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
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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
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