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 of1350Gy(grays). (For comparison, humans cannot withstand more than10Gy.) A study was conducted on a sample of18randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of1375Gy, with a sample standard deviation of75Gy. 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 the0.05level of significance, to support the claim thatμ, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to1350Gy. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test.EspañolHo: 0H1: 0OSOO=0(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=• The p-value is two times the area under the curve to the right of the value of the test statistic.Student's t Distribution0.4Step 1: Enter the numberof degrees of freedom.0.3Step 2: Select one-tailedor two-tailed.O One-tailedO Two-tailed0.2Step 3: Enter the teststatistic.(Round to 3 decimalplaces.)0.HStep 4: Shade the arearepresented by the p-value.(c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claimmade by the expert.Since the p-value is less than (or equal to) the level of significance, the null hypothesis isrejected. So, there is enough evidence to support the claim that the mean amount ofgamma radiation needed to sterilize a colony of tardigrades is not equal to 1350 Gy.?Since the p-value is less than (or equal to) the level of significance, the null hypothesis isnot rejected. So, there is not enough evidence to support the claim that the mean amountof gamma radiation needed to sterilize a colony of tardigrades is not equal to 1350 Gy.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 amount of gammaradiation needed to sterilize a colony of tardigrades is not equal to 1350 Gy.Since the p-value is greater than the level of significance, the null hypothesis is notrejected. Šo, there is not enough evidence to support the claim that the mean amount ofgamma radiation needed to sterilize a colony of tardigrades is not equal to 1350 Gy.

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Answered: Tardigrades, or water bears, are a type…

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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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

1350

(grays). (For comparison, humans cannot withstand more than

.) A study was conducted on a sample of

randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of

1375

, with a sample standard deviation of

. 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

0.05

level of significance, to support the claim that

, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to

1350

(a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test.
Español
Ho: 0
H1: 0
OSO
O=0
(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=
• The p-value is two times the area under the curve to the right of the value of the test statistic.
Student's t Distribution
0.4
Step 1: Enter the number
of degrees of freedom.
0.3
Step 2: Select one-tailed
or two-tailed.
O One-tailed
O Two-tailed
0.2
Step 3: Enter the test
statistic.
(Round to 3 decimal
places.)
0.H
Step 4: Shade the area
represented by the p-
value.
(c) Based on your answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim
made by the expert.
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 amount of
gamma radiation needed to sterilize a colony of tardigrades is not equal to 1350 Gy.
?
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 amount
of gamma radiation needed to sterilize a colony of tardigrades is not equal to 1350 Gy.
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 amount of gamma
radiation needed to sterilize a colony of tardigrades is not equal to 1350 Gy.
Since the p-value is greater than the level of significance, the null hypothesis is not
rejected. Šo, 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 1350 Gy.

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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