Question

According to a study on reptiles from decades ago, the mean lifespan of giant Aldabra tortoises in the wild is 88.1 years. Many of the areas where these tortoises live have become polluted with plastic waste. Because of this, a biologist claims the mean lifespan of these tortoises has decreased. To test this claim the biologist conducted a study of 27 randomly selected, giant Aldabra tortoises in the wild. In the study, the sample meanifespan was 86.5 years with a sample standard deviation of 11.4 years. Assume that the population of lifespans of glont Aldabra tortoises in the wild 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 lifespan of giant Aldabra tortoises in the wild, is now less than 88.1 years D (a) State the nult.hypothesis Hy and the alternative hypothesis that you would use for the test. x < OS 020 0-0 OND XS ? Student's t Distribution Step 1: Enter the number of degrees of freedom. 04+ 0 Step 2: Select one-tailed or two-tailed. One-tailed OTwo-tailed Step 3: Enter the test statistic. (Round to 3 decimal places.) 02 Step 4: Shad the area represented by the p-value. 01 Step 5: Enter the p-value. (Round to 3 decimal places.) Seu Ol You answer to part (b), choose what can be concluded, at the 0.05 level of significance, about the claim made by the biologist. 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 lifespan of giant Aldabra tortoises in the wild is now less than 88.1 years. х 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 lifespan of giant Aldabra tortoises in the wild is now less than 88.1 years. 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 lifespan of giant Aldabra tortoises in the wild is now less than 88.1 years. Since the pyalue 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 lifespan of giant Aldabra tortoises in the wild is now less than 88.1 years.

Answer 1

The null hypothesis for a test on the mean lifespan of giant Aldabra tortoises is that it has not decreased and remains at 88.1 years. A one-tailed test is used because the biologist's claim suggests a decrease. Without the actual test statistic and p-value, we cannot determine the conclusion of the hypothesis test.

Step-by-step explanation:

The hypothesis test for the lifespan of giant Aldabra tortoises involves stating the null hypothesis (H0) and the alternative hypothesis (Ha). In this case, the null hypothesis, H0: μ = 88.1, states that the mean lifespan has not decreased and remains at 88.1 years. The alternative hypothesis, Ha: μ < 88.1, claims that the mean lifespan is now less than 88.1 years.

To perform the test, we calculate the test statistic using the given sample mean, standard deviation, and sample size. Since the population standard deviation is not known and the sample size is small (<30), we use the t-distribution:

Select one-tailed test since we are interested in a decrease in lifespan.

Calculate the test statistic (t).

If the calculated p-value is less than the level of significance (α = 0.05), we will reject the null hypothesis indicating there is evidence that the mean lifespan is now less. Without the actual test statistic and p-value provided, we cannot finish the hypothesis test.