A poll of 1068 adult Americans reveals that 48% of the voters surveyed prefer the Democractic candidate for the presidency. How many populations? 01 02 What is the parameter? O Mean O Proportion O Variance O Difference between Means O tandard Deviation
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
![**Title: What is the Test Statistic?**
In statistics, selecting the appropriate test statistic is crucial for hypothesis testing. Below are different formulas indicating various test statistics and scenarios where they might be used:
1. **Z-Test for Proportion:**
\[
z = \frac{\hat{p} - p}{\sqrt{\frac{p \cdot q}{n}}}
\]
**Description:** This formula is used to test the hypothesis about a population proportion.
2. **Two-Sample T-Test:**
\[
t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}
\]
**Description:** This test compares the means of two independent samples to evaluate if there is a significant difference.
3. **F-Test (Variance Ratio Test):**
\[
F = \frac{s_1^2}{s_2^2}
\]
**Description:** Used to compare variances between two populations to see if they are equal.
4. **Z-Test for Population Mean:**
\[
z = \frac{\bar{x} - \mu}{\frac{\sigma}{\sqrt{n}}}
\]
**Description:** A hypothesis test to determine whether the sample mean is significantly different from the population mean.
5. **Chi-Squared Test:**
\[
\chi^2 = \frac{(n - 1) \cdot s^2}{\sigma^2}
\]
**Description:** Often used for testing relationships between categorical variables or the goodness of fit.
6. **One-Sample T-Test for Population Mean:**
\[
t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}
\]
**Description:** Tests if the sample mean is significantly different from a known value.
7. **Alternative Two-Sample T-Test:**
\[
t = \frac{(\bar{x}_1 - \bar{x}_2) - (\mu_1 - \mu_2)}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}}](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff9076e7a-57c1-402a-997f-53718f1a9a67%2Fb7473238-64d2-4761-8882-230d0a0abc50%2F90dkmjm_processed.png&w=3840&q=75)
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