"Kind words can be short and easy to speak, but their echoes are truly endless“ - Mother Teresa

Two Sample Means Problem The board of directors at the Anchor Pointe Marina is studying the usage of boats among its members. A sample of 30 members who have boats 10 to 20 feet in length showed that they used their boats an average of 11 days last July. The standard deviation of the sample was 3.88 days. For a sample of 40 member with boats 21 to 40 feet in length, the average number of days they used their boats in July was 7.67 with a standard deviation of 4.42 days. At the.02 significance level, can the board of directors conclude that those with the smaller boats use their crafts more frequently?

Step 1 State the null and alternative hypothesis. H 0 : Large boat usage = small boat usage H 1 : Smaller boat usage > large boat usage

Step 2 Select a level of significance. This will be given to you. In this problem it is.02.

Step 3 Formulate a decision rule =.4800 = 2.05z

Step 4 Identify the test statistic. 11 – 7.67 = 3.35z

Step 5 Arrive at a decision. The test statistic falls in the critical region, therefore we reject the null.

p-Value in Hypothesis Testing p-Value: The probability, assuming that the null hypothesis is true, of getting a value of the test statistic at least as extreme as the computed value for the test. If the p-value area is smaller than the significance level, H 0 is rejected. If the p-value area is larger than the significance level, H 0 is not rejected.

Statistical Significance p-Value: The probability of getting a sample outcome as far from what we would expect to get if the null hypothesis is true. The stronger that p-value, the stronger the evidence that the null hypothesis is false.

Statistical Significance P-values can be determined by - computing the z-score - using the standard normal table The null hypothesis can be rejected if the p- value is small enough.

P-Value 1.64 Z 2.05Z

Tests Concerning Proportions Proportion: A fraction or percentage that indicates the part of the population or sample having a particular trait of interest.

Tests Concerning Proportions The sample proportion is denoted by p, where: p = number of successes in the sample number sampled

Test for One Proportion π = population proportion p = sample proportion

Party, Party, Party!!!! Statistics is almost over.

One Sample Proportion Problem An urban planner claims that, nationally, 20 percent of all families renting condos move during a given year. A random sample of 200 families renting condos in Dallas revealed that 56 had moved during the past year. At the.01 significance level, does this suggest that a larger proportion of condo owners moved in the Dallas area? Determine the p-value.

Step 1 State the null and alternative hypothesis. H 0 : Proportion =.20 H 1 : Proportion >.20

Step 2 Select a level of significance. This will be given to you. In this problem, it is.01.

Step 3 Formulate a decision rule =.4900 = 2.32z

Step 4 Identify the test statistic. Z = = 2.83z.20(1-.20) 200

Step 5 Arrive at a decision. The test statistic falls in the critical region, therefore, we reject the null.

Test for Two Proportions

Two Proportion Problem Suppose that a random sample of 1,000 American-born citizens revealed that 198 favored resumption of full diplomatic relations with Cuba. Similarly, 117 of a sample of 500 foreign-born citizens favored it. At the.05 significance level, is there a difference in the proportion of American-born versus foreign- born citizens who favor restoring diplomatic relations with Cuba?

Step 1 State the null and alternative hypothesis. H 0 : Proportion of American-born = Foreign born H 1 : Proportion of American-born ≠ Foreign-born

Step 2 Select a level of significance. This will be given to you. In this problem it is.05.

Step 3 Formulate a decision rule = /2 =.4750 = 1.96z

Step 4 – Part I Identify the test statistic. P C = =

Step 4 – Part II Identify the test statistic. Z = = -1.61z.21(1-.21) +.21(1-.21)

Step 5 Arrive at a decision. The test statistic falls in the null hypothesis region, therefore we fail to reject the null.

Type I and Type II Errors Type I Error: Type I Error: Rejecting the null hypothesis when H 0 is actually true. Type II Error: Type II Error: Accepting the null hypothesis when H 0 is actually false.

Type I Error Rejecting the null hypothesis when H 0 is actually true.

Type II Error Accepting the null hypothesis when H 0 is actually false.