Questions: Only 20% of registered voters voted in the last election. Will voter participation increase for the upcoming election? Of the 393 randomly selected registered voters surveyed, 98 of them will vote in the upcoming election. What can be concluded at the α=0.10 level of significance? c. The test statistic ? v̂ = (please show your answer to 3 decimal places.) d. The p -value = (Please show your answer to 4 decimal places.)

Only 20% of registered voters voted in the last election. Will voter participation increase for the upcoming election? Of the 393 randomly selected registered voters surveyed, 98 of them will vote in the upcoming election. What can be concluded at the α=0.10 level of significance? c. The test statistic ? v̂ = (please show your answer to 3 decimal places.) d. The p -value = (Please show your answer to 4 decimal places.)
Transcript text: Only 20% of registered voters voted in the last election. Will voter participation increase for the upcoming election? Of the 393 randomly selected registered voters surveyed, 98 of them will vote in the upcoming election. What can be concluded at the $\alpha=0.10$ level of significance? c. The test statistic ? $\hat{v}=$ $\square$ (please show your answer to 3 decimal places.) d. The p -value $=$ $\square$ (Please show your answer to 4 decimal places.)
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Solution

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Solution Steps

Step 1: Calculate the sample proportion (p̂)

The sample proportion is the number of successes divided by the sample size. In this case, the number of successes is 98 (voters who will vote in the upcoming election) and the sample size is 393. p̂ = 98/393 ≈ 0.2494

Step 2: Calculate the test statistic (z)

The test statistic for a one-sample proportion hypothesis test is given by: z = (p̂ - p₀) / sqrt(p₀(1-p₀)/n) where p̂ is the sample proportion, p₀ is the hypothesized population proportion, and n is the sample size. In this case, p₀ = 0.20 and n = 393. z = (0.2494 - 0.20) / sqrt(0.20 * 0.80 / 393) z ≈ 2.468

Step 3: Calculate the p-value

Since this is a one-tailed test (testing for an _increase_ in voter participation), the p-value is the area to the right of the test statistic in the standard normal distribution. Using a z-table or calculator: p-value = P(Z > 2.468) ≈ 0.0068

Final Answer:

c. The test statistic = 2.468 d. The p-value = 0.0068

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