3.6: Putting it all Together Using the Classical Method
- Page ID
- 2888
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Putting it all Together Using the Classical Method
To Test a Claim about μ when σ is Known
- Write the null and alternative hypotheses.
- State the level of significance and get the critical value from the standard normal table.
- Compute the test statistic.
\[z=\frac {\bar {x}-\mu}{\frac {\sigma}{\sqrt {n}}}\]
- Compare the test statistic to the critical value (Z-score) and write the conclusion.
To Test a Claim about μ When σ is Unknown
- Write the null and alternative hypotheses.
- State the level of significance and get the critical value from the student’s t-table with n-1 degrees of freedom.
- Compute the test statistic.
\[t=\frac {\bar {x}-\mu}{\frac {s}{\sqrt {n}}}\]
- Compare the test statistic to the critical value (t-score) and write the conclusion.
To Test a Claim about p
- Write the null and alternative hypotheses.
- State the level of significance and get the critical value from the standard normal distribution.
- Compute the test statistic.
\[z=\frac {\hat {p}-p}{\sqrt {\frac {p(1-p)}{n}}}\]
- Compare the test statistic to the critical value (Z-score) and write the conclusion.
Table \(PageIndex{1}\). A summary table for critical Z-scores.
|
|
Two-sided Test |
One-sided Test |
|---|---|---|
|
Alpha (á) |
|
Z á |
|
0.01 |
2.575 |
2.33 |
|
0.05 |
1.96 |
1.645 |
|
0.10 |
1.645 |
1.28 |
á 
To Test a Claim about Variance
- Write the null and alternative hypotheses.
- State the level of significance and get the critical value from the chi-square table using n-1 degrees of freedom.
- Compute the test statistic.
\[\chi^2 = \frac {(n-1)S^2}{\sigma^{2}_{0}}\]
- Compare the test statistic to the critical value and write the conclusion.