l. A random sample of 10 tems gives 614.5 and s = 42.9. a) Use a hypothesis test
ID: 3363123 • Letter: L
Question
l. A random sample of 10 tems gives 614.5 and s = 42.9. a) Use a hypothesis test to determine whether there is sufficient evidence for the experimenter to conclude that the population average is not 600. State the hypothesis: Find the critical value and identify the critical (rejection) region =0.01. ( Draw Picture) Calculate the test statistic and decide whether to reject or fail to reject the null hypothesis Interpret your results. b) Construct a 99% two-sided CI for the population average. What comment can you make about the relationship between hypothesis testing and confidence intervals?Explanation / Answer
Solution:
1) Given information x = 614.5, s = 42.9, n = 10
a) Test Hypothesis:
H0: = 600
Ha: 600
Critical value tcritical = t(/2, n-1) = t(0.005, 9) = 3.250
Test statistics:
t = x- /(s/n) = 614.5- 600/(42.9/10) = 1.069
Since t <3.25 and >-3.25, we fail to reject the null hypothesis.
So we have enough evidence that the mean is equal to 600.
b) Confidence interval:
CI = x ± t/2,n-1 * s/n
= 614.5 ± 3.250 * (42.9/10)
= 614.5 ± 44.0900563
= (570.4099, 658.5901)
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