possible that the mean
number of accidents is 17.4 per day
D. The null hypothesis is rejected and it’s possible that the mean
number of accidents is 17.4 per day
E. There is not enough information provided to make a decision for a
hypothesis test
Question 15
The 95% confidence interval for the proportion of people who support
the new budget scheme is (0.34 – 0.60). Find the margin of error and
standard error of this estimate.
A. The margin of error is 0.130 and the standard error of the estimate is
0.0663
B. The margin of error is 0.130 and the standard error of the estimate is
0.0790
C. The margin of error is 0.260 and the standard error of the estimate is
0.0663
D. The margin of error is 0.260 and the standard error of the estimate is
0.0790
Question 16
In a sample of 400 high school students, the proportion of students who
support a new teaching method is 0.25. Give an interpretation for a 99%
confidence interval for the proportion of students who support the new
teaching method.
A. There is 99% confidence that the sample proportion of students who
support the new teaching method lies between 0.1941 and 0.3059
B. There is 99% confidence that the population proportion of students
who support the new teaching method lies between 0.1941 and 0.3059
C. There is 99% confidence that the sample proportion of students who
support the new teaching method lies between 0.1996 and 0.3004
D. There is 99% confidence that the population proportion of students
who support the new teaching method lies between 0.1996 and 0.3004
Question 17
Which of the following is inversely proportional to the width of the
confidence interval for proportions?
A. Confidence level is inversely proportional to the width of the
confidence interval for proportions
B. Sample size is inversely proportional to the width of the confidence
interval for proportions
C. Standard Error is inversely proportional to the width of the
confidence interval for proportions
D. Sample proportion (0