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Question 6 ot \( 10(12 \) pointa) eucstion Attempt: 1 of 1
Time Remaining: \( 2: 59.08 \)
Nath
A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean lifetime, \( \mu \), of 20 years. To test the company's claim, a competitor has selected 39 of these batteries at random. The mean lifetime of the sample is 21.1 years. Suppose the population standard deviation of these lifetimes is known to be 4.1 years.
Is there enough evidence to reject the claim that the mean lifetime of the newest model is 20 years? Perform a hypothesis test, using the 0.10 level of significance.
(a) State the null hypothesis \( H_{0} \) and the alternative hypothesis \( H_{1} \).
\[
\begin{array}{l}
H_{0}: \square \\
H_{1}: \square
\end{array}
\]
\begin{tabular}{ccc}
\( \mu \) & \( \bar{x} \) & \( \square^{0} \) \\
\( \square<\square \) & \( \square \leq \square \) & \( \square>\square \) \\
\( \square \geq \square \) & \( \square=\square \) & \( \square * \square \) \\
\( \times \) & & 5
\end{tabular}
(b) Perform a Z-test and find the \( p \)-value.
Here is some information to help you with your Z-test.
- The value of the test statistic is given by \( \frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \)
- The \( p \)-value is two times the area under the curve to the right of the value of the test statistic.
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