Question

Listed below are speeds (mi/h) measured from south bound traffic on I-280 near Cupertino, CA. This simple random sample was obtained at 3:30 PM on a weekday. Apply Chi-Square distribution Table A-4, 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 estimate of the population variance.

(b) Use the sample data to construct a 95% confidence interval estimate of the population standard deviation.

(c) Do you think you can accept the results you got in (a) and (b)? Why or why not? (Hint: Requirements)

Answer #1

**Answer:**

a)

Given,

alpha = 0.05

sample n = 16

degree of freedom = n - 1 = 16 - 1 = 15

Sample variance = 18.529

95% Ci = [ ((n-1)s^2/(alpha/2 , df)) , ((n-1)s^2/(alpha/2 , df)) ]

substitute values

= [15*18.529/24.488 , 15*18.529/6.262]

= (10.11 , 44.38)

So 95% CI = 10.11 < < 44.38

b)

Here for population standard deviation

sqrt(10.11) < < sqrt(44.38)

3.18 < < 6.66

c)

If they fall in the above interval , then we accept the result or else we reject.

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 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 a 90% confidence
interval estimate of the population standard deviation 60 63 63 57
63 54 59 58 59 69 58 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.
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 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 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 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...

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...

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