H0 : μ= 375
H1 : μ ≠ 375 (claim)
α = 0.05 (significance level)
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, μ0:375, σ:120, x:350, n:64, μ: ≠μ0, CALCULATE.
p-value=.096 which is greater than α=0.05. Therefore we support the null hypothesis(H0)and reject the claim of the alternative hypothesis(H1).
C .Using graphing calculator TI-83: STATS, TESTS,7↓ZInterval...,Stats, σ:120, x:350, n:64, C-Level:.95, Calculate=
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, H0,
and support the claim(H1) that the mean life is different from 375. Also, 375 was not within the 95%CI = (325.5,374.5).