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 900 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy .) A study was conducted on a sample of 27 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 907 Gy , with a sample standard deviation of 17 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 μ , the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 900 Gy . (a) State the null hypothesis H0 and the alternative hypothesis H1 (b)Perform a t test and find 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 900Gy . 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 900Gy. 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 900Gy . 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 900Gy

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 900 Gy (grays). (For comparison, humans cannot withstand more than 10 Gy .) A study was conducted on a sample of 27 randomly selected tardigrade colonies, finding that the amount of gamma radiation needed to sterilize a colony had a sample mean of 907 Gy , with a sample standard deviation of 17 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 μ , the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not equal to 900 Gy . (a) State the null hypothesis H0 and the alternative hypothesis H1 (b)Perform a t test and find 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 900Gy . 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 900Gy. 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 900Gy . 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 900Gy

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter5: A Survey Of Other Common Functions

Section5.3: Modeling Data With Power Functions

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Related questions

Question

900

(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

907

, 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

900

(a) State the null hypothesis

and the alternative hypothesis

(b)Perform a t test and find 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

900Gy

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

900Gy.

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

900Gy

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

900Gy

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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