A private opinion poll is conducted for a politician to determine what proportion of the population...

Transcribed Image Text:

A private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national monuments. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 4.2%? a) a pilot study indicates that the percentage is 68.4%? b) no prior estimates are used? Spinning a coin, unlike tossing it, may not give heads and tails equal probabilities. I spun a penny 225 times and got 98 heads. We wish to find how significant is this evidence against equal probabilities. a. What is the sample proportion of heads? Round to 3 places. b. Heads do not make up half of the sample. Is this sample evidence that the probabilities of heads and tails are different? Let's investigate with a hypothesis test. Take p to be the probability of getting heads in a spin of a penny. Which hypotheses do we want to test? Ho: p = 0.5 HA: p <0.5 Ho: p = 0.5 HA: P = 0.5 Ho: p = 0.5 HA: p = 0.5 O Ho: p = 0.5 HA: p > 0.5 c. Are the conditions satisfied to conduct a hypothesis Z-test for a one-sample proportion? Can the results of the 225 coin spins be considered random? yes no Is the sample independent? Check with n 0.05N < 0.05N A private opinion poll is conducted for a politician to determine what proportion of the population favors adding more national monuments. How large a sample is needed in order to be 99% confident that the sample proportion will not differ from the true proportion by more than 4.2%? a) a pilot study indicates that the percentage is 68.4%? b) no prior estimates are used? Spinning a coin, unlike tossing it, may not give heads and tails equal probabilities. I spun a penny 225 times and got 98 heads. We wish to find how significant is this evidence against equal probabilities. a. What is the sample proportion of heads? Round to 3 places. b. Heads do not make up half of the sample. Is this sample evidence that the probabilities of heads and tails are different? Let's investigate with a hypothesis test. Take p to be the probability of getting heads in a spin of a penny. Which hypotheses do we want to test? Ho: p = 0.5 HA: p <0.5 Ho: p = 0.5 HA: P = 0.5 Ho: p = 0.5 HA: p = 0.5 O Ho: p = 0.5 HA: p > 0.5 c. Are the conditions satisfied to conduct a hypothesis Z-test for a one-sample proportion? Can the results of the 225 coin spins be considered random? yes no Is the sample independent? Check with n 0.05N < 0.05N