Question

True or false:

**1. When constructing a confidence interval for a sample
Mean, the t distribution is appropriate whenever the sample size is
small.**

**2. The sampling distribution of X (X-bar) is not always
a normal distribution.**

**3. The reason sample variance has a divisor of n-1
rather than n is that it makes the sample standard deviation an
unbiased estimate of the population standard
deviation.**

4. **The error term is the difference between the actual
value of the dependent variable and the corresponding mean value of
the dependent variable.**

**5.** **The Coefficient of Determination
shows the direction of relationship between the dependent and the
independent variables.**

**6. Assuming the same level of significanceα, as the
sample size increases, the value of tα/2 (t- half alpha) becomes
larger and larger than the value of zα/2(Z-half
alpha).**

**7. When the level of confidence and the sample size
remain the same, a confidence interval for a population mean µ will
be narrower, when the sample standard deviation s is smaller than
when s is larger.**

Answer #1

Ans:

1)False,when population standard deviation is known and is normal,we can use z interval even for smaller sample sizes.

2)True,when population is not normally distributed or sample size is small.

3)True

4)False,error is difference between observed and predicted value of dependent variable.

5)False,direction is measured by coefficient of correlation.

6)False,as the sample size increases,t value becomes smaller and approaches toward the value of z.

7)True,smaller the standard deviation,smaller the margin of error,hence narrower the confidence interval.

true or false
When the level of confidence and sample proportion p remain the
same, a confidence interval for a population proportion p based on
a sample of n = 200 will be narrower than a confidence interval for
p based on a sample of n = 100.
When the level of confidence and the sample size remain the
same, a confidence interval for a population mean µ will
be narrower, when the sample standard deviation s is larger than...

29. When the level of confidence and the sample size remain the
same, a confidence interval for a population mean µ will be _____,
when the sample standard deviation s is smaller than when s is
larger.
A. narrower
B. sometimes wider, sometimes narrower
C. wider
D. the same

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...

The value of tα/2 when determine the 99%
confidence interval for µ when the sample standard deviation of the
population is unknown and a sample size of 35 was taken from a
normally distribution random variable

The value of zα/2 when determine the 96%
confidence interval for p.
The decision rule (aka, the rejection region) for testing the
following pair of hypotheses at the .05 level of significance when
the population standard deviation is unknown and a random sample of
size 28 is taken.
H0: µ = 18
Ha: µ < 18
The value of tα/2 when determine the 99%
confidence interval for µ when the sample standard deviation of the
population is unknown and a...

Which of the following will not result in a narrower confidence
interval?
a- Smaller sample mean
b- Larger sample size
c- Smaller population standard deviation
d-Lower confidence level
d-Lower confidence level

a. Use the one-mean t-interval procedure with the sample mean,
sample size, sample standard deviation, and confidence level
given below to find a confidence interval for the mean of the
population from which the sample was drawn.
b. Obtain the margin of error by taking half the length of the
confidence interval. c. Obtain the margin of error by using the
formula t Subscript alpha divided by 2 Baseline times StartFraction
s Over StartRoot n EndRoot EndFraction .
x=30 n=25...

Indicate whether the following statement is true or false.
1. When estimating a confidence interval for the difference
between the means of two independent populations, the pooled
variance is the average of two sample variances, if the two sample
sizes are equal.
2. Both the t-distribution and standard normal distribution have
the same mean, but the t-distribution has a smaller standard
deviation than the standard normal distribution.
3. The standard deviation of the distribution
of (i.e. standard error of the mean)...

True or false?:
13) For a sample mean, the 99% confidence interval is wider than
the 95% confidence interval. 14) The larger the sample size the
more likely x̅ is close to μ.
15) Changing sample size has no effect on power when using the t
test.
16) For the independent two-sample t test, increasing sample
variances decreases power.

Provide an appropriate response.
In constructing a confidence interval for σ or σ2, a
table is used to find the critical values and for values
of n ≤ 101. For larger values of n, and can be
approximated by using the following formula: χ2
= [± zα/2 + ]2 where k
is the number of degrees of freedom and zα/2 is the
critical z score. Construct the 90% confidence interval for σ using
the following sample data: a sample of size yields a
mean...

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