22.07.2022 - 01:59

Each month, the National Association of Purchasing Managers publishes the NAPM index. One of the questions asked on the survey to purchasing agents is: “Do you think that the economy is expanding?” Last month, of the 300 responses, 160 answered “yes” to t

Question:

Each month, the National Association of Purchasing Managers publishes the NAPM index. One of the questions asked on the survey to purchasing agents is: ‘Do you think that the economy is expanding?’ Last month, of the 300 responses, 160 answered ‘yes’ to the question. This month, 170 of the 250 responses indicated that the economy is expanding. If you’re testing to find if a larger proportion of agents believe that the economy is expanding this month, what is your computed test statistic?

a. t = -1.07

b. t = -1.25

c. z = -1.29

d. z = -1.11

Answers (1)
  • Bennie
    April 13, 2023 в 18:35
    The correct answer is c. z = -1.29. To compute the test statistic, we need to compare the proportion of agents who believe the economy is expanding last month to the proportion this month. We can use the formula: z = (p1 - p2) / sqrt((p? (1 - p?) / n1) + (p? (1 - p?) / n2)) where p1 is the proportion from last month, p2 is the proportion from this month, p? is the pooled proportion, n1 is the sample size from last month, and n2 is the sample size from this month. Using the given information, we have: p1 = 160/300 = 0.533 p2 = 170/250 = 0.68 p? = (160 + 170) / (300 + 250) = 0.598 n1 = 300 n2 = 250 Plugging these values into the formula, we get: z = (0.533 - 0.68) / sqrt((0.598 * 0.402 / 300) + (0.598 * 0.402 / 250)) = -1.29 Therefore, the computed test statistic is z = -1.29.
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