In the study of marine adaptations of reptiles, previous work has indicated that Galápagos Island marine iguanas can hold their breath underwater a mean of 35.0 minutes. The ocean temperatures in the Galápagos have risen over the past decade which forces the iguanas to dive deeper for food more regularly. Due to this, an oceanographer claims that the mean time these iguanas can hold their breath underwater has increased. To test this claim, the oceanographer studied 29 randomly selected, Galápagos Island marine iguanas. In the study, the sample mean time the iguanas could hold their breath underwater was 37.5 minutes with a sample standard deviation of 7.5 minutes. Assume that the population of amounts of time Galápagos Island marine iguanas can hold their breath underwater 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 that μ, the mean time Galápagos Island marine iguanas can hold their breath underwater, is now more than 35.0 minutes.(a) State the null hypothesis H0 and the alternative hypothesis H1 that you would use for the test.H0: H1: (b)Perform a hypothesis test. The test statistic has a t distribution (so the test is a "t test"). Here is some other information to help you with your test.t0.10 is the value that cuts off an area of 0.10 in the right tail.The value of the test statistic is given by =t−xμsn.Student's t DistributionStep 1: Enter the number of degrees of freedom.Step 2: Select one-tailed or two-tailed.One-tailedTwo-tailedStep 3: Enter the critical value(s).(Round to 3 decimal places.)Step 4: Enter the test statistic.(Round to 3 decimal places.)0.10.20.30.41−12−23−3(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 oceanographer.a)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 time Galápagos Island marine iguanas can hold their breath underwater is now more than 35.0 minutes.b)Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean time Galápagos Island marine iguanas can hold their breath underwater is now more than 35.0 minutes.c)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 time Galápagos Island marine iguanas can hold their breath underwater is now more than 35.0 minutes.d)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 time Galápagos Island marine iguanas can hold their breath underwater is now more than 35.0 minutes.

Question

In the study of marine adaptations of reptiles, previous work has indicated that Galápagos Island marine iguanas can hold their breath underwater a mean of 35.0 minutes. The ocean temperatures in the Galápagos have risen over the past decade which forces the iguanas to dive deeper for food more regularly. Due to this, an oceanographer claims that the mean time these iguanas can hold their breath underwater has increased. To test this claim, the oceanographer studied 29 randomly selected, Galápagos Island marine iguanas. In the study, the sample mean time the iguanas could hold their breath underwater was 37.5 minutes with a sample standard deviation of 7.5 minutes. Assume that the population of amounts of time Galápagos Island marine iguanas can hold their breath underwater 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 that μ, the mean time Galápagos Island marine iguanas can hold their breath underwater, is now more than 35.0 minutes.(a) State the null hypothesis H0 and the alternative hypothesis H1 that you would use for the test.H0: H1: (b)Perform a hypothesis test. The test statistic has a t distribution (so the test is a &#34;t test&#34;). Here is some other information to help you with your test.t0.10 is the value that cuts off an area of 0.10 in the right tail.The value of the test statistic is given by =t−xμsn.Student's t DistributionStep 1: Enter the number of degrees of freedom.Step 2: Select one-tailed or two-tailed.One-tailedTwo-tailedStep 3: Enter the critical value(s).(Round to 3 decimal places.)Step 4: Enter the test statistic.(Round to 3 decimal places.)0.10.20.30.41−12−23−3(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 oceanographer.a)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 time Galápagos Island marine iguanas can hold their breath underwater is now more than 35.0 minutes.b)Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to support the claim that the mean time Galápagos Island marine iguanas can hold their breath underwater is now more than 35.0 minutes.c)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 time Galápagos Island marine iguanas can hold their breath underwater is now more than 35.0 minutes.d)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 time Galápagos Island marine iguanas can hold their breath underwater is now more than 35.0 minutes.

Accepted Answer

Given,
population mean ( µ ) = 35
sample size (n) = 29
sample mean (x̄) = 37.5
sample standard…