Question

**1-** The following data show the number of times
a sample of students cut their hair in a year:

7,9,20,18,7,10,12,12,20,18,6,8,9,12,20,18,16,12,6,7,10,12,4,6,9

Obtain the 95% confidence interval for the mean number of times the students cut their hair in a year.

**2-** A survey of 1006 Americans showed that 804
believe that Congress should consider reallocating federal
subsidies from fossil fuels to solar. Find the 94% confidence
interval for the proportion of Americans who believe that Congress
should so reallocate subsidies. Obtain the 90% confidence interval
for the population proportion.

**3-** A survey of 1006 Americans showed that 804
believe that Congress should consider reallocating federal
subsidies from fossil fuels to solar. Find the 90% confidence
interval for the proportion of Americans who believe that Congress
should so reallocate subsidies. Obtain the standard error for the
sample proportion.

**4-** The number of calories in a hamburger
depends on what ingredients are included. The following are
determinations of calorific values of a sample of homemade large
hamburgers:

350 375 400 356 378 379 340 320 330 324 360 390

Assume that the calorific values for the hamburgers are normally distributed.

** a)** Find the standard error of the
sample mean.

** b)** Obtain the 95% confidence intervals
for the mean calorific values of the burgers.

**5-** The following show the number of hours a
sample of High school students from a local high school studied a
week:

21, 15, 18, 24, 15, 18, 20, 23, 24, 12, 10, 20, 12, 18, 20, 14, 17

Assume that the weekly study hours are normally distributed.

** a)** find the 90% confidence intervals
for the mean number of study hours.

** b)** find the margin of error for the
95% confidence interval of the mean number of study hours for all
students in this high school. The margin of error equals half
length of the confidence interval.

**6-** In a study, 566 patients were treated with a
medication for a disease of which 202 recovered fully. In the same
study, 365 patients were given placebo (an inert substance that
looks like the medication), 96 recovered fully.

** a)** Obtain a 95% confidence interval
for the difference between proportions of patients who recovered
fully for both groups.

** b)** Test whether there is difference
between proportions of patients who recovered fully for both
groups. Use α=0.05

**7-** A survey of 1006 Americans showed that 804
believe that Congress should consider reallocating federal
subsidies from fossil fuels to solar. Find the 90% confidence
interval for the proportion of Americans who believe that Congress
should so reallocate subsidies. Obtain the standard error for the
sample proportion.

Answer #1

**Let us answer question 1**

The number of times a sample of students cut their hair in a year is as follows

7,9,20,18,7,10,12,12,20,18,6,8,9,12,20,18,16,12,6,7,10,12,4,6,9

We have to find the 95% confidence interval for the mean number of times the students cut their hair in a year.

For this, first we find the mean of the values

The standard devaition of the sample is given by,

At 95% confidence level, critical value of z is given by, z*=1.96

The 95% confidence interval is given by,

Therefore, the required 95% confidence interval of mean number of times the students cut their hair in a year is

Exhibit E
Suppose a simple random sample of 150 students to study the
proportion of students who live in dormitories indicates a sample
proportion of 0.35.
Refer to Exhibit E. To construct a 95% confidence interval for
the population proportion, p, the margin of error is:

Problem 1: Healthcare for all American
A Gallup poll found that 493 of 1050 adult Americans believe it
is the responsibility of the federal government to make sure all
Americans have healthcare coverage.
What is the sample in this study? What is the population of
interest?
What is the variable of interest in this study? Is it
qualitative or quantitative?
Based on the results of this study, obtain a point estimate for
the proportion of adult Americans who believe it...

The mean number of hours of study time per week for a sample of
554 students is 22. If the margin of error for the population mean
with a 95% confidence interval is 2.1, construct a 95% confidence
interval for the mean number of hours of study time per week for
all students.

1.)
You want to obtain a sample to estimate a population mean. Based
on previous evidence, you believe the population standard deviation
is σ=49.3σ=49.3. You would like to be 99% confident that you
estimate is within 5 of the true population mean.
How large of a sample size is required?
n =
Note: Use z-scores rounded to 3 decimal places in your
calculations.
2.)
You want to obtain a sample to estimate a population mean. Based
on previous evidence, you...

22
A researcher is interested in finding a 98% confidence interval
for the mean number minutes students are concentrating on their
professor during a one hour statistics lecture. The study included
101 students who averaged 35.2 minutes concentrating on their
professor during the hour lecture. The standard deviation was 12.1
minutes. Round answers to 3 decimal places where possible.
a. To compute the confidence interval use a
distribution.
b. With 98% confidence the population mean minutes of
concentration is between...

In a simple random sample of 500 freshman students, 276 of them
live on campus. You want to claim that majority of college freshman
students in US live on campus.
A) Are the assumptions for making a 95% confidence interval for
the true proportion of all college freshman students in the United
States who live on campus satisfied? yes/no?
B) What is the sample proportion?
C.) A 95% confidence interval for the actual proportion of
college freshman students in the...

In a survey of 800 college students in the United States, 624
indicated that they believe that a student or faculty member on
campus who uses language considered racist, sexist, homophobic, or
offensive should be subject to disciplinary action. Assuming that
the sample is representative of college students in the United
States, construct a 95% confidence interval for the proportion of
college students who have this belief. (Use a table or technology.
Round your answers to three decimal places.)
(...

1.) Suppose that 45% of students have taken an online course. A
random sample of 200 students is taken, of which 100 have taken an
online course.
A.) What is the probability of obtaining a sample proportion
this high or higher?
B.) There is some thought that the proportion taking online
courses is no longer 45%. Based on the random sample, construct a
95% confidence interval for the proportion of students who have
taken an online course.
C.) Compute the...

Answer the following questions and be sure to show your
work:-
1. Based on a sample of college students, a researcher
calculates a 95% confidence interval of the number of drinks per
week consumed. The result is 4.5 ± 1 drink. Based on a sample of
college students from a different institution, a researcher
calculates a 95% confidence interval of the number of drinks per
week consumed and finds a result of 8.5 ± 2 drinks. What if
anything can...

4. Find the margin of error E. In a random sample of 151 college
students, 84 had part-time jobs. Find the margin of error E for the
95% confidence interval used to estimate the population proportion.
Round your answer to four decimal places. Answer 0.0792
5. Find the minimum sample size required to estimate the
population proportion p: Margin of error: 0.10; confidence level:
95%; from a prior study, is known to be 66%.
6. Find the minimum sample size...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 21 minutes ago

asked 21 minutes ago

asked 30 minutes ago

asked 34 minutes ago

asked 40 minutes ago

asked 57 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago