To answer this question, we first need to calculate the test statistic and then use it to find the p-value.

Step 1: Calculate the test statistic
The test statistic for a proportion is calculated using the formula:
Z = (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.

In this case, p̂ = 100/400 = 0.25, p0 = 0.28, and n = 400.

Substituting these values into the formula gives:
Z = (0.25 - 0.28) / sqrt((0.28 * (1 - 0.28)) / 400) = -1.443

Step 2: Calculate the p-value
The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. Because this is a two-tailed test (H1 : p ≠ 0.28), we need to find the probability of observing a Z value less than -1.443 or greater than 1.443.

Using a standard normal distribution table or a calculator, we find that the probability of observing a Z value less than -1.443 is approximately 0.0745. Because this is a two-tailed test, we multiply this by 2 to get the p-value: 0.0745 * 2 = 0.149.

So, the p-value for this test is approximately 0.149. This is not one of the options given in the question, so there may be a mistake in the question or in the options provided.

Question

To answer this question, we first need to calculate the test statistic and then use it to find the p-value.

Step 1: Calculate the test statistic
The test statistic for a proportion is calculated using the formula: 
Z = (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.

In this case, p̂ = 100/400 = 0.25, p0 = 0.28, and n = 400.

Substituting these values into the formula gives: 
Z = (0.25 - 0.28) / sqrt((0.28 * (1 - 0.28)) / 400) = -1.443

Step 2: Calculate the p-value
The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. Because this is a two-tailed test (H1 : p ≠ 0.28), we need to find the probability of observing a Z value less than -1.443 or greater than 1.443.

Using a standard normal distribution table or a calculator, we find that the probability of observing a Z value less than -1.443 is approximately 0.0745. Because this is a two-tailed test, we multiply this by 2 to get the p-value: 0.0745 * 2 = 0.149.

So, the p-value for this test is approximately 0.149. This is not one of the options given in the question, so there may be a mistake in the question or in the options provided.

Knowee AI · Accepted Answer

To answer this question, we first need to calculate the test statistic and then use it to find the p-value.

Step 1: Calculate the test statistic
The test statistic for a proportion is calculated using the formula: 
Z = (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.

In this case, p̂ = 100/400 = 0.25, p0 = 0.28, and n = 400.

Substituting these values into the formula gives: 
Z = (0.25 - 0.28) / sqrt((0.28 * (1 - 0.28)) / 400) = -1.443

Step 2: Calculate the p-value
The p-value is the probability of observing a test statistic as extreme as the one calculated, assuming the null hypothesis is true. Because this is a two-tailed test (H1 : p ≠ 0.28), we need to find the probability of observing a Z value less than -1.443 or greater than 1.443.

Using a standard normal distribution table or a calculator, we find that the probability of observing a Z value less than -1.443 is approximately 0.0745. Because this is a two-tailed test, we multiply this by 2 to get the p-value: 0.0745 * 2 = 0.149.

So, the p-value for this test is approximately 0.149. This is not one of the options given in the question, so there may be a mistake in the question or in the options provided.

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