Question

1.

The confidence intervals for the population proportion are generally based on ________.

the t distribution when the population standard deviation is not known |
||

the z distribution |
||

the t distribution |
||

the z distribution when the sample size is very small |

2.

The difference between the two sample means 1 – 2 is an interval estimator of the difference between two population means μ 1 – μ 2.

True

False

3.

Excel does not have a special function that allows to calculate t values.

True

False

4.

The sampling distribution of is based on a normal distribution on samples of any size.

True

False

5.

A medical devices company wants to know the number of hours its MRI machines are used per day. A previous study found a standard deviation of four hours. How many MRI machines must the company find data for in order to have a margin of error of at most 0.5 hour when calculating a 98% confidence interval?

425 |
||

347 |
||

346.26 |
||

424.69 |

Answer #1

Solution-:

**(1)** The confidence
intervals for the population proportion are generally based on
**the Z- distribution.**

**(2)** The difference
between the two sample means1 - sample mean2 is an interval
estimator of the difference

between two population means
: **True**

**Because,
t**he point estimate for
the difference in population means
is
the difference in sample means is

**(3) True,**
MS-excel have a special command that
follows to calculate t-value:

function used: "TDIST(x,degree of freedom,tails)"

**(4)** The sampling
distribution of is based on a normal distribution on samples of any
size **false.**

**Becasuse,** If x1,
x2, .....xn is random sample from
then probability distribution of statistic T( x1, x2, .....xn) is
called as sampling distribution.

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...

Why is it important to compute confidence intervals for
estimates of population means or percentages?
A. Because every sample statistic is subject to error.
B. Because managers don’t like point estimates.
C. Because every sample statistic must be presented without
error.
D. Because the sample statistic = the population parameter.
The calculated z or t value is inversely related to the size of
the differences between two means or percentages (i.e., as the
difference between two means or percentage increases,...

Consider the following statements concerning confidence interval
estimates:
A. The use of the pooled variance estimator when constructing a
confidence interval for the difference between means requires the
assumption that the population variances are equal.
B. The width of a confidence interval estimate for the proportion,
or for mean when the population standard deviation is known, is
inversely proportional to the square root of the sample size.
C. To determine the sample size required to achieve a desired
precision in...

For this term, we will create confidence intervals to estimate a
population value using the general formula:
sample estimator +/- (reliability factor)(standard error
of the estimator)
Recall that the (reliability factor) x (standard error of the
estimator)= margin of error (ME) for the interval.
The ME is a measure of the uncertainty in our estimate of the
population parameter. A confidence interval has a width=2ME.
A 95% confidence interval for the unobserved population
mean(µ), has a confidence level =
1-α...

Sampling, Confidence Intervals, Sample Sizes
SKETCH required. PLACE ANSWER WITH PROBABILITY NOTATION IN
RECTANGE.
5. A medical devices company wants to know the number of hours
its MRI machines are used per day. A previous study found a
standard deviation of four hours. How many MRI machines must the
company study in order to have a margin of error of 0.5 hours when
calculating a 98% confidence interval?
6. 2,007 adults were asked their preference for improving the
sewer system...

T/F Question and explain
1.A 95% confidence interval for population mean μ is 65.6±12.8
from a sample of size n=96. If one took a second random sample of
the same size, then the probability that the 95% confidence
interval for μ based on the second sample contains 65.6 is
0.95.
2.The probability of a Type I error when α=0.05 and the null
hypothesis is true is 0.05.
3.Because an assumption of ANOVA is that all of the population
variances are...

Find the following critical t-scores used in an 88% confidence
interval for a population mean when the population’s standard
deviation (σσ) is unknown. Give each answer to at least three
decimal places.
The t-critical value for an 88% confidence interval with sample
size 38 is:
The t-critical value for an 88% confidence interval with sample
size 48 is:
The t-critical value for an 88% confidence interval with sample
size 64 is:
The t-critical value for an 88% confidence interval with...

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...

The margin of error for a confidence interval for a population
is equivalent to the standard deviation times the z-score value, or
t-score value depending on the size of the population, for the
probability of interest times the standard deviation of the
population. True or False

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

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