According to a study on reptiles from decades ago, the mean lifespan of giant Aldabra tortoises in the wild is 98.3 years. Many of the areas where these tortoises live have become polluted with plastic waste. Because of this, a biologist claims the mean lifespan of these tortoises has decreased. To test this claim, the biologist conducted a study of 21 randomly selected, giant Aldabra tortoises in the wild. In the study, the sample mean lifespan was 96.3 years with a sample standard deviation of 15.2 years. Assume that the population of lifespans of giant Aldabra tortoises in the wild is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to support the claim that μ , the mean lifespan of giant Aldabra tortoises in the wild, is now less than 98.3 years. (a) State the null hypothesis H0 and the alternative hypothesis H1 that you would use for the test. H0 : H1 : (b)Perform a t test and find the p-value. Here is some information to help you with your t test. The value of the test statistic is given by =t−xμsn . The p-value is the area under the curve to the left of the value of the test statistic. Student's t Distribution Step 1: Enter the number of degrees of freedom. Step 2: Select one-tailed or two-tailed. One-tailed Two-tailed Step 3: Enter the test statistic. (Round to 3 decimal places.) Step 4: Shade the area represented by the p-value. Step 5: Enter the p-value. (Round to 3 decimal places.) 0.1 0.2 0.3 0.4 1 −1 2 −2 3 −3 (c)Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the biologist. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than 98.3 years. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than 98.3 years. Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than 98.3 years. Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than 98.3 years.

According to a study on reptiles from decades ago, the mean lifespan of giant Aldabra tortoises in the wild is 98.3 years. Many of the areas where these tortoises live have become polluted with plastic waste. Because of this, a biologist claims the mean lifespan of these tortoises has decreased. To test this claim, the biologist conducted a study of 21 randomly selected, giant Aldabra tortoises in the wild. In the study, the sample mean lifespan was 96.3 years with a sample standard deviation of 15.2 years. Assume that the population of lifespans of giant Aldabra tortoises in the wild is approximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.10 level of significance, to support the claim that μ , the mean lifespan of giant Aldabra tortoises in the wild, is now less than 98.3 years. (a) State the null hypothesis H0 and the alternative hypothesis H1 that you would use for the test. H0 : H1 : (b)Perform a t test and find the p-value. Here is some information to help you with your t test. The value of the test statistic is given by =t−xμsn . The p-value is the area under the curve to the left of the value of the test statistic. Student's t Distribution Step 1: Enter the number of degrees of freedom. Step 2: Select one-tailed or two-tailed. One-tailed Two-tailed Step 3: Enter the test statistic. (Round to 3 decimal places.) Step 4: Shade the area represented by the p-value. Step 5: Enter the p-value. (Round to 3 decimal places.) 0.1 0.2 0.3 0.4 1 −1 2 −2 3 −3 (c)Based on your answer to part (b), choose what can be concluded, at the 0.10 level of significance, about the claim made by the biologist. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than 98.3 years. Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than 98.3 years. Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than 98.3 years. Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than 98.3 years.

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

According to a study on reptiles from decades ago, the mean lifespan of giant Aldabra tortoises in the wild is

98.3

years. Many of the areas where these tortoises live have become polluted with plastic waste. Because of this, a biologist claims the mean lifespan of these tortoises has decreased. To test this claim, the biologist conducted a study of

randomly selected, giant Aldabra tortoises in the wild. In the study, the sample mean lifespan was

96.3

years with a sample standard deviation of

15.2

years. Assume that the population of lifespans of giant Aldabra tortoises in the wild is approximately normally distributed.

Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the

0.10

level of significance, to support the claim that

, the mean lifespan of giant Aldabra tortoises in the wild, is now less than

98.3

years.

(a) State the null hypothesis

and the alternative hypothesis

that you would use for the test.

H0 :
H1 :

(b)Perform a

test and find the p-value.
Here is some information to help you with your

test.

The value of the test statistic is given by

=t−xμsn

.
The p-value is the area under the curve to the left of the value of the test statistic.

Student's t Distribution

Step 1: Enter the number of degrees of freedom.

Step 2: Select one-tailed or two-tailed.

One-tailed

Two-tailed

Step 3: Enter the test statistic.
(Round to 3 decimal places.)

Step 4: Shade the area represented by the p-value.

Step 5: Enter the p-value.
(Round to 3 decimal places.)

0.1

0.2

0.3

0.4

−1

−2

−3

(c)Based on your answer to part (b), choose what can be concluded, at the

0.10

level of significance, about the claim made by the biologist.

Since the p-value is less than (or equal to) the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than

98.3

years.

Since the p-value is less than (or equal to) the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than

98.3

years.

Since the p-value is greater than the level of significance, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than

98.3

years.

Since the p-value is greater than the level of significance, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean lifespan of giant Aldabra tortoises in the wild is now less than

98.3

years.

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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