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ACTIVITY I Formulate the alternative and null hypothesis. 1. A doctor claims that only 10% of all patients exposed to a certain amount of radiation will feel ill effects. If in random sample, 5 of 18 patients exposed to such radiation feel some ill effects, test the doctor's claim at 0.01 level of significance. Solution: Step 1: Formulate the null and alternative hypotheses Ho: Ha: 1. A researcher claims that the United Nationalist Alliance (UNA) will win the election. A total of 4300 voters were polled and 2200 said they would vote for UNA. Is there enough evidence at 0.05 level of significance to support the claim? Ho: Ha: Activity 2: 1. A concerned citizen group claims that 45% of the people in city A support making beers illegal. You decide to test this claim and ask random sample of 200 people on the concerned city whether or not they support making beers illegal. Of the 200 people, 49% support this bill. At 0.05 significance level, is there enough evidence to support this claim? Ho: Ha: 2. A researcher claims that the United Nationalist Alliance (UNA) will win the election. A total of 4300 voters were polled and 2200 said they would vote for UNA. Is there enough evidence at 0.05 level of significance to support the claim?Ho: Ha: Activity 3: 1. A doctor claims that only 10% of all patients exposed to a certain amount of radiation will feel ill effects. If in random sample, 5 of 18 patients exposed to such radiation feel some ill effects, test the doctor's claim at 0.01 level of significance. Solution: Step 1: Formulate the null and alternative hypotheses Ho: Ha: Step 2: Type of test: Step 3: Compute the test value Draw the rejection region Step 4: Decision Step 5: Conclusion:Activity 4: 1. A concerned citizen group claims that 45%%% of the people in city A support making beers illegal. You decide to test this claim and ask random sample of 200 people on the concerned city whether or not they support making beers illegal. Of the 200 people, 49% support this bill. At 0.05 significance level, is there enough evidence to support this claim? Solution:Step 1: Formulate the null and alternative hypotheses Ho: Ha: Step 2: Type of test: Step 3: Compute the test value Draw the rejection region Step 4: Decision Step 5: Conclusion:In our previous lesson, you have compared sample mean and population. There are some instances wherein we want to compare are proportions. In this lesson we shall learn how to determine if a proportion from a sample differs significantly from a proportion from a population. To compare sample proportion and population proportion, we use the z-test for one-sample mean proportion. The test statistic for this test is Z = - P - Po Po(1 - Po) n Where p= sample proportion Po= population proportion n=sample size x= number of successes Table A: TYPE OF TEST LEVEL OF SIGNIFICANCE 1=0.01 a=0.05 ONE-TAILED + 2.33 +1.65 TWO-TAILED + 2.58 + 1.96 Example: It has been claimed that less than 60% of all purchases of a certain kind of computer program will call the manufacturer's hotline with one month purchase. If 55 out of 100 software purchasers selected at random call the hotline within a month of purchase, test the claim at 0.05 level of significance. Solution: Step 1: Formulate the null and alternative hypotheses Ho: The proportion of purchasers that will call the manufacturer's hotline within one month of purchase is 60% or 0.60 ( po= 0.60) Ha: The proportion of purchasers that will call the manufacturer's hotline within one month of purchase is less than 60% or 0.60 ( po