Question
The value of the statistic is
2.31. Find p-value if H0: p=0.3, H1: p>0.3
2.31. Find p-value if H0: p=0.3, H1: p>0.3
Answers
GPT-4o mini
To find the p-value for the given statistic of 2.31 in the context of a hypothesis test where \( H_0: p = 0.3 \) and \( H_1: p > 0.3 \), we will assume that this statistic is based on a standard normal distribution (z-test).
1. **Calculate the p-value**: The test statistic \( z = 2.31 \) tells us how many standard deviations the sample proportion is away from the null hypothesis value.
2. **Use a standard normal distribution table** or calculator: You can find the area to the right of \( z = 2.31 \) in a standard normal distribution to find the p-value.
The steps to find the p-value:
- Look up the z-value of 2.31 in the standard normal distribution (Z) table, or use a calculator. The area to the left of \( z = 2.31 \) is approximately \( 0.9890 \).
- To find the p-value for a right-tailed test, subtract the area from 1:
\[
\text{p-value} = 1 - P(Z < 2.31) = 1 - 0.9890 = 0.0110
\]
Thus, the p-value is approximately **0.0110**.
This means there is about a 1.10% chance of seeing a test statistic as extreme as, or more extreme than, 2.31 if the null hypothesis is true. If this p-value is less than your significance level (commonly 0.05 or 0.01), you would reject the null hypothesis in favor of the alternative hypothesis.
1. **Calculate the p-value**: The test statistic \( z = 2.31 \) tells us how many standard deviations the sample proportion is away from the null hypothesis value.
2. **Use a standard normal distribution table** or calculator: You can find the area to the right of \( z = 2.31 \) in a standard normal distribution to find the p-value.
The steps to find the p-value:
- Look up the z-value of 2.31 in the standard normal distribution (Z) table, or use a calculator. The area to the left of \( z = 2.31 \) is approximately \( 0.9890 \).
- To find the p-value for a right-tailed test, subtract the area from 1:
\[
\text{p-value} = 1 - P(Z < 2.31) = 1 - 0.9890 = 0.0110
\]
Thus, the p-value is approximately **0.0110**.
This means there is about a 1.10% chance of seeing a test statistic as extreme as, or more extreme than, 2.31 if the null hypothesis is true. If this p-value is less than your significance level (commonly 0.05 or 0.01), you would reject the null hypothesis in favor of the alternative hypothesis.