Hypothesis Testing for a Proportion

Master hypothesis testing for proportions with these practice problems!

A large-scale study found that 42% of Americans play video games. A random sample of 1100 teenagers were asked whether they play games online; 575 said they did. Is there sufficient evidence to suggest that the proportion of teens who play video games is different from the national figure? Use a 5% level of significance. 1. State the null and alternative hypotheses.2. Calculate the test statistic and the p-value.3. Use α=0.05 to make a decision.4. State your conclusion in context. A nationwide survey of 1500 adults asked about attitudes toward “alternative medicine” such as acupuncture, massage therapy, etc. Among the 1500 respondents, 660 said they would use alternative medicine if traditional medicine was not producing the results they wanted. Do these data provide enough evidence to suggest that less than half of all adults would use alternative medicine if traditional medicine didn’t produce their desired results? Use a 5% level of significance. 1. State the null and alternative hypotheses.2. Calculate the test statistic and the p-value.3. Use α=0.05 to make a decision.4. State your conclusion in context. Sally reads a newspaper report claiming that 12% of all adults in the U.S. are left-handed. She decides to test this claim. Sally selects a random sample of 55 classmates and finds that 9 were left-handed. Does this provide sufficient evidence that the proportion of lefties in Sally’s school is different than the national figure? Use α = 0.01. 1. State the null and alternative hypotheses.2. Calculate the test statistic and the p-value.3. Use α=0.05 to make a decision.4. State your conclusion in context. About 76% of college professors said that if they could pick a career over again, they would choose to be a professor again. A random sample of 59 college professors in Colorado showed that 47 claim they would choose college teaching again. Does this indicate the proportion of professors in Colorado who would choose the career again is greater than the national rate of 76%? Use a 1% level of significance. 1. State the null and alternative hypotheses.2. Calculate the test statistic and the p-value.3. Use α=0.05 to make a decision.4. State your conclusion in context. Use the normal curve below to sketch the p-value and z-score for the previous question.