A campaign manager for a political candidate released advertisements criticizing …

Business Questions
Short Answer
Step by Step Solution
Business Questions

A campaign manager for a political candidate released a series of advertisements criticizing the opposing candidate in an upcoming election. the opposing candidate previously had the support of 45% of voters, so the manager wants to test h0: p = 0.45 versus ha: p < 0.45, where p is the proportion of voters that support the opposing candidate. after running the advertisements, the campaign manager obtained a random sample of 500 voters and found that 200 of those sampled supported the opposing candidate. assuming that the conditions for inference have been met, identify the correct test statistic for this significance test.

Short Answer

The significance test statistic can be calculated by first determining the sample proportion (p-hat) as 0.4 from 200 successes out of 500. Using this value and the null hypothesis proportion of 0.45, the z-score formula yields a test statistic of approximately -2.04.

Step-by-Step Solution

Step 1: Understand the Variables

To calculate the significance test statistic, it’s essential to identify and understand the variables involved. In this context, we have:

  • p-hat: This is the sample proportion, calculated by dividing the number of successes by the sample size.
  • p0: The null hypothesis proportion, which in this case is 0.45.
  • n: The sample size, given as 500.

Step 2: Calculate the Sample Proportion

Using the provided data, we can calculate the sample proportion, p-hat. Here’s how to compute it:

  • Divide the number of successes (200) by the total sample size (500).
  • This results in p-hat = 200/500 = 0.4.

Step 3: Compute the Test Statistic

Now, we can apply the values into the z-score formula to obtain the test statistic. Follow these steps:

  • Use the formula: z = (p-hat – p0) / sqrt(p0(1-p0)/n).
  • Plug in the values: z = (0.4 – 0.45) / sqrt(0.45(1-0.45)/500).
  • The result is approximately -2.04, which is the correct test statistic for the significance test.

Related Concepts

P-Hat

Sample proportion calculated by dividing the number of successes by the sample size

P0

Null hypothesis proportion, the expected value under the null hypothesis

N

Sample size, the total number of observations in the sample.

Table Of Contents
  1. A campaign manager for a political candidate released a series of advertisements criticizing the opposing candidate in an upcoming election. the opposing candidate previously had the support of 45% of voters, so the manager wants to test h0: p = 0.45 versus ha: p < 0.45, where p is the proportion of voters that support the opposing candidate. after running the advertisements, the campaign manager obtained a random sample of 500 voters and found that 200 of those sampled supported the opposing candidate. assuming that the conditions for inference have been met, identify the correct test statistic for this significance test.

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