Suppose we want to test the null hypothesis H0 : p = 0.34 against the alternative hypothesis H1 : p > 0.34. Suppose also that we observed 120 successes in a random sample of 300 subjects and the level of significance is 0.05. What is the observed test statistic for this test? Question 1Select one:a.-2.194b.0.4c.0.05d.2.194
Question
Suppose we want to test the null hypothesis H0 : p = 0.34 against the alternative hypothesis H1 : p > 0.34. Suppose also that we observed 120 successes in a random sample of 300 subjects and the level of significance is 0.05. What is the observed test statistic for this test? Question 1Select one:a.-2.194b.0.4c.0.05d.2.194
Solution
To calculate the observed test statistic for this test, we will use the formula for the test statistic in hypothesis testing for proportions, which is (p̂ - p0) / sqrt((p0*(1 - p0))/n), where p̂ is the sample proportion, p0 is the proportion in the null hypothesis, and n is the sample size.
Here, p̂ = 120/300 = 0.4 (the proportion of successes in the sample), p0 = 0.34 (the proportion in the null hypothesis), and n = 300 (the sample size).
Substituting these values into the formula, we get:
Test statistic = (0.4 - 0.34) / sqrt((0.34*(1 - 0.34))/300) = 0.06 / sqrt((0.34*0.66)/300) = 0.06 / sqrt(0.2244/300) = 0.06 / sqrt(0.000748) = 0.06 / 0.02736 = 2.194.
So, the observed test statistic for this test is 2.194. Therefore, the correct answer is d. 2.194.
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