According to a study on reptiles from decades ago, the mean lifespan of giant Aldabra tortoises in the wild is 98.5 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 19 randomly selected, giant Aldabra tortoises in the wild. In the study, the sample mean lifespan was 95.7 years with a sample standard deviation of 8.2 years. Assume that the population of lifespans of giant 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 0.10 level of significance, to support the claim that \( \mu \), the mean lifespan of giant Aldabra tortoises in the wild, is now less than 98.5 years.
(a) State the null hypothesis \( H_{0} \) and the alternative hypothesis \( H_{1} \) that you would use for the test.
\[
\begin{array}{l}
H_{0}: \mu \geq 98.5 \\
H_{1}: \mu \leq 98.5
\end{array}
\]
(b) Perform a \( t \) 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 \( t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}} \).
- The \( p \)-value is the area under the curve to the left of the value of the test statistic.
Student's t Distribution
Step 1: Enter the number of degrees of freedom.
\( \square \)
Step 2: Select one-tailed or two-tailed.
One-tailed
Two-tailed
Step 3: Enter the test statistic. (Round to 3 decimal places.)
\( \square \)
Step 4: Shade the area represented by the \( p \)-value.
Step 5: Enter the \( p \)-value. (Round to 3 decimal places.)
\( \square \)
