Answered: Listed below are time intervals (min)…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

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

0.01

Recent	78

100

102


Past	90

Let

be the recent times and let

be the past times. What are the null and alternative hypotheses?

H0:

1not equalsmu

H1:

1equalsmu

H0:

1equalsmu

H1:

1not equalsmu

H0:

1less thanmu

H1:

1equalsmu

H0:

1equalsmu

H1:

1greater thanmu

Calculate the test statistic.

tequals

enter your response here

(Round to two decimal places as needed.)

Find the P-value.

P-valueequals

enter your response here

(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

▼

Reject

Fail to reject

because the P-value is

▼

greater than

less than or equal to

the significance level. There

▼

is not

sufficient evidence that the mean time interval has changed.

Is the conclusion affected by whether the significance level is

0.10

0.01

Yes, the conclusion is affected by the significance level because

is rejected when the significance level is

0.01

but is not rejected when the significance level is

0.10

No, the conclusion is not affected by the significance level because

is rejected regardless of whether a significance level of

0.10

0.01

is used.

Yes, the conclusion is affected by the significance level because

is rejected when the significance level is

0.10

but is not rejected when the significance level is

0.01

No, the conclusion is not affected by the significance level because

is not rejected regardless of whether a significance level of

0.10

0.01

is used.

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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