It is claimed that 71% of adults are in favor of more government regulation over artificial intelligence. Believing the true population parameter is smaller than this claimed value, a researcher surveys a random sample of 600 adults, and 414 of these surveyed adults say they are in favor of more government regulation over artificial intelligence. When a hypothesis test is conducted at a significance level of 0.05, the resulting test statistic is found to be -1.1. The researcher ultimately concludes that if we assume the null hypothesis is true, the probability of observing a sample result at least as extreme as what was observed is approximately 0.14. The value of p in this example is equal to ________.

Enter your answer in the form of a number in the textbox below. To earn credit, your answer must be expressed to exactly two decimal places.

Question

It is claimed that 71% of adults are in favor of more government regulation over artificial intelligence.  Believing the true population parameter is smaller than this claimed value, a researcher surveys a random sample of 600 adults, and 414 of these surveyed adults say they are in favor of more government regulation over artificial intelligence.  When a hypothesis test is conducted at a significance level of 0.05, the resulting test statistic is found to be -1.1.  The researcher ultimately concludes that if we assume the null hypothesis is true, the probability of observing a sample result at least as extreme as what was observed is approximately 0.14.   The value of p in this example is equal to ________.

Enter your answer in the form of a number in the textbox below.  To earn credit, your answer must be expressed to exactly two decimal places.

BlackTom AI · Accepted Answer

p represents the claimed population proportion under the null hypothesis, so p = 0.71.

Relevant concepts: In a one-sample proportion test the null hypothesis uses the claimed population proportion p (often written p0). The sample proportion is p̂ = x/n, and the test statistic is z = (p̂ − p0) / sqrt[p0(1 − p0)/n]. The p-value is the probability, under H0, of observing a test statistic at least as extreme as the observed one.

Step-by-step reasoning and calculations:
1. Compute the sample proportion: x = 414, n = 600, so p̂ = 414/600 = 0.69.
2. The problem states the claim is 71% in favor, so the null hypothesis value is p0 = 0.71.
3. Compute the standard error using p0:
   p0(1 − p0) = 0.71 × 0.29 = 0.2059.
   Divide by n: 0.2059 / 600 = 0.0003431667.
   Standard error = sqrt(0.0003431667) ≈ 0.01852.
4. Compute the z statistic:
   z = (p̂ − p0) / SE = (0.69 − 0.71) / 0.01852 = −0.02 / 0.01852 ≈ −1.0798 ≈ −1.1 (matches the given test statistic).
5. The researcher’s reported p-value ≈ 0.14 corresponds to P(Z ≤ −1.1) ≈ 0.1357 (rounded to 0.14), consistent with a left-tailed test.

Why this is correct:
- The symbol p in the hypothesis-test context denotes the population proportion under H0, which was stated as 71% in the problem text. The computed z and reported p-value are consistent with p0 = 0.71.

Why other numbers are not p:
- The sample proportion p̂ = 0.69 is an estimate, not the hypothesized p.
- The p-value ≈ 0.14 is the tail probability, not the population proportion.

Conclusion: The value of p in this example is 0.71.

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