Question

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

Answer #1

the ratio of sample variance (S2) and population variation (K2) is a chi-squared distribution.

So, if the sample size is n, the statistic (n-1)S2 / K2 has a chi-squared distribution with n-1 degrees of freedom

Proceed with finding the sample mean which comes out to be 60.83

Variance S2 = 16.972

Now, chi-squared distribution is not symmetrical like normal distribution.

90% confidence interval lies between the two black lines. Two find the chi-squared values at the two points we will divide 10% into two 5% parts.

Note : while reading a chi-squared table the values correspond to area to the right of the values.

Values of A and B can be found from chi-squared table and are B=19.67 and A=4.57

therefore, estimate for population standard deviation is

((n-1)S2 / B) < K2 < ((n-1)S2 / A)

9.49< K2<40.85

3.08 < K < 6.39

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 95% confidence
interval estimate of the population standard deviation.
64
61
61
56
61
52
59
58
59
68
60
69
The confidence interval estimate is ____ mi/h < σ < ____
mi/h.

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
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
confidence interval estimate.

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 a 98% confidence
interval estimate of the population standard deviation. 64 62 62 56
62 53 60 59 60 69 61 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 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 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...

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...

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. 64 62 62 56
62 53 60 59 60 70 61 69 LOADING... Click the icon to view the table
of Chi-Square critical values. The confidence interval estimate is
nothing mi/h less thansigmaless than nothing mi/h. (Round to one
decimal...

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