To calculate the test statistic for the given hypothesis test, we will use the formula for the test statistic for a proportion:

$$ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} $$

where:
- $\hat{p}$ is the sample proportion
- $p_0$ is the hypothesized population proportion
- $n$ is the sample size

Given:
- $p_0 = 0.72$
- $n = 90$
- Number of subjects with the characteristic = 68

First, calculate the sample proportion $\hat{p}$:

$$ \hat{p} = \frac{68}{90} = 0.756 $$

Next, calculate the standard error of the proportion:

$$ \text{SE} = \sqrt{\frac{p_0 (1 - p_0)}{n}} = \sqrt{\frac{0.72 \times (1 - 0.72)}{90}} = \sqrt{\frac{0.72 \times 0.28}{90}} = \sqrt{\frac{0.2016}{90}} = \sqrt{0.00224} \approx 0.047 $$

Now, calculate the test statistic $z$:

$$ z = \frac{\hat{p} - p_0}{\text{SE}} = \frac{0.756 - 0.72}{0.047} = \frac{0.036}{0.047} \approx 0.766 $$

Therefore, the test statistic is approximately $0.766$.

Question

To calculate the test statistic for the given hypothesis test, we will use the formula for the test statistic for a proportion:

$$ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} $$

where:
- $\hat{p}$ is the sample proportion
- $p_0$ is the hypothesized population proportion
- $n$ is the sample size

Given:
- $p_0 = 0.72$
- $n = 90$
- Number of subjects with the characteristic = 68

First, calculate the sample proportion $\hat{p}$:

$$ \hat{p} = \frac{68}{90} = 0.756 $$

Next, calculate the standard error of the proportion:

$$ \text{SE} = \sqrt{\frac{p_0 (1 - p_0)}{n}} = \sqrt{\frac{0.72 \times (1 - 0.72)}{90}} = \sqrt{\frac{0.72 \times 0.28}{90}} = \sqrt{\frac{0.2016}{90}} = \sqrt{0.00224} \approx 0.047 $$

Now, calculate the test statistic $z$:

$$ z = \frac{\hat{p} - p_0}{\text{SE}} = \frac{0.756 - 0.72}{0.047} = \frac{0.036}{0.047} \approx 0.766 $$

Therefore, the test statistic is approximately $0.766$.

Knowee AI · Accepted Answer

To calculate the test statistic for the given hypothesis test, we will use the formula for the test statistic for a proportion:

$$ z = \frac{\hat{p} - p_0}{\sqrt{\frac{p_0 (1 - p_0)}{n}}} $$

where:
- $\hat{p}$ is the sample proportion
- $p_0$ is the hypothesized population proportion
- $n$ is the sample size

Given:
- $p_0 = 0.72$
- $n = 90$
- Number of subjects with the characteristic = 68

First, calculate the sample proportion $\hat{p}$:

$$ \hat{p} = \frac{68}{90} = 0.756 $$

Next, calculate the standard error of the proportion:

$$ \text{SE} = \sqrt{\frac{p_0 (1 - p_0)}{n}} = \sqrt{\frac{0.72 \times (1 - 0.72)}{90}} = \sqrt{\frac{0.72 \times 0.28}{90}} = \sqrt{\frac{0.2016}{90}} = \sqrt{0.00224} \approx 0.047 $$

Now, calculate the test statistic $z$:

$$ z = \frac{\hat{p} - p_0}{\text{SE}} = \frac{0.756 - 0.72}{0.047} = \frac{0.036}{0.047} \approx 0.766 $$

Therefore, the test statistic is approximately $0.766$.

Suppose that the following is to be tested: H0: p = 0.72 and Ha: p ≠ 0.72. Calculate the test statistic for thefollowing sample data: Sixty-eight out of ninety test subjects have the characteristic of interest. Round tothe nearest thousandth

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