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If the null hypothesis is true and the researchers do not reject it then a correct decision has been made?
True because the point of the hypothesis test is to figure out the probability of the null hypothesis being true or false. If it is tested and it is true, then you do not reject but you reject it, when it is false.
What is the probability of making a Type II error if the null hypothesis is actually true?
zero. We have a sample from which a statistic is calculated and will challenge our held belief or "status quo" or null hypothesis. Now you present a case where the null hypothesis is true, so the only possible error we could make is to reject the null hypothesis- a type I error. Hypothesis testing generally sets a criteria for the test statistic to reject Ho or fail to reject Ho, so both type 1 and 2 errors are possible.
Reject or accept null hypothesis F-test?
F-test results will determine if the null hypothesis will be rejected or accepted. All test are ran with the assumption that the null hypothesis is true.
What does a p value of 0.66 tell us?
A p-value is the probability of obtaining a test statistic as extreme or more extreme than the one actually obtained if the null hypothesis were true. If this p-value is less than the level of significance (usually set by the experimenter as .05 or .01), we reject the null hypothesis. Otherwise, we retain the null hypothesis. Therefore, a p-value of 0.66 tell us not to reject the null hypothesis.
How is the null hypothesis used in hypothesis testing?
Statistical tests compare the observed (or more extreme) values against what would be expected if the null hypothesis were true. If the probability of the observation is high you would retain the null hypothesis, if the probability is low you reject the null hypothesis. The thresholds for high or low probability are usually set arbitrarily at 5%, 1% etc. Strictly speaking, when rejecting the null hypothesis, you do not accept the alternative hypothesis because it is possible that neither are true and it is the model itself that is wrong.
