H_{0} :_{ }μ= 375

H_{1 }: μ ≠ 375 (claim)

α = 0.05 (significance level)

α/2= 0.025(two-tailed)

*A*. Since the key word "different" is the question, then this is a **
two-tailed test**. Therefore, divide 0.05 by 2 = .025(per tail). We find the critical values by going to the z-score tables for normal distribution. Notice that the area= .025 corresponds to z-scores**(critical values)= ±1.96**. To calculate
**test-statistic** manually: (350-375)/(120/√64) =-25/15=** -1.66 **. Since the test-statistic does not land within the critical values region, then
**we can conclude at a 0.05 significance level that there is not sufficient evidence to support the claim that the mean life is different from 375 hours**.

*B*. Using Graphing calculator TI-83: go to STATS, TESTS, Z-Test, Stats, μ_{0}:375, σ:120, x:350, n:64, μ: ≠μ_{0}, CALCULATE.
**p-value=.096** which is greater than α=0.05. Therefore we support the null hypothesis(H_{0})and reject the claim of the alternative hypothesis(H_{1}).

*C *.Using graphing calculator TI-83: STATS, TESTS,7↓ZInterval...,Stats, σ:120, x:350, n:64, C-Level:.95, Calculate=
**(320.6, 379.4) **

*D. ***The TRUE mean lies within the interval. So, 375 does lie between 320.6 and 379.4, and, therefore, still could be 375.**

*E*. Entering in σ=100 in calculations above (instead of σ=0), we get
**p-value=0.04 which is less than α=0.05.** Therefore, we** reject the null, H**_{0,
}and support the claim(H_{1}) that the mean life is different from 375. Also, 375 was not within the 95%CI = (325.5,374.5).