statistics in business/econ-Hypothesis tests about the mean or proportion of a single population-ch 9.3, 9.5, 9.6, 10.1

State decision and conclusion appropriately in the original context:

compare zstats or p values. either reject or fail to reject null there is significant evidence or not significant evidence that -------------------.

Determine if the test is one-tailed or two-tailed:

-If issue is whether a population mean differs from a particular hypothesized value, and it seems immaterial whether the difference is is to the low side or the high side of that value, you should set up a twp tailed test. -if the specific direction of the difference is important, then set up a one tailed test. -In the above sample questions, you were given specific wording like "greater than" or "less than" then use one tailed. - if statement that something is exactly or equal to and we need to know if it varies is either direction, we use two tailed test. *sometimes you can decide and its just your discretion.

Conduct the test using the p-value method

-The P-value approach involves determining "likely" or "unlikely" by determining the probability — assuming the null hypothesis were true — of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed. If the P-value is small, say less than (or equal to) α, then it is "unlikely." And, if the P-value is large, say more than α, then it is "likely." If the P-value is less than (or equal to) α, then the null hypothesis is rejected in favor of the alternative hypothesis. And, if the P-value is greater than α, then the null hypothesis is not rejected. Specifically, the four steps involved in using the P-value approach to conducting any hypothesis test are: Specify the null and alternative hypotheses. Using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic. Again, to conduct the hypothesis test for the population mean μ, we use the t-statistic t∗=x¯−μs/n√ which follows a t-distribution with n - 1 degrees of freedom. Using the known distribution of the test statistic, calculate the P-value: "If the null hypothesis is true, what is the probability that we'd observe a more extreme test statistic in the direction of the alternative hypothesis than we did?" (Note how this question is equivalent to the question answered in criminal trials: "If the defendant is innocent, what is the chance that we'd observe such extreme criminal evidence?") Set the significance level, α, the probability of making a Type I error to be small — 0.01, 0.05, or 0.10. Compare the P-value to α. If the P-value is less than (or equal to) α, reject the null hypothesis in favor of the alternative hypothesis. If the P-value is greater than α, do not reject the null hypothesis. -in two tailed, have to multiply pvalue by two and compare it to alpha.

Determine if one of the above three tests is appropriate for a described situation:

-Use printed sheet attached that gives conditions:)

Conduct the test using the critical value method

Critical value approach The critical value approach involves determining "likely" or "unlikely" by determining whether or not the observed test statistic is more extreme than would be expected if the null hypothesis were true. That is, it entails comparing the observed test statistic to some cutoff value, called the "critical value." If the test statistic is more extreme than the critical value, then the null hypothesis is rejected in favor of the alternative hypothesis. If the test statistic is not as extreme as the critical value, then the null hypothesis is not rejected. Specifically, the four steps involved in using the critical value approach to conducting any hypothesis test are: Specify the null and alternative hypotheses. Using the sample data and assuming the null hypothesis is true, calculate the value of the test statistic. To conduct the hypothesis test for the population mean μ, we use the t-statistic t∗=x¯−μs/n√ which follows a t-distribution with n - 1 degrees of freedom. Determine the critical value by finding the value of the known distribution of the test statistic such that the probability of making a Type I error — which is denoted α (greek letter "alpha") and is called the "significance level of the test" — is small (typically 0.01, 0.05, or 0.10). Compare the test statistic to the critical value. If the test statistic is more extreme in the direction of the alternative than the critical value, reject the null hypothesis in favor of the alternative hypothesis. If the test statistic is less extreme than the critical value, do not reject the null hypothesis.

Understand use of z-table and t-table. Be able to "bracket" p-values when tables have a limited selection of values:

Z table-use area of significance to find zstat and for p value, use the ztest to find p value t table-use the degrees of freedom and the area to find zstat or use ztest to find p value just bracket as z<ztest<z and look at pvalue that corresponds so p<value<p. *use appropriate formulas to find all values.

State the relevant hypotheses:

mu= mu> population proportion= population proportion> use z table, but is standard dev. of population not given, use t distribution.

Know and check the conditions for validity:

refer to sheet attached with conditions.