Question

Answer the following questions. (a) Why do we need to use the t-distribution when estimating the population mean? (b) Name a circumstance where we would not need to use the t-distribution when estimating the population mean?

Answer #1

a) when the sample size is small (n<30) then t-test can estimate mean better than z-test with high power of the test so, we use exact t-test to estimate the mean of a population.

b)

When sample size is large then on that case due to central limit theorem the distribution used is normal.

When the parent population from which the sample is drawn is not normal.

When the sample is not random.

When the standard deviation sigma is known.

In all the above circumstances we would need not to use t-distribution.

We use Student’s t distribution when creating confidence
intervals for the mean when the population standard deviation is
unknown because....
We are estimating two parameters from the data and wish to have
a wider confidence interval
The central limit theorem does not apply in this case
We do not want a confidence interval that is symmetric about the
sample mean
We have greater certainty of our estimate

To find the sampling distribution of x bar, we need to:
Group of answer choices
Compute the mean of the standard error
Compute the mean of the proportion
Collect many samples, then find the mean of each sample
Collect many samples, then find the mean of the proportion
To use the Central Limit Theorem:
Group of answer choices
We need to know the type of distribution the underlying
population follows
We do not need to know the type of distribution...

We use the t distribution to construct a confidence
interval for the population mean when the underlying population
standard deviation is not known. Under the assumption that the
population is normally distributed, find
t??2,df for the following scenarios. Use Table
2. (Round your answers to 3 decimal places.)
t?/2,df
a. A 95% confidence
level and a sample of 8 observations.
b. A 90% confidence
level and a sample of 8 observations.
c. A 95% confidence
level and a...

When, if ever, is it appropriate to use the standard normal
distribution as a substitute for the t distribution with n – 1
degrees of freedom in estimating a population mean?

When, if ever, is it appropriate to use the standard normal
distribution as a substitute for the t distribution with n – 1
degrees of freedom in estimating a population mean?

When do we use a mean and SD to define a continuous variable
distribution ? When do we use a median and IQR to define a
continuous variable distribution?

We use the t distribution to construct a confidence
interval for the population mean when the underlying population
standard deviation is not known. Under the assumption that the
population is normally distributed, find
tα/2,df for the following
scenarios. (You may find it useful to
reference the t table. Round your
answers to 3 decimal places.)
tα/2,df
a.
A 90% confidence level and a sample of 11 observations.
b.
A 95% confidence level and a sample of 11 observations.
c.
A...

We use the t distribution to construct a confidence
interval for the population mean when the underlying population
standard deviation is not known. Under the assumption that the
population is normally distributed, find
tα/2,df for the following
scenarios. (You may find it useful to
reference the t table. Round your
answers to 3 decimal places.)
tα/2,df
a.
A 95% confidence level and a sample of 10 observations.
b.
A 99% confidence level and a sample of 10 observations.
c.
A...

When do we use Z-Test and when do we use t-Test?

In this case ,Why do we use the left-tailed hypothesis instead
of the right-tailed hypothesis？When do we use the right-tailed
hypothesis and when do we use the left-tailed hypothesis? Explain
only the above two questions and do not need to answer the
following questions. Thanks!!
During the period 1990-1998 there were 46 Atlantic hurricanes, of
which 19 struck the United States. During the period 1999-2006
there were 70 hurricanes, of which 45 struck the United States. (a)
State the hypotheses...

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