**Tardigrades and Gamma Radiation Hypothesis Testing**Tardigrades, or water bears, are noted for their resilience. An experiment was conducted to examine the effect of gamma radiation on these organisms. An expert claimed that the mean amount of gamma radiation needed to sterilize a colony of tardigrades is 1150 Gy (grays).A sample of 25 tardigrade colonies showed a mean radiation level of 1133 Gy with a standard deviation of 62 Gy. Our objective is to determine if there is enough evidence, at the 0.05 level of significance, to challenge the expert's claim.### (a) Hypotheses- **Null Hypothesis (H₀):** μ = 1150 Gy- **Alternative Hypothesis (H₁):** μ ≠ 1150 Gy### (b) Performing the TestThe test statistic follows a t-distribution, as the sample size is small and the population standard deviation is unknown.- **Critical t-value (t₀.₀₂₅):** This value corresponds to an area of 0.025 in the right tail of the distribution.- **Test Statistic Formula:** \[ t = \frac{\bar{X} - \mu}{\frac{s}{\sqrt{n}}} \]#### Diagram ExplanationThe diagram is a graph of Student's t-distribution. Instructions include:1. **Degrees of Freedom:** Enter here.2. **Tail Selection:** Choose one-tailed or two-tailed.3. **Critical Value Input:** Enter the calculated critical values.4. **Test Statistic Input:** Enter the calculated test statistic.### (c) Conclusion- **Options:** 1. **Reject H₀:** If the test statistic lies in the rejection region. There is enough evidence to support the claim that the mean radiation needed to sterilize tardigrades is not 1150 Gy. 2. **Fail to Reject H₀:** If the test statistic does not lie in the rejection region. There isn't enough evidence to challenge the expert's claim.Overall, this exercise teaches conducting hypothesis tests and interpreting Student's t-distribution in the context of tardigrade radiation research.

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 1150 Cy (grays). (For comparison, humans cannot withstand more than 10 Gy.) A random sample of 25 tardigrade colonies found that the amount of gamma radiation needed to sterilize a colony had a sample mean of 1133 Gy, with a sample standard deviation of 02 Gy. Assume that the population of amounts of gamma radiation needed to stenilize a colony of tardigrades is appraximately normally distributed. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level af significance, to support that H, the mean amount of gamma radiation needed to sterilize a colony of tardigrades, is not ngual to 1150 Gy. (a) State the null hypothesis H, and the alternative hypothesis H that you would use for the test. H: 0 (b) Perform a hypothesis test. The test statistic has a I distribution (so the test is a I test"). Here is some other information to help you with your test. • hons is the value that cuts off an area of 0.025 in the right tail. The value of the test statistic is given byf = Student's t Distribution 04. Step 1: Enter the number af degres of freedom. Step 2: Select ane-laled or two-tailed. O One-tailed O Two tailed 02. Step 3: Enter the crilical value(s). (Round to 3 decimal places.) Step 4: Enter the test statistic. (Round to 3 decimal places.) (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 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 1150 Gy, O Since the value of the test statistic lies in the rejection region, the null hypathesis 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 1150 Gy. O 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 1150 Gy. O 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