Question

3. What does the test statistic tell us?

4. Why do we divide by the standard error when computing a test statistic?

5. Why do we reject the null hypothesis when the p-value is small? Explain as if to someone unfamiliar with

statistics.

Answer 1

Solution :-

3)

A test statistic is a random variable that is calculated from sample data and used in a hypothesis test. Test statistics used to determine whether to reject the null hypothesis. The test statistic compares data with what is expected under the null hypothesis. The test statistic is used to calculate the p-value.

A test statistic measures the degree of agreement between a sample of data and the null hypothesis. Its observed value changes randomly from one random sample to a different sample. A test statistic contains information about the data that is relevant for deciding whether to reject the null hypothesis. The sampling distribution of the test statistic under the null hypothesis is called the null distribution.

Different hypothesis tests use different test statistics based on the probability model assumed in the null hypothesis. Common tests and their test statistics include:

Hypothesis test	Test statistic
Z-test	Z-statistic
t-tests	t-statistic
ANOVA	F-statistic
Chi-square tests	Chi-square statistic

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4)

The standard error (SE) of a statistic (usually an estimate of a parameter) is the standard deviation of its sampling distribution or an estimate of that standard deviation.

The relationship between the standard error and the standard deviation is such that, for a given sample size, the standard error equals the standard deviation divided by the square root of the sample size. In other words, the standard error of the mean is a measure of the dispersion of sample means around the population mean.

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5 )

The p-value represents how likely we would be to observe such an extreme sample if the null hypothesis were true. The closer the number is to 0 means the event is “unlikely.” So if p-value is “small,” (typically, less than 0.05), we can then reject the null hypothesis.

If the p-value is less than or equal to the alpha (p < 0. 05), then we reject the null hypothesis, and we say the result is statistically significant. If the p-value is greater than alpha (p > 0. 05), then we fail to reject the null hypothesis, and we say that the result is statistically nonsignificant