how to find null hypothesis in minitab

Perform a hypothesis test for 1-Sample Sign

Perform a hypothesis test, enter a test median, and select the alternative hypothesis.

• To perform a hypothesis test, select Test median and enter a value. Use a hypothesis test to determine whether the population median (denoted as η) differs significantly from the hypothesized median (denoted as η 0 ) that you specify. If you don't perform the test, Minitab still displays a confidence interval, which is a range of values that is likely to include the population median. For more information, go to What is a hypothesis test? .
• Enter a value for Test median . The value you enter for Test median defines your null hypothesis (H 0 : η = η 0 ). Think of this value as a target value or a reference value. For example, a chemist enters 12 as the test median to determine whether the median time that it takes for a newly developed antacid to relieve symptoms is different from 12 minutes (H 0 : η = 12).

Use this one-sided test to determine whether the population median is less than the test median, and get an upper bound. This one-sided test gives greater power, it cannot detect when the population median is greater.

For example, a researcher uses this one-sided test to determine whether the median time that it takes a drug to relieve symptoms is less than 12 minutes. This one-sided test has greater power to determine whether the median is less than 12, but it cannot detect whether the median is greater than 12.

Use this two-sided test to determine whether the population median differs from the test median, and to get a two-sided confidence interval. A two-sided test can detect differences that are less than or greater than the hypothesized value, but it has less power than a one-sided test.

For example, an inspector tests whether the median chromium content in stainless steel differs from the specification of 0.18. Because any difference from the specification is important, the inspector uses this two-sided test to determine whether the median is greater than or less than the specification.

Use this one-sided test to determine whether the population median is greater than the test median and get a lower bound. This one-sided test gives greater power, it cannot detect when the population median is less than the test median.

For example, a hospital administrator uses this one-sided test to determine whether the median patient satisfaction rating is greater than 90. This one-sided test has greater power to determine whether the median is greater than 90, but it cannot determine whether the median is less than 90.

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6a.6 - minitab: one-sample \(p\) hypothesis testing.

Note about Software and Hypothesis Testing! In general, as we will learn, software usually performs tests using the p-value method. That is, the output from software will provide the test statistic and the p-value, along with some other general information (e.g. a confidence interval). To perform rejection region tests you would need to find the critical values from the tables. However, at the end of this lesson, we do demonstrate how to find the correct critical value from the standard normal distribution.

Minitab ®  – Conduct a One-Sample Proportion Z-Test

To conduct the one-sample proportion Z-test in Minitab...

• Click Stat > Basic Stat > 1 Proportion .
• In the drop-down box use "One or more samples, each in a column" if you have the raw data, otherwise select "Summarized data" if you only have the sample statistics.
• If using the raw data enter the column of interest into the blank variable window below the drop down selection. If using summarized data enter the number of successes for Events and the sample size for Trials .
• Click the check box for "Perform hypothesis test" and enter the null hypothesis value.
• Click Options .
• Enter the confidence level associated with alpha (e.g. 95% for alpha of 5%).
• From the drop down list for "Alternative hypothesis" select the correct alternative.
• If conditions are satisfied to perform a z-test for one proportion, select from the "Method" field "normal approximation"
• Click OK and OK .

Minitab ®

Example 6-6: penn state students from pennsylvania section  .

Recall our one-proportion example at the beginning of this lesson on whether the majority of Penn State students are from Pennsylvania. In that example, we took a random sample of 500 Penn State students and found that 278 are from Pennsylvania. Can we conclude that the proportion is larger than 0.5 at a 5% level of significance? Also recall in that example we found by hand a test statistic of \(z^* = 2.504 \) and p -value of 0.0062.

Our hypotheses were: \(H_0\colon p=0.5 \) and \(H_a \colon p>0.5 \)

Using Minitab...

• Select Stat > Basic Stat > 1 Proportion .
• Choose the summarized data option and enter 278 for "Events" and 500 as the "Trials".
• Check the box for "Perform Hypothesis Test" and enter the null value of 0.5
• Click Options . With our stated alpha value of 5% we keep the default confidence level of 95.
• Select Proportion > hypothesized proportion from the Alternative Hypothesis list. Since we verified the the conditions were satisfied, select Normal Approximation under Method.
• Click OK and OK again.

The output is:

As the output indicates, our by-hand calculations were very accurate!

Minitab ®  – Finding the Critical Value for a One-Sample Proportion Test

Although we can find values on the standard normal table, it is more accurate to find values using software. Finding values for the standard normal is discussed in more detail in Lesson 3 . We present this here as a review. In order to obtain the exact critical value to use in order to conduct the rejection region approach we can use a statistical package such as Minitab.

To find the critical value...

• Choose Calc > Probability Distributions > Normal distribution
• Choose the radio button for "Inverse Cumulative Distribution" (this finds the z-value that produces the entered probability to the left of it).
• Choose the radio button for "Input constant" and enter the alpha value (if one-side alternative) or alpha/2 (if two-sided alternative).