Question

In: Statistics and Probability

The eruption height and the time interval after eruption of a geyser were measured and are...

The eruption height and the time interval after eruption of a geyser were measured and are shown below. Answer parts ​a-c.

Height​ (x)

125

135

85

95

100

95

115

105

Interval after​ (y)

58

62

40

45

47

48

57

50

a. Find the value of the linear correlation coefficient r.

b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using

alpha=0.05.

c. Is there sufficient evidence to conclude that there is a linear correlation between the two​ variables?

Solutions

Expert Solution

solution :

a)The linear correlation is r=0.9781


Related Solutions

The eruption height and the time interval after eruption of a geyser were measured and are...
The eruption height and the time interval after eruption of a geyser were measured and are shown below. Answer parts ​a-c. Height (x)   Interval after (y) 140   75 130   71 115   59 140   73 112   64 110   56 100   54 120   68 a. Find the value of the linear correlation coefficient r. b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using α=0.05 c. Is there sufficient evidence to conclude...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain geyser. Find the regression​ equation, letting the height of the current eruption be the explanatory variable​ (denoted by​ x). Then use this equation to determine the predicted length of the time interval after an eruption given that the current eruption has a height of 113feet. Height (ft), Interval after (min) 96 66 128 85 75 59 128 86 88 70 73 75 80 73...
The data show the time intervals after an eruption (to the next eruption) of a certain...
The data show the time intervals after an eruption (to the next eruption) of a certain geyser. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 120 feet. Use a significance level of 0.05. Height (ft) Height (ft)   Interval after (min) 96   68 111   80 76   66 91   72 66   58 108   79 116   84 91  ...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain geyser. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 126 feet. Use a significance level of 0.05. Height (ft)   Interval after (min) 84   76 122   77 78   67 108   87 73   61 105   77 122   87 78   70 What...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain geyser. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 149 feet. Use a significance level of 0.05. Height​ (ft) 136 140 134 144 102 109 104 116 Interval after​ (min) 83 84 94 92 67 67 84 84. What...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain...
The data show the time intervals after an eruption​ (to the next​ eruption) of a certain geyser. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted time of the interval after an eruption given that the current eruption has a height of 148 feet. Use a significance level of 0.05. Height (ft) Interval after (min) 136 83 140 84 134 94 144 92 102 67 109 67 104 84 116 84
The data below shows the duration of eruption (in seconds) of a geyser in a national...
The data below shows the duration of eruption (in seconds) of a geyser in a national park and the height (in feet) of the eruptions for a typical day. Use Excel to find the best fit linear regression equation, where duration of eruption is the explanatory variable. Round the slope and intercept to one decimal place. Duration   Height 240   140 237   154 122   140 267   140 113   160 258   140 232   150 105   150 186   160 248   155 243   125...
Suppose a geyser has a mean time between eruptions of 71 minutes.Let the interval of time...
Suppose a geyser has a mean time between eruptions of 71 minutes.Let the interval of time between the eruptions be normally distributed with standard deviation 24 minutes. Complete parts ​(a) through ​(e) below. ​(a) What is the probability that a randomly selected time interval between eruptions is longer than 83 ​minutes? The probability that a randomly selected time interval is longer than 83 minutes is approximately ____ ​ (Round to four decimal places as​ needed.) ​(b) What is the probability...
Suppose a geyser has a mean time between eruptions of 71 minutes.Let the interval of time...
Suppose a geyser has a mean time between eruptions of 71 minutes.Let the interval of time between the eruptions be normally distributed with standard deviation 24 minutes. Complete parts ​(a) through ​(e) below. ​(a) What is the probability that a randomly selected time interval between eruptions is longer than 83 ​minutes? The probability that a randomly selected time interval is longer than 83 minutes is approximately ____ ​ (Round to four decimal places as​ needed.) ​(b) What is the probability...
Suppose a geyser has a mean time between eruptions of 76 minutes . If the interval...
Suppose a geyser has a mean time between eruptions of 76 minutes . If the interval of time between the eruptions is normally distributed with standard deviation 27 minutes ​, answer the following questions. (b) What is the probability that a random sample of 13 time intervals between eruptions has a mean longer than 87 minutes? (c) What is the probability that a random sample of 100 time intervals between eruptions has a mean longer than 120 ​minutes? (d) What...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT