1)When computing the test statistic for a hypothesis test, who do we assume Ho i

Question

1)When computing the test statistic for a hypothesis test, who do we assume Ho is true?

2)In a hypothesis test, what does the P-value measure? I.e. what is the P-value the probability of? Hint: The sampling space for this probabiltiy is the set of all possible sample of size n.

3) Explain how to use the following confidence interval to test the hypothesis that the mean IQ of mice in the lab is less than 55. Given data from a large sample, we are 95% confident that the mean IQ of mice in our lab is in the interval 45<u<55. Hint: What would the P-value be for this hypothesis test? What would be your conclusion using a significance level of a=4%?

Explanation / Answer

The null hypothesis is generally assumed to be true until evidence indicates otherwise, we assume innocent until proven guilty. It's also called hypothesis of no difference, that there is no relationship between two measured phenomena or no association among groups.

Then, make a decision based on the available evidence.

If there is not enough evidence, do not reject the null hypothesis. (Behave as if the defendant is not guilty.)

If the observed outcome, e.g., a sample statistic, is surprising under the assumption that the null hypothesis is true, but more probable if the alternative is true, then this outcome is evidence against H0 and in favor of HA.

An observed effect so large that it would rarely occur by chance is called statistically significant (i.e., not likely to happen by chance).

(2)
The p-value represents how likely we would be to observe such an extreme sample if the null hypothesis were true. The p-value is a probability computed assuming the null hypothesis is true, that the test statistic would take a value as extreme or more extreme than that actually observed. Since it's a probability, it is a number between 0 and 1. The closer the number is to 0 means the event is “unlikely.” So if the p-value is “small,” (typically, less than 0.05), we can then reject the null hypothesis.

There is an extremely close relationship between confidence intervals and hypothesis testing. When a 95% confidence interval is constructed, all values in the interval are considered plausible values for the parameter being estimated. Values outside the interval are rejected as relatively implausible. If the value of the parameter specified by the null hypothesis is contained in the 95% interval then the null hypothesis cannot be rejected at the 0.05 level. If the value specified by the null hypothesis is not in the interval then the null hypothesis can be rejected at the 0.05 level. If a 99% confidence interval is constructed, then values outside the interval are rejected at the 0.01 level.

Here we have a given confidence interval 45<u<55 and we are 95% confident that the mean IQ of mice lies between this interval.the null hypothesis is that u<55, and the alternative is that u>55.

If the hypothesis test shows significant evidence that the mean IQ is greater than 55, we reject H0.We have significance level a=0.04, so we reject Ho if P<0.04. Otherwise we won't reject Ho.

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