16-To test the hypothesis H0 : ì = 100 against H1 : ì > 100, a statistics practioner randomly sampled T
observations and found the mean x = 106 and the standard deviation sx = 35. The value of the test
statistic is equal to
(1) 1.1743
(2) −1.7143
(3) 0.1714
(4) 17.143
(5) 1.7143
ANSWER:1
18-Suppose we want to test the null hypothesis H0 : ì = 400 against H1 :ì < 400. The test statistic is
calcuated as −1.23 and the two-tailed critical value is 1.96. The appopriate p–value will be
(1) −0.0500
(2) 0.3907
(3) 0.1093
(4) 0.8907
(5) −0.1093
ANSWER: 3
19- Determine the p–value associated with the values of the standardized test statistic z = 1.05 for one-tail
test.
(1) 0.3531
(2) 0.1469
(3) 0.8531
(4) 0.0146
(5) 0.2938
ANSWER: 3
20-Using the confidence interval when conducting a two-tail test for the population mean, we do not reject
the null hypothesis if the hypothesized value:
(1) is to the left of the lower confidence limit
(2) is to the right of the upper confidence limit
(3) falls between the lower and upper confidence limits
(4) falls in the rejection region
(5) all the above statements are correct
ANSWER: 3
16. Your fail to indicate your sample size to determine the standard error of the mean. SE = SD/√(n-1) is needed to determine the significance of difference between means.
However, it seems like the alternatives are using the SD rather than SE. Then Z = (x - μ)/SD =
(106-100)/35 = 6/35 = .1714
18. Your H1 indicates a one-tailed test, but you are using a two-tailed critical value. I'm not sure what you are looking for with the "p-value." If this is probability of Alpha error, then .1093 is correct.
19. I'm not sure what you are looking for with the "p-value." If this is probability of Alpha error, then .1469 is correct.
20. Correct
16- To determine the test statistic, we need to calculate the z-score, which is the difference between the sample mean and the null hypothesis mean divided by the standard deviation. The formula for the test statistic is:
test statistic = (x - ì) / (sx / sqrt(T))
Given that x = 106, ì = 100, sx = 35, and T is not provided in the question, we can't calculate the exact test statistic. However, we can still determine the answer by reasoning. Since the null hypothesis is ì = 100 and the alternative hypothesis is ì > 100, a positive test statistic is expected. Among the given options, only option 1 (1.1743) is positive, so the answer is (1) 1.1743.
18- The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. In a one-tailed test with the alternative hypothesis ì < 400, a negative test statistic is expected. Given that the test statistic is -1.23, which is negative, and the two-tailed critical value is 1.96, which is positive, we can conclude that the test statistic falls in the rejection region corresponding to the null hypothesis being false. Since the p-value associated with the test statistic is less than the significance level (which is not provided in the question), we reject the null hypothesis. From the given options, (3) 0.1093 is the closest to the p-value, so the answer is (3) 0.1093.
19- The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. In a one-tailed test, depending on whether it is a left-tail or right-tail test, we compare the test statistic with the appropriate critical value. Since the question does not specify the direction of the alternative hypothesis, we can't determine whether it's a left-tail or right-tail test. Therefore, we can't calculate the p-value using the given test statistic. Among the given options, only option 3 (0.8531) is positive, so the answer is (3) 0.8531.
20- When conducting a two-tail test for the population mean with a confidence interval, we reject the null hypothesis if the hypothesized value falls outside the range between the lower and upper confidence limits. In other words, we reject the null hypothesis if the hypothesized value is not within the confidence interval. Therefore, the correct statement is (3) falls between the lower and upper confidence limits.