Question

Question 1

A researcher wishes to find a 90% confidence interval estimate for an unknown population mean using a sample of size 25. The population standard deviation is 7.2.

The confidence factor z α 2for this est

Group of answer choices

1.28

1.645

1.96

Question 2

A 90% confidence interval estimate for an unknown population mean μ is (25.81, 29.51).

The length of this CI estimate is

Group of answer choices

1.96

1.85

3.7

1.645

Question 3

Data below refers to the waiting time in minutes for a sample of 10 customers for an oil change at a certain oil change station. It follows that the time for an oil change for the station follows a normal distribution with population standard deviation σ = 7.5 minutes.

38 42 47 45 35 45 37 34 33 41

Find a 90% CI of unknown mean time μ for an oil change.

Group of answer choices

[35.8, 43.6]

[23.4, 31.5]

[37.2, 46.1]

Question 4

A 85% confidence interval for the mean time, in minutes, spent by the employees of a company to get to the work is found to be (25 hours, 45 hours). The length for this 85% CI for the mean time is

Group of answer choices

20 hours

10 hours

70 hours

Answer #1

1)

Given CI level is 90%, hence α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.6449

answer is 1.645

2)

Length = 29.51 - 25.81

= 3.7

3)

sample mean, xbar = 39.7

sample standard deviation, σ = 7.5

sample size, n = 10

Given CI level is 90%, hence α = 1 - 0.9 = 0.1

α/2 = 0.1/2 = 0.05, Zc = Z(α/2) = 1.6449

ME = zc * σ/sqrt(n)

ME = 1.6449 * 7.5/sqrt(10)

ME = 3.9

CI = (xbar - Zc * s/sqrt(n) , xbar + Zc * s/sqrt(n))

CI = (39.7 - 1.6449 * 7.5/sqrt(10) , 39.7 + 1.6449 *
7.5/sqrt(10))

CI = (35.8 , 43.6)

4)

length = 45 - 25 = 20hours

In order to use a 90% confidence interval to compare admission
exam scores for sophomores (group #1) and freshmen (group #2), two
independent random samples were selected. The results showed:
1-Sophomores: Sample mean = 85, sample standard deviation = 10,
sample size = 50.
2-Freshmen: Sample mean = 78, sample standard deviation = 12,
sample size = 72.
For forming a 90% confidence interval for μ 1 − μ 2, the
multiplier is __________ .
Group of answer choices
1.645...

Sample mean is always:
The lower endpoint of the 99% confidence interval.
The middle of the confidence 99% interval.
The upper endpoint of the 99% confidence interval.
The average monthly electricity consumption in a random sample
of 100 households in February 2016 in North Kingstown was 637
kilowatt hours (kWh) with sample standard deviation s=45kwh. A 95%
confidence interval for the true electricity consumption in North
Kingstown is
637 ± 1.95 * 45/10
637 ± 1.96 * 45
637 ±...

Construct a 90% confidence interval to estimate the population
mean using the data below.
x? = 90
? = 10
n = 30
N = 300
The? 90% confidence interval for the population mean is?
(_,_).

A researcher is interested in finding a 90% confidence interval
for the mean number minutes students are concentrating on their
professor during a one hour statistics lecture. The study included
102 students who averaged 34.1 minutes concentrating on their
professor during the hour lecture. The standard deviation was 12.5
minutes. Round answers to 3 decimal places where possible.
a. To compute the confidence interval use a ? t
z distribution.
b. With 90% confidence the population mean minutes of
concentration is...

Suppose you construct a confidence interval for the population
mean. Then, your point estimate – the sample mean – will ALWAYS
fall inside the confidence interval no matter what level of
confidence you use.
Group of answer choices
True
False

3. Use the margin of error of 4, confidence interval of 90% and
?=28 to find the minimum sample size required to estimate an
unknown population mean ?.

Lisa decides that she wants to know the 85% confidence interval
for a population mean despite originally setting out to find the
90% confidence interval. How will this affect the width and the
margin of error of her confidence interval for a population mean?
Assume that the population standard deviation is unknown and the
population distribution is approximately normal.
Select your answer from the choices below.
The width will decrease, and the margin of error will
increase.
The width will...

Find the margin of error for the 95% confidence interval
used to estimate the population proportion.
In a sample of 178 observations, there were 100 positive
outcomes.
Group of answer choices
0.0656
0.128
0.00271
0.0729

Use the margin of error of 4, confidence interval of 90% and
?=28 to find the minimum sample size required to estimate an
unknown population mean ?. (If using TI-84 plus, show steps)

A 99% confidence interval estimate of the population mean ? can
be interpreted to mean:
a) if all possible sample are taken and confidence intervals
created, 99% of them would include the true population mean
somewhere within their interval.
b) we have 99% confidence that we have selected a sample whose
interval does include the population mean.
c) we estimate that the population mean falls between the lower
and upper confidence limits, and this type of estimator is correct
99%...

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