Question

A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean lifetime, \( \mu \), of 15 years. To test the company's claim, a competitor has selected 62 of these batteries at random. The mean lifetime of the sample is 13.9 years. Suppose the population standard deviation of these lifetimes is known to be 3.2 years. Is there enough evidence to reject the claim that the mean lifetime of the newest model is 15 years? Perform a hypothesis test, using the 0.05 level of significance. (a) State the null hypothesis \( H_{0} \) and the alternative hypothesis \( H_{1} \). \[ \begin{array}{l} H_{0}: \square \\ H_{1}: \square \end{array} \] (b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your test. - \( z_{0.025} \) is the value that cuts off an area of 0.025 in the right tail. - The test statistic has a normal distribution and the value is given by \( z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \).

          A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean lifetime, \( \mu \), of 15 years. To test the company's claim, a competitor has selected 62 of these batteries at random. The mean lifetime of the sample is 13.9 years. Suppose the population standard deviation of these lifetimes is known to be 3.2 years.

Is there enough evidence to reject the claim that the mean lifetime of the newest model is 15 years? Perform a hypothesis test, using the 0.05 level of significance.
(a) State the null hypothesis \( H_{0} \) and the alternative hypothesis \( H_{1} \).
\[
\begin{array}{l}
H_{0}: \square \\
H_{1}: \square
\end{array}
\]
(b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your test.
- \( z_{0.025} \) is the value that cuts off an area of 0.025 in the right tail.
- The test statistic has a normal distribution and the value is given by \( z=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}} \).

A company that manufactures batteries used in electric cars is reporting that their newest model of battery has a mean lifetime, μ, of 15 years. To test the company's claim, a competitor has selected 62 of these batteries at random. The mean lifetime of the sample is 13.9 years. Suppose the population standard deviation of these lifetimes is known to be 3.2 years.

Is there enough evidence to reject the claim that the mean lifetime of the newest model is 15 years? Perform a hypothesis test, using the 0.05 level of significance.
(a) State the null hypothesis H0 and the alternative hypothesis H1.

H0: □

H1: □

(b) Perform a hypothesis test. The test statistic has a normal distribution (so the test is a "Z-test"). Here is some other information to help you with your test.
- z0.025 is the value that cuts off an area of 0.025 in the right tail.
- The test statistic has a normal distribution and the value is given by z=(x̅-μ)/((σ)/(√(n))).

Added by John Paul O.

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