Listed below are time intervals (min) between eruptions of a geyser. Assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Does it appear that the mean time interval has changed? Is the conclusion affected by whether the significance level is 0.10 or 0.01? Recent 77 91 88 80 58 100 63 87 69 88 82 82 55 82 74 103 62 Past 90 88 93 94 64 84 84 92 86 91 89 91
Listed below are time intervals (min) between eruptions of a geyser. Assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Does it appear that the mean time interval has changed? Is the conclusion affected by whether the significance level is 0.10 or 0.01? Recent 77 91 88 80 58 100 63 87 69 88 82 82 55 82 74 103 62 Past 90 88 93 94 64 84 84 92 86 91 89 91
Listed below are time intervals (min) between eruptions of a geyser. Assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Does it appear that the mean time interval has changed? Is the conclusion affected by whether the significance level is 0.10 or 0.01? Recent 77 91 88 80 58 100 63 87 69 88 82 82 55 82 74 103 62 Past 90 88 93 94 64 84 84 92 86 91 89 91
Listed below are time intervals (min) between eruptions of a geyser. Assume that the "recent" times are within the past few years, the "past" times are from around 20 years ago, and that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Does it appear that the mean time interval has changed? Is the conclusion affected by whether the significance level is 0.10 or 0.01?
Recent
77
91
88
80
58
100
63
87
69
88
82
82
55
82
74
103
62
Past
90
88
93
94
64
84
84
92
86
91
89
91
Transcribed Image Text:Listed below are time intervals (min) between eruptions of a geyser. Assume that the "recent" times are
within the past few years, the "past" times are from around 20 years ago, and that the two samples are
independent simple random samples selected from normally distributed populations. Do not assume that the
population standard deviations are equal. Does it appear that the mean time interval has changed? Is the
conclusion affected by whether the significance level is 0.10 or 0.01?
Recent 77 91 88 80 58 100 63 87 69 88 82 82 55 82 74 103 62
Past
90 88 93 94 64 84 84 92 86 91 89 91
Let μ, be the recent times and let μ₂ be the past times. What are the null and alternative hypotheses?
OA Hồ- Hi-t
H₁: Hy > H₂
OC. Ho: H₁ H₂
H₁: H₂=H₂
Calculate the test statistic.
t=
Find the P-value.
OB. Ho: H₁ H₂
H₁: H₁ = H₂
(Round to two decimal places as needed.)
P-value =
(Round to three decimal places as needed.)
Make a conclusion about the null hypothesis and a final conclusion that addresses the original claim. Use a
significance level of 0.10.
OD. Ho Hì-H
H₁: H₁ H₂
(1).
H, because the P-value is (2).
(3)
sufficient evidence that the mean time interval has changed.
Is the conclusion affected by whether the significance level is 0.10 or 0.01?
O A. Yes, the conclusion is affected by the significance level because Ho is rejected when the
significance level is 0.10 but is not rejected when the significance level is 0.01.
(1)
O B. Yes, the conclusion is affected by the significance level because H, is rejected when the
significance level is 0.01 but is not rejected when the significance level is 0.10.
O C.
No, the conclusion is not affected by the significance level because Ho is not rejected regardless of
whether a significance level of 0.10 or 0.01 is used.
O Reject
O Fail to reject
the significance level. There
O D.
No, the conclusion is not affected by the significance level because H, is rejected regardless of
whether a significance level of 0.10 or 0.01 is used.
(2)
greater than
less than or equal to
(3)
O is
is not
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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