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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 950 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A study was conducted on a sample of 24 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 965 Gy, with a sample standard deviation of 43 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 0.05 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 950 Gy. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. H₁ O Student's t Distribution Step 1: Enter the number of degrees of freedom. Step 2: Select one-tailed or two-tailed. O One-tailed ○ Two-tailed μ (b) Perform a I test and find the p-value. Here is some information to help you with your I test. The value of the test statistic is given by t= Step 3: Enter the test statistic (Round to 3 decimal places.) Step 4: Shade the area represented by the p-value. OO Ţn The p-value is two times the area under the curve to the right of the value of the test statistic. Step 5: Enter the p-value. (Round to 3 decimal places.) |x 20 ローロ ロメロ x 04+ 03+ a2+ 0.1+ !!

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 950 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A study was conducted on a sample of 24 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 965 Gy, with a sample standard deviation of 43 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 0.05 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 950 Gy. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. H₁ O Student's t Distribution Step 1: Enter the number of degrees of freedom. Step 2: Select one-tailed or two-tailed. O One-tailed ○ Two-tailed μ (b) Perform a I test and find the p-value. Here is some information to help you with your I test. The value of the test statistic is given by t= Step 3: Enter the test statistic (Round to 3 decimal places.) Step 4: Shade the area represented by the p-value. OO Ţn The p-value is two times the area under the curve to the right of the value of the test statistic. Step 5: Enter the p-value. (Round to 3 decimal places.) |x 20 ローロ ロメロ x 04+ 03+ a2+ 0.1+ !!

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
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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 950 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A study was conducted on a sample of 24 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 965 Gy, with a sample standard deviation of 43 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 0.05 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 950 Gy. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. H₁ O Student's t Distribution Step 1: Enter the number of degrees of freedom. Step 2: Select one-tailed or two-tailed. O One-tailed ○ Two-tailed μ (b) Perform a I test and find the p-value. Here is some information to help you with your I test. The value of the test statistic is given by t= Step 3: Enter the test statistic (Round to 3 decimal places.) Step 4: Shade the area represented by the p-value. O<O<O>O Ţn The p-value is two times the area under the curve to the right of the value of the test statistic. Step 5: Enter the p-value. (Round to 3 decimal places.) |x 20 ローロ ロメロ x 04+ 03+ a2+ 0.1+ X € !!
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 950 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A study was conducted on a sample of 24 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 965 Gy, with a sample standard deviation of 43 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 0.05 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 950 Gy. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. H₁ O Student's t Distribution Step 1: Enter the number of degrees of freedom. Step 2: Select one-tailed or two-tailed. O One-tailed ○ Two-tailed μ (b) Perform a I test and find the p-value. Here is some information to help you with your I test. The value of the test statistic is given by t= Step 3: Enter the test statistic (Round to 3 decimal places.) Step 4: Shade the area represented by the p-value. O<O<O>O Ţn The p-value is two times the area under the curve to the right of the value of the test statistic. Step 5: Enter the p-value. (Round to 3 decimal places.) |x 20 ローロ ロメロ x 04+ 03+ a2+ 0.1+ X € !!
(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. O 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 950 Gy. O 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 950 Gy. O 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 950 Gy. O 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 amount of gamma radiation needed to sterilize a colony of tardigrades is not equal to 950 Gy. x
Transcribed Image Text:(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. O 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 950 Gy. O 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 950 Gy. O 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 950 Gy. O 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 amount of gamma radiation needed to sterilize a colony of tardigrades is not equal to 950 Gy. x
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