Question

the lifetime of a certain type of battery is known to be normally distributed with standard deviation σ≈22 hours. a sample of 50 batteries had a mean lifetime of 120.1 hours. it is desired to construct a 95% confidence interval for the mean lifetime for this type of battery.
part 1 of 6
(a) what is the point estimate?
the point estimate is 120.1.
part 1 / 6
part 2 of 6
(b) find the critical value.
the critical value is .

Explanation:

Step1: Identify Distribution and Confidence Level

We have a normal distribution with known standard deviation, so we use the z - distribution. The confidence level is 95%, so the significance level $\alpha=1 - 0.95 = 0.05$. The critical value is the z - score that leaves $\frac{\alpha}{2}=0.025$ in each tail.

Step2: Find Critical Value from Z - Table

Looking at the standard normal (z - table), the z - score corresponding to a right - tail area of 0.025 (or a cumulative probability of $1 - 0.025=0.975$) is $z_{\alpha/2}=1.96$.

Answer:

1.96