A Hypothesis Is a Claim

A assumption is a claim Population mean The mean monthly mobile phone 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 riseed Is always intimately a population parameter, non about a sample statistic Is the opposite of the null hypothesis e. g. , The fair diameter of a manufactured bolt is non equal to 30mm ( H1 ? ? 30 ) Challenges the status quo election never contains the =sign May or may not be provenIs generally the hypothesis that the tec is seek 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 population mean, the null hypothesis is not averted. If the sample mean is far from the stated population mean, the null hypothesis is egested. How far is far nice to reject H0? The critical value of a essay statistic creates a line in the sand for end making it answers the question of how far is far enough. Type I phantasm Reject a on-key null hypothesis Considered a serious type of error The probability of a Type I Error is ? Called level of conditional relation of the testSet by researcher in advance Type II Error Failure to reject a false null hypothesis The probability of a Type II Error is ? Type I and Type II errors cannot happen at the same time A Type I error can only occur if H0 is true A Type II error can only occur if H0 is false Critical Value Approach to Testing For a two-tail test for the mean, ? known Determine the critical Z values 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 utility(a) hypothesis, H1 Determine the appropriate test statistic and try distribution Determine the critical values that divide the rejection and nonrejection regions Collect data and compute the value of the test statistic Make 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 problem p-Value Approach to Testing -value Probability of obtaining a test statistic equal to or more than extreme than the observed sample value given H0 is true The p-value is also call ed the observed level of significance H0 can be rejected if the p-value is less than ? Hypothesis Testing ? Unknown If the population standard bending 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 absorb the population you are sampling from follows a practice distribution.All other steps, concepts, and conclusions are the same. One-Tail Tests In many cases, the excerption hypothesis focuses on a particular direction H0 ? ? 3 H1 ? 3 This is a lower-tail test since the alternative hypothesis is focused on the lower tail below the mean of 3 H0 ? ? 3 H1 ? 3 This is an upper-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 two X and n X are at least 5, p can be approximated by a norm al distribution with mean and standard deviationPotential Pitfalls and Ethical 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 amid one-tail and two-tail test, or to determine the level of significance Do not practice data cleansing to plow observations that do not support a stated hypothesis Report all pertinent findings including both statistical significance and practical importance