The Sign Test is also known as the Binomial Test. Let's recap what we found. The research question was to see if it took longer than minutes to complete the form.
The measurement was the time in minutes to complete the form. Here is a summary:. Hypothesis testing involves the careful construction of two statements: the null hypothesis and the alternative hypothesis.
These hypotheses can look very similar but are actually different. How do we know which hypothesis is the null and which one is the alternative? We will see that there are a few ways to tell the difference. The null hypothesis reflects that there will be no observed effect in our experiment. In a mathematical formulation of the null hypothesis, there will typically be an equal sign.
This hypothesis is denoted by H 0. The null hypothesis is what we attempt to find evidence against in our hypothesis test. We hope to obtain a small enough p-value that it is lower than our level of significance alpha and we are justified in rejecting the null hypothesis. If our p-value is greater than alpha, then we fail to reject the null hypothesis.
If the null hypothesis is not rejected, then we must be careful to say what this means. The thinking on this is similar to a legal verdict. Just because a person has been declared "not guilty", it does not mean that he is innocent. Note that the null hypothesis always contains the equal sign.
Null hypothesis: The sample data provides no evidence to support some claim being made by an individual. Alternative hypothesis: The sample data does provide sufficient evidence to support the claim being made by an individual. However, one botanist claims the true average height is greater than 20 inches. To test this claim, she may go out and collect a random sample of plants. She can then use this sample data to perform a hypothesis test using the following two hypotheses:.
If the sample data gathered by the botanist shows that the mean height of this species of plants is significantly greater than 20 inches, she can reject the null hypothesis and conclude that the mean height is greater than 20 inches.
Suppose that it is somehow known that the population standard deviation is 1. If you were conducting a hypothesis test to determine if the mean length of jail time has increased, what would the null and alternative hypotheses be? The distribution of the population is normal. A random survey of 75 death row inmates revealed that the mean length of time on death row is If you were conducting a hypothesis test to determine if the population mean time on death row could likely be 15 years, what would the null and alternative hypotheses be?
The National Institute of Mental Health published an article stating that in any one-year period, approximately 9. Suppose that in a survey of people in a certain town, seven of them suffered from depression or a depressive illness. If you were conducting a hypothesis test to determine if the true proportion of people in that town suffering from depression or a depressive illness is lower than the percent in the general adult American population, what would the null and alternative hypotheses be?
Some of the following statements refer to the null hypothesis, some to the alternate hypothesis. State the null hypothesis, H 0 , and the alternative hypothesis. Researchers surveyed a group of randomly selected teen girls living in Massachusetts between 12 and 15 years old. After four years the girls were surveyed again. Sixty-three said they smoked to stay thin. Is there good evidence that more than thirty percent of the teen girls smoke to stay thin? The alternative hypothesis is:. She surveys 84 of her students and finds that 11 attended the midnight showing.
An appropriate alternative hypothesis is:. Previously, an organization reported that teenagers spent 4. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was 4. Conduct a hypothesis test. The null and alternative hypotheses are:.
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