Question

The procedures for (1) determining confidence intervals to estimate the mean and (2) hypothesis testing based on the difference between one sample mean and a test value or on the difference between two sample means both rely on sampling distributions. Explain why sampling distributions are important for each procedure.

Answer #1

Consider the non-parametric methods for creating confidence
intervals for a single mean and hypothesis testing for a single
mean. Answer each of the following questions with one of the
following options: confidence interval estimation, hypothesis
testing, both, or neither.
a. (1 point) Which method involves shifting the sample data?
b. (1 point) Which method creates a distribution that is
centered at the observed sample mean?
c. (1 point) Which method involves using sample data and
sampling with replacement?
d. (1...

Consider the non-parametric methods for
creating confidence intervals for a single mean and hypothesis
testing for a single mean. Answer each of the following questions
with one of the following options: confidence
interval estimation, hypothesis testing, both, or neither.
(1 point) Which method involves shifting the sample data?
(1 point) Which method creates a distribution that is centered
at the observed sample mean?
(1 point) Which method involves using sample data and sampling
with replacement?
(1 point) Which method requires...

Confidence Intervals & Hypothesis Tests
The manager of a restaurant wants to know if there is a
correlation between the amount of a customer’s bill and the percent
that they tip. In other words, as people spend more money, do they
tend to tip at different rates? With data from a random sample of
157 receipts, he used StatKey to construct a 95% bootstrap
confidence interval for r. The results were: [0.018, 0.292].
A. If the manager wanted to conduct...

How does the population mean and proportion affect confidence
intervals and hypothesis testing?

What are three questions that you have about hypothesis testing
and confidence intervals?
What are two things that you've noticed about hypothesis testing
and confidence intervals?
What is one thing that you are wondering about hypothesis
testing and confidence intervals?

a.
How well do the 95% confidence intervals do at capturing the
true population mean when
samples sizes are small?
b. Does a larger sample size mean that the intervals are more
likely to capture the true population value? Why? Note THIS is
an
important concept and relates back to the Sampling Distribution
of Sample Means.

Describe the connection between confidence intervals and
hypothesis testing, in particular for single sample T tests.

Part 1: z-Procedures In this part, we will use z-procedures.
z-procedures are both confidence intervals and hypothesis tests
that use a Normal distribution. They are called z-procedures
because they rely on a z-test statistic and/or a z-critical value.
So far, we can use z-procedures for a population mean knowing the
population standard deviation. In Part 1, you will use the data
file TempSample00-18.
(THIS IS DATA) YEAR,Month,High Temperature
2000,Jan,45
2000,Jan,48
2001,Jan,49
2003,Jan,62
2003,Jan,53
2004,Jan,42
2004,Jan,47
2005,Jan,40
2005,Jan,47
2006,Jan,48
2006,Jan,47
2007,Jan,51...

Explain what a p-value means relative to hypothesis
testing.
b. Explain why a |z critical value|
and corresponding p-value are inversely related. (Vertical bars
denote absolute value.)
c. Explain the difference between a
one-tail and a two-tail test relative to hypothesis testing.

a. Compute the 95% and 99% confidence intervals on the mean
based on a sample mean of 50 and population standard deviation of
10, for a sample of size 15.
b. What percent of the 95% confidence intervals would you expect
to contain µ? What percent of the 95% confidence intervals would
you expect to contain x̅? What percent of the 95% confidence
intervals would you expect to contain 50?
c. Do you think that the intervals containing µ will...

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