Question

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 775 hours. A random sample of 23 light bulbs has a mean life of 763 hours. Assume the population is normally distributed and the population standard deviation is 64 hours. At alpha equals 0.08​, do you have enough evidence to reject the​ manufacturer's claim? Complete parts​ (b) through​ (d) ​(b) Identify the critical​ value(s). Use technology. ​(c) Identify the standardized test statistic. ​(d) Decide whether to reject or fail to reject the null hypothesis.

Answer 1

Here claim is that the mean life of a certain type of light bulb is at least 775 hours

So hypothesis here is

As population standard deviation is known so we will use z statistics

b.The z-critical value for a left-tailed test, for a significance level of α=0.08 is

zc​=−1.41

Graphically

c. Test statistics is

d. As test statistics do not fall in the rejection region we fail to reject the null hypothesis