Homework Help is Here – Start Your Trial Now!
Math
Statistics
Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 850 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A random sample of 28 tardigrade colonies found that the amount of gamma radiation needed to sterilize a colony had a sample mean of 862 Gy, with a sample standard deviation of 60 Gy. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades 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 that μ, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 850 Gy. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. μ Ho: H₁: O

Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 850 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A random sample of 28 tardigrade colonies found that the amount of gamma radiation needed to sterilize a colony had a sample mean of 862 Gy, with a sample standard deviation of 60 Gy. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades 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 that μ, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 850 Gy. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. μ Ho: H₁: O

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question
Help please!!! Parts a-c
Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 850 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A random sample of 28 tardigrade colonies found that the amount of gamma radiation needed to sterilize a colony had a sample mean of 862 Gy, with a sample standard deviation of 60 Gy. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades 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 that μ, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 850 Gy. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. μ Ho: H₁: O<O x □ㄨˇ □□ ロ=ロ □≠□ (b) Perform a hypothesis test. The test statistic has a t distribution (so the test is a "t test"). Here is some other information to help you with your test. 10.05 is the value that cuts off an area of 0.05 in the right tail. χμ The value of the test statistic is given by t S 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 critical value(s). (Round to 3 decimal places.) Step 4: Enter the test statistic. (Round to 3 decimal places.) 3 0.4- 0.3- 0.2- 0.1+ 2
Transcribed Image Text:Tardigrades, or water bears, are a type of micro-animal famous for their resilience. In examining the effects of radiation on organisms, an expert claimed that the amount of gamma radiation needed to sterilize a colony of tardigrades no longer has a mean of 850 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A random sample of 28 tardigrade colonies found that the amount of gamma radiation needed to sterilize a colony had a sample mean of 862 Gy, with a sample standard deviation of 60 Gy. Assume that the population of amounts of gamma radiation needed to sterilize a colony of tardigrades 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 that μ, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 850 Gy. (a) State the null hypothesis Ho and the alternative hypothesis H₁ that you would use for the test. μ Ho: H₁: O<O x □ㄨˇ □□ ロ=ロ □≠□ (b) Perform a hypothesis test. The test statistic has a t distribution (so the test is a "t test"). Here is some other information to help you with your test. 10.05 is the value that cuts off an area of 0.05 in the right tail. χμ The value of the test statistic is given by t S 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 critical value(s). (Round to 3 decimal places.) Step 4: Enter the test statistic. (Round to 3 decimal places.) 3 0.4- 0.3- 0.2- 0.1+ 2
(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 expert. Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean amount of gamma radiation needed to sterilize a colony of tardigrades is not equal to 850 Gy. Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean amount of gamma radiation needed to sterilize a colony of tardigrades is not equal to 850 Gy. Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean amount of gamma radiation needed to sterilize a colony of tardigrades is not equal to 850 Gy. Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean amount of gamma radiation needed to sterilize a colony of tardigrades is not equal to 850 Gy. ك
Transcribed Image Text:(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 expert. Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean amount of gamma radiation needed to sterilize a colony of tardigrades is not equal to 850 Gy. Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean amount of gamma radiation needed to sterilize a colony of tardigrades is not equal to 850 Gy. Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to support the claim that the mean amount of gamma radiation needed to sterilize a colony of tardigrades is not equal to 850 Gy. Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean amount of gamma radiation needed to sterilize a colony of tardigrades is not equal to 850 Gy. ك
Expert Solution
steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS