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.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 4BGP

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Related questions

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.

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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