Question

A sample of 15 speeds measured from the southbound traffic on I-65 near downtown Montgomery have a sample mean of 62.5 miles/hour. The population standard deviation is known to be 4.5 miles/hour. The speed limit on this area of the road is 55 miles/hour. Calculate a 90% confidence interval for the mean speed.

Answer #1

Solution :

Given that,

Point estimate = sample mean =
= 62.5

Population standard deviation =
= 4.5

Sample size = n = 15

At 90% confidence level

= 1 - 90%

= 1 - 0.90 =0.10

/2
= 0.05

Z/2
= Z_{0.05 = 1.645}

Margin of error = E = Z/2
* (
/n)

= 1.645 * ( 4.5 / 15
)

= 1.91

At 90% confidence interval estimate of the population mean is,

± E

62.5 ± 1.91

( 60.59, 64.41)

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or statistics technology ( calculators) to solve the following
questions:
62, 61, 61, 57, 61, 54, 59, 58, 59, 69, 60, 67, 65, 64, 56 ,
54
(a) Use the sample data to construct a 95% confidence interval
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(b) Use the sample data...

A simple random sample of speeds (miles/hour) measured from
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Test Statistic:
Diagrama:
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Test Statistic:
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Diagram:
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listed below are speeds (mi/h) measured from traffic
on a busy highway. This simple random sample was obtained at 3:30
PM on a weekday. Use the sample data to construct a 95% confidence
interval estimate of the population standard deviation.
61 63 63 55 63 55 60 70 59 67

Listed below are speeds (mi/h) measured from traffic on a busy
highway. This simple random sample was obtained at 3:30 P.M. on a
weekday. Use the sample data to construct
an
80%
confidence interval estimate of the population standard
deviation.
65
61
61
56
61
52
59
58
59
69
62
67
The confidence interval estimate is ?

Listed below are speeds (mi/h) measured from traffic on a busy
highway. This simple random sample was obtained at 3:30 P.M. on a
weekday. Use the sample data to construct a 98% confidence
interval estimate of the population standard deviation. 63 64 64 55
64 53 61 60 61 69 62 68

Listed below are speeds (mi/h) measured from traffic on a busy
highway. This simple random sample was obtained at 3:30 P.M. on a
weekday. Use the sample data to construct
a 98% confidence interval estimate of the population standard
deviation.
63
64
64
56
64
55
61
60
61
68
59
69

Listed below are speeds (mi/h) measured from traffic on a busy
highway. This simple random sample was obtained at 3:30 P.M. on a
weekday. Use the sample data to construct
a 99% confidence interval estimate of the population standard
deviation.
61
60
60
57
60
55
59
58
59
68
58
66
Use the table of Chi-Square critical values to find the
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Listed below are speeds (mi/h) measured from traffic on a busy
highway. This simple random sample was obtained at 3:30 P.M. on a
weekday. Use the sample data to construct a 90% confidence
interval estimate of the population standard deviation 60 63 63 57
63 54 59 58 59 69 58 67

isted below are speeds (mi/h) measured from traffic on a busy
highway. This simple random sample was obtained at 3:30 P.M. on a
weekday. Use the sample data to construct a 90% confidence interval
estimate of the population standard
deviation.
61 63 63 57 63 52 60 59 60 70 62 68
The confidence interval estimate is ------mi/h < σ <------
mi/h.
(Round to one decimal place as needed.)
Does the confidence interval describe the standard deviation for
all times...

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