A Hypothesis Is a Claim

A supposition is a claim creation mean The mean monthly cell phone bill in this city is ? = $42 Population proportion Example The proportion of adults in this city with cell phones is ? = 0. 68 States the claim or assertion to be tested Is always around a cosmos parameter, non about a sample statistic Is the opposer of the vigour dead reckoning e. g. , The average diameter of a manufactured expire is not represent to 30mm ( H1 ? ? 30 ) Challenges the spot quo Alternative never contains the = star sign May or may not be provenIs largely the theory that the researcher is onerous to prove Is the opposite of the null hypothesis e. g. , The average diameter of a manufactured bolt is not equal to 30mm ( H1 ? ? 30 ) Challenges the status quo Alternative never contains the =sign May or may not be proven Is generally the hypothesis that the researcher is trying to prove Is the opposite of the null hypothesis e. g. , The average diameter of a manufactured bolt is not equal to 30mm ( H1 ? ? 30 ) Challenges the status quo Alternative never contains the =sign May or may not be provenIs generally the hypothesis that the researcher is trying to prove If the sample mean is close to the stated universe of discourse mean, the null hypothesis is not deflected. If the sample mean is far from the stated population mean, the null hypothesis is culled. How far is far enough to reject H0? The small value of a test statistic creates a line in the anchor for decision making it answers the question of how far is far enough. Type I fracture Reject a original null hypothesis Considered a serious type of error The probability of a Type I Error is ? Called direct of signifi privyce of the testSet by researcher in supercharge Type II Error Failure to reject a phony null hypothesis The probability of a Type II Error is ? Type I and Type II errors cannot happen at the uniform time A Type I error can barely occur if H0 is true A Type II error can only occur if H0 is fal se Critical Value Approach to interrogatory For a two-tail test for the mean, ? known turn back the critical Z set for a specified level of significance ? from a table or computer Decision Rule If the test statistic falls in the rejection region, reject H0 otherwise do not reject H0State the null hypothesis, H0 and the alternative hypothesis, H1 Determine the appropriate test statistic and sampling distribution Determine the critical tally that divide the rejection and nonrejection regions Collect data and compute the value of the test statistic have got the statistical decision and state the managerial conclusion. If the test statistic falls into the nonrejection region, do not reject the null hypothesis H0. If the test statistic falls into the rejection region, reject the null hypothesis. Express the managerial conclusion in the context of the riddle p-Value Approach to Testing -value Probability of obtaining a test statistic equal to or more extreme than the observed samp le value given H0 is true The p-value is also called the observed level of significance H0 can be spurned if the p-value is less than ? Hypothesis Testing ? Unknown If the population standard release is unknown, you instead use the sample standard deviation S. Because of this change, you use the t distribution instead of the Z distribution to test the null hypothesis about the mean. When using the t distribution you must assume the population you are sampling from follows a normal distribution.All other steps, concepts, and conclusions are the same. One-Tail Tests In many cases, the alternative hypothesis focuses on a particular path H0 ? ? 3 H1 ? 3 This is a lower-tail test since the alternative hypothesis is focussed on the lower tail below the mean of 3 H0 ? ? 3 H1 ? 3 This is an focal ratio-tail test since the alternative hypothesis is focused on the upper tail above the mean of 3 Proportions Sample proportion in the category of interest is denoted by p When both X and n X are at least 5, p can be approximated by a normal distribution with mean and standard deviationPotential Pitfalls and estimable Considerations Use randomly collected data to reduce selection biases Do not use human subjects without informed consent Choose the level of significance, ? , and the type of test (one-tail or two-tail) before data collection Do not employ data snooping to choose between one-tail and two-tail test, or to determine the level of significance Do not practice data ablutionary to hide observations that do not support a stated hypothesis Report all pertinent findings including both statistical significance and hard-nosed importance