Listed below are time intervals (min) between eruptions of a geyser. The "recent" times are within the past few years, and the "past" times are from 1995. Does it appear that the variation of the times between eruptions has changed? Use a 0.05 significance level. Assume that the two populations are normally distributed. ### Recent vs. Past Performance DataThis dataset compares two sets of performance scores labeled "Recent" and "Past." Each category contains the following scores:- **Recent**: 82, 95, 92, 79, 54, 96, 61, 83, 66, 90, 85, 81- **Past**: 93, 91, 100, 94, 67, 85, 82, 97, 83, 98, 89, 98These scores appear to represent a series of measured values over a defined time period, allowing for a comparative analysis of recent and past performance. An analysis of these scores could provide insights into trends, improvements, or declines in performance over time.

Given Information : Listed below are time intervals (min) between eruptions of a geyser. The "recent" times are within the past few years, and the "past" times are from 1995. These two populations are normally distributed. The following table is obtained: Recent Past Difference = Recent - Past 82 93 -11 95 91 4 92 100 -8 79 94 -15 54 67 -13 96 85 11 61 82 -21 83 97 -14 66 83 -17 90 98 -8 85 89 -4 81 98 -17 Average 80.333 89.75 -9.417 St. Dev. 13.473 9.392 9.278 n 12 12 12 From the sample data, it is found that the corresponding sample means are: Also, the provided sample standard deviations are: and the sample size is n = 12. For the score differences we have Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: Mean variation of the times between eruptions has not changed. i.e. μD = 0 Ha: Mean variation of the times between eruptions has changed. i.e. μD < 0 This corresponds to a left-tailed test, for which a t-test for two paired samples be used. Rejection Region Based on the information provided, the significance level is \alpha = 0.05α=0.05, and the degrees of freedom are df = 11df=11. Hence, it is found that the critical value for this left-tailed test is t_c = -1.796tc=−1.796, for \alpha = 0.05α=0.05 and df = 11df=11. The rejection region for this left-tailed test is R = \{t: t < -1.796\}R={t:t<−1.796}. Test Statistics The t-statistic is computed as shown in the following formula : Test Statistic : t = 3.516 Decision about the null hypothesis Since it is observed that t = -3.516 < t_c = -1.796t=−3.516<tc=−1.796, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p=0.0024, and since p=0.0024<0.05, it is concluded that the null hypothesis is rejected. Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that eruptions of a geyser from past to recent times has changed, at the 0.05 significance level.

Answered: Listed below are time intervals (min)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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Listed below are time intervals (min) between eruptions of a geyser. The "recent" times are within the past few years, and the "past" times are from 1995. Does it appear that the variation of the times between eruptions has changed? Use a 0.05 significance level. Assume that the two populations are normally distributed.

### Recent vs. Past Performance Data

This dataset compares two sets of performance scores labeled "Recent" and "Past." Each category contains the following scores:

- **Recent**: 82, 95, 92, 79, 54, 96, 61, 83, 66, 90, 85, 81
- **Past**: 93, 91, 100, 94, 67, 85, 82, 97, 83, 98, 89, 98

These scores appear to represent a series of measured values over a defined time period, allowing for a comparative analysis of recent and past performance. An analysis of these scores could provide insights into trends, improvements, or declines in performance over time.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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