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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 850 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A study was conducted on a sample of 28 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 864 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 the claim that u, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 850 Gy. (a) State the null hypothesis H and the alternative hypothesis H, that you would use for the test. Ho: u = 850 H: u> 850 OSO (b) Perform at 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.

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 study was conducted on a sample of 28 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 864 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 the claim that u, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 850 Gy. (a) State the null hypothesis H and the alternative hypothesis H, that you would use for the test. Ho: u = 850 H: u> 850 OSO (b) Perform at 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.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 31EQ
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Shelia Esp Try Again Your answer is incorrect. 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 study was conducted on a sample of 28 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 864 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 the claim that u, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 850 Gy. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. Ho: u = 850 H: u > 850 O<O (b) Perform at 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'er Dictribution Explanation Recheck © 2021 McGraw Hil LLC. AN Rights Reserved Terms of Use Privacy Conter Accessibility 78°F Clear ()回国回回
Transcribed Image Text:Shelia Esp Try Again Your answer is incorrect. 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 study was conducted on a sample of 28 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 864 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 the claim that u, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 850 Gy. (a) State the null hypothesis H, and the alternative hypothesis H, that you would use for the test. Ho: u = 850 H: u > 850 O<O (b) Perform at 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'er Dictribution Explanation Recheck © 2021 McGraw Hil LLC. AN Rights Reserved Terms of Use Privacy Conter Accessibility 78°F Clear ()回国回回
Student's t Distribution Step 1: Enter the number of degrees of freedom. 0.4 27 Step 2: Select one-tailed or two-tailed, O One-tailed 03- O Two-tailed Step 3: Enter the test statistic. (Round to 3 decimal places.) 1.235 02- Step 4: Shade the area represented by the p-value. 0.1- Area = 0.886 Step 5: Enter the p-value. (Round to 3 decimal places.) 0.886 1= 1.235 (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. 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 850 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 850 Gy. Explanation Recheck O2021 McGraw Hill LLC. A Rights Reserved Terms of Use Prvacy Center Accessibility
Transcribed Image Text:Student's t Distribution Step 1: Enter the number of degrees of freedom. 0.4 27 Step 2: Select one-tailed or two-tailed, O One-tailed 03- O Two-tailed Step 3: Enter the test statistic. (Round to 3 decimal places.) 1.235 02- Step 4: Shade the area represented by the p-value. 0.1- Area = 0.886 Step 5: Enter the p-value. (Round to 3 decimal places.) 0.886 1= 1.235 (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. 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 850 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 850 Gy. Explanation Recheck O2021 McGraw Hill LLC. A Rights Reserved Terms of Use Prvacy Center Accessibility
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