Question

1- Which of the following statements is true?

I. For a certain confidence level, you get a higher margin of error if you reduce your sample size.

II. For a given sample size, increasing the margin of error will mean higher confidence.

III. For a fixed margin of error, smaller samples will mean lower confidence.

I only

II only

III only

II and III only

All of them

----------------------------------

2- Which must be true about a 90% confidence interval based on a given sample?

I. The interval contains 90% of the population.

II. The interval is narrower than a 95% confidence interval would be.

III. The interval is wider than a 95% confidence interval would be.

I only

II only

III only

I and II only

I and III only

Answer #1

1)

margin of error = criitcal value*σ/√n

since, margin of error is inversely proportional to sample size,

**so, statement I is true**

**---------------**

**for a given sample ,** if confidence level will
increase, then critical value will increase and hence, margin of
error increase,

**so, statement II is also true**

------------------------------------------------

a smaller sample size increases the the std error(σ/√n) of sample proportion ,which for a fixed margin of error decreases the critical value

**so, statement III is also true**

hence answer is ALL of them

===================================================================

2)

The interval is narrower than a 95% confidence interval would be because smaller confidence level, smaller critical value, so smaller the margin of error, hence, interval is narrower.

so, answer is III only

Which of the following statements is true?
The 95% confidence interval is wider than the 99% confidence
interval.
The ONLY way to reduce the width of a confidence interval is to
reduce the confidence level.
The required sample size for a population mean is ONLY
dependent on population variance.
Given population variance and sampling error, higher confidence
level results in larger sample size.

Which of the following is TRUE?
A.
The confidence interval is narrower if the sample size is
smaller.
B.
The confidence interval is narrower if the level of significance
is smaller.
C.
The confidence interval is wider if the level of confidence
level is larger.
D.
The confidence interval is wider if the sample size is
larger.

If you construct a 90% confidence interval for the population
mean instead of a 95% confidence interval and the sample size is
smaller for the 90%, but with everything else being the same, the
confidence interval would: a. remain the same b. become narrower c.
become wider d. cannot tell without further information.

he sample data below have been collected based on a simple
random sample from a normally distributed population. Complete
parts a and b.
7
5
0
7
6
5
9
8
9
3
a. Compute a 90% confidence interval estimate for the
population mean. The 90% confidence interval for the population
mean is from ______ to _________ (Round to two decimal places as
needed. Use ascending order.)
b. Show what the impact would be if the confidence level is
increased...

Which of the following statements is true with
regards to a confidence interval?
Select one:
a. The true population value is always inside the constructed
interval
b. Most calculations of confidence intervals require a point
estimate and the margin of error
c. Given the same confidence level, building a t-interval is
always narrower than a z-interval
d. A 90% confidence interval means there is a 90% chance the
population value is within the constructed interval
e. You need to know...

Which of the following is true about confidence intervals?
I. If the sample size increases, the width of the confidence
interval tends to increase.
II. If the sample size increases, we will have a higher level of
confidence that the confidence interval contains the parameter.
A) Both (I) and (II).
B) Only (II).
C) Only (I).
D) Neither (I) nor (II).

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

The width of a confidence interval will be:
Narrower for 98 percent confidence than for 90 percent
confidence.
Wider for a sample size of 64 than for a sample size of 36.
Wider for a 99 percent confidence than for 95 percent
confidence.
Narrower for a sample size of 25 than for a sample size of
36.
None of these.

Find the margin of error for a 95% confidence interval for
estimating the population mean when the sample standard deviation
equals 90 with a sample size of (i) 484 and (ii) 1600
(i) Find the margin of error for a 95% confidence interval for
estimating the population mean when the sample standard deviation
equals 90 with a sample size of 484
(ii).
(ii) Find the margin of error for a 95% confidence interval
for estimating the population mean when the...

A researcher measured the body temperatures of a randomly
selected group of adults. He wishes to estimate the average
temperature among the adult population. Summaries of the data he
collected are presented in the table below. Complete parts? (a)
through? (d) below.
Summary
Count
Mean
Median
MidRange
StdDev
Range
IntQRange
tempeture
43
98.457
98.000
98.600
0.8847
2.800
1.050 ?
a) Would a 90?% confidence interval be wider or narrower than
the 98?% confidence? interval? Explain. Choose the correct...

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