1. Advanced Math Topics 10.8 Tests Concerning Proportions

2. In this lesson, a claim will be made that a certain percentage of items will fit into a certain category. Example: The Dean of Students at a college claims that only 12% of the students commute to school. This number is known as p. To test this claim a sample will be taken to see how many items fall into this category. A sample of 80 students was taken and 14 of these students commute to college. p = 0.12 14/80 = 0.175 This number is known as p, (p hat is the sample ratio as a decimal). > In this lesson, the sample size will be large. n > 30. We can find z using the formula.... Then we can see which region the z-score lies and either accept or reject the original claim.

3. A senator claims that 55% of the of Americans are in favor of governmental health care. To test this claim, a newspaper editor selected a random sample of 1000 people and 490 of them said that they supported governmental health care. Is the senator’s claim justified? Use a 1% level of significance. p is 0.55 p is 490/1000 =0.49 > z = -3.81 2-tail or 1-tail? 2-tail How big is each rejection region? 0.5% How big is each middle region? 49.5% =.495 What are the z-scores in the picture? z = -2.58 and z = 2.58 Reject the senator’s claim!

4. Officials claim that 29% of local residents are against building a power plant. conservation groups claim that the percentage is much higher. They select 81 residents and find that 38 of them are against building the power plant. Can we conclude that the government’s claim is inaccurate? Use a 5% level of significance. p is 0.29 p is 38/81 =0.4691358 > z = 3.55 2-tail or 1-tail? 1-tail How big is the rejection region? 5% How big is the middle region? 45% =.45 What is the z-score in the picture? z = 1.645 Reject the official’s claim! Everyone participates!

5. From the HW P. 516 2) A claim was made in a newspaper article that 70% of people are in favor of stricter gun control legislation. Sixty-five people are selected at random and 40 are in favor of stricter gun laws. Can we accept the claim made by the newspaper? Use a 5% level of significance. z = -1.49 which is inside the z-scores of z = -1.96 and z = 1.96. We can accept the newspaper’s claim.

6. HW P. 516 #1-8