291 Problems 32. Let X1,. .., Xn+1 be a sample from a population with mean u and variance o2. As noted in the text, the natural predictor of X„+1 based on the data values X1, ... , Xn is Xn = =1 X;/n. Determine the mean square error of this predictor. That is, find E[(X,+1 – X„)²]. 33. National Safety Council data show that the number of accidental deaths due to drowning in the United States in the years from 1990 to 1993 were (in units of one thousand) 5.2, 4.6, 4.3, 4.8. Use these data to give an interval that will, with 95 percent confidence, contain the number of such deaths in 1994. 34. The daily dissolved oxygen concentration for a water stream has been recorded over 30 days. If the sample average of the 30 values is 2.5 mg/liter and the sample standard deviation is 2.12 mg/liter, determine a value which, with 90 percent confidence, exceeds the mean daily concentration. 35. Verify the formulas given in Table 7.1 for the 100(1 – a) percent lower and upper confidence intervals for o². 36. The capacities (in ampere-hours) of 10 batteries were recorded as follows: 140, 136, 150, 144, 148, 152, 138, 141, 143, 151 (a) Estimate the population variance o?. (b) Compute a 99 percent two-sided confidence interval for o2. (c) Compute a value v that enables us to state, with 90 percent confidence, that o² is less than v. 37. Find a 95 percent two-sided confidence interval for the variance of the diameter of a rivet based on the data given here. 6.68 6.66 6.62 6.72 6.76 6.67 6.70 6.72 6.78 6.66 6.76 6.72 6.76 6.70 6.76 6.76 6.74 6.74 6.81 6.66 6.64 6.79 6.72 6.82 6.81 6.77 6.60 6.72 6.74 6.70 6.64 6.78 6.70 6.70 6.75 6.79 Assume a normal population. 38. The following are independent samples from two normal populations, both of which have the same standard deviation o. 16, 17, 19, 20, 18 and 3, 4, 8 Use them to estimate o.
291 Problems 32. Let X1,. .., Xn+1 be a sample from a population with mean u and variance o2. As noted in the text, the natural predictor of X„+1 based on the data values X1, ... , Xn is Xn = =1 X;/n. Determine the mean square error of this predictor. That is, find E[(X,+1 – X„)²]. 33. National Safety Council data show that the number of accidental deaths due to drowning in the United States in the years from 1990 to 1993 were (in units of one thousand) 5.2, 4.6, 4.3, 4.8. Use these data to give an interval that will, with 95 percent confidence, contain the number of such deaths in 1994. 34. The daily dissolved oxygen concentration for a water stream has been recorded over 30 days. If the sample average of the 30 values is 2.5 mg/liter and the sample standard deviation is 2.12 mg/liter, determine a value which, with 90 percent confidence, exceeds the mean daily concentration. 35. Verify the formulas given in Table 7.1 for the 100(1 – a) percent lower and upper confidence intervals for o². 36. The capacities (in ampere-hours) of 10 batteries were recorded as follows: 140, 136, 150, 144, 148, 152, 138, 141, 143, 151 (a) Estimate the population variance o?. (b) Compute a 99 percent two-sided confidence interval for o2. (c) Compute a value v that enables us to state, with 90 percent confidence, that o² is less than v. 37. Find a 95 percent two-sided confidence interval for the variance of the diameter of a rivet based on the data given here. 6.68 6.66 6.62 6.72 6.76 6.67 6.70 6.72 6.78 6.66 6.76 6.72 6.76 6.70 6.76 6.76 6.74 6.74 6.81 6.66 6.64 6.79 6.72 6.82 6.81 6.77 6.60 6.72 6.74 6.70 6.64 6.78 6.70 6.70 6.75 6.79 Assume a normal population. 38. The following are independent samples from two normal populations, both of which have the same standard deviation o. 16, 17, 19, 20, 18 and 3, 4, 8 Use them to estimate o.
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Question
pbm 34
![291
Problems
32. Let X1,. .., Xn+1 be a sample from a population with mean u and variance
o2. As noted in the text, the natural predictor of X„+1 based on the data
values X1, ... , Xn is Xn = =1 X;/n. Determine the mean square error of this
predictor. That is, find E[(X,+1 – X„)²].
33. National Safety Council data show that the number of accidental deaths due to
drowning in the United States in the years from 1990 to 1993 were (in units of
one thousand) 5.2, 4.6, 4.3, 4.8. Use these data to give an interval that will, with
95 percent confidence, contain the number of such deaths in 1994.
34. The daily dissolved oxygen concentration for a water stream has been recorded
over 30 days. If the sample average of the 30 values is 2.5 mg/liter and the sample
standard deviation is 2.12 mg/liter, determine a value which, with 90 percent
confidence, exceeds the mean daily concentration.
35. Verify the formulas given in Table 7.1 for the 100(1 – a) percent lower and
upper confidence intervals for o².
36. The capacities (in ampere-hours) of 10 batteries were recorded as follows:
140, 136, 150, 144, 148, 152, 138, 141, 143, 151
(a) Estimate the population variance o?.
(b) Compute a 99 percent two-sided confidence interval for o2.
(c) Compute a value v that enables us to state, with 90 percent confidence, that
o² is less than v.
37. Find a 95 percent two-sided confidence interval for the variance of the diameter
of a rivet based on the data given here.
6.68
6.66
6.62
6.72
6.76
6.67
6.70
6.72
6.78
6.66
6.76
6.72
6.76
6.70
6.76
6.76
6.74
6.74
6.81
6.66
6.64
6.79
6.72
6.82
6.81
6.77
6.60
6.72
6.74
6.70
6.64
6.78
6.70
6.70
6.75
6.79
Assume a normal population.
38. The following are independent samples from two normal populations, both of
which have the same standard deviation o.
16, 17, 19, 20, 18
and
3, 4, 8
Use them to estimate o.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc75d2948-de5d-4252-902e-2fb229e41c51%2Ff978152f-4994-4854-88f5-c975172a588e%2Fqpeetgs.jpeg&w=3840&q=75)
Transcribed Image Text:291
Problems
32. Let X1,. .., Xn+1 be a sample from a population with mean u and variance
o2. As noted in the text, the natural predictor of X„+1 based on the data
values X1, ... , Xn is Xn = =1 X;/n. Determine the mean square error of this
predictor. That is, find E[(X,+1 – X„)²].
33. National Safety Council data show that the number of accidental deaths due to
drowning in the United States in the years from 1990 to 1993 were (in units of
one thousand) 5.2, 4.6, 4.3, 4.8. Use these data to give an interval that will, with
95 percent confidence, contain the number of such deaths in 1994.
34. The daily dissolved oxygen concentration for a water stream has been recorded
over 30 days. If the sample average of the 30 values is 2.5 mg/liter and the sample
standard deviation is 2.12 mg/liter, determine a value which, with 90 percent
confidence, exceeds the mean daily concentration.
35. Verify the formulas given in Table 7.1 for the 100(1 – a) percent lower and
upper confidence intervals for o².
36. The capacities (in ampere-hours) of 10 batteries were recorded as follows:
140, 136, 150, 144, 148, 152, 138, 141, 143, 151
(a) Estimate the population variance o?.
(b) Compute a 99 percent two-sided confidence interval for o2.
(c) Compute a value v that enables us to state, with 90 percent confidence, that
o² is less than v.
37. Find a 95 percent two-sided confidence interval for the variance of the diameter
of a rivet based on the data given here.
6.68
6.66
6.62
6.72
6.76
6.67
6.70
6.72
6.78
6.66
6.76
6.72
6.76
6.70
6.76
6.76
6.74
6.74
6.81
6.66
6.64
6.79
6.72
6.82
6.81
6.77
6.60
6.72
6.74
6.70
6.64
6.78
6.70
6.70
6.75
6.79
Assume a normal population.
38. The following are independent samples from two normal populations, both of
which have the same standard deviation o.
16, 17, 19, 20, 18
and
3, 4, 8
Use them to estimate o.
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