Use the information below to answer Questions 1 through 4.
Given a sample size of 36, with sample mean 670.3 and sample standard deviation 114.9, we perform the following hypothesis test.
Null Hypothesis
Alternative Hypothesis
1. What is the test statistic?
670.3-700 ÷ 114.9/√36
= -29.7÷19.15
= -1.55
2. At a 10% significance level (90% confidence level), what is the critical value in this test? Do we reject the null hypothesis?
Table V value of .01 is 1.645
-1.645 < z > 1.645
z= 1.55 which falls within so we accept.
3. What are the border values between acceptance and rejection of this hypothesis?
700 +/- 1.645 (100/√ 36) =
700 +/- 1.645 (100/16.6666) =
700 +/- 1.645 (6.00) =
700 + 9.87 = 709.87
700- 9.87 = 690.13
666.87, 733.13
4. What is the power of this test if the assumed true mean were 710 instead of 700?
ZL = 709.87 - 710 -0.13 = -0.0013 Zl= .0040
100 100
ZU = = 690.13 - 710 -19.87 = -0.1987 Zu = .0753
100 100
.0753 - .0040 = .0749 β = 1. - .0749 = .9251
Questions 5 through 8 involve rolling of dice.
Given a fair, six-sided die, what is the probability of rolling