The beta shoe museum states that 68% of women wear shoes that are too small for their feet. A researcher wants to be 98% confident that this proportion is within 0.02 of the true proportion.  how large a sample is necessary?

You are conducting a study to estimate the mean height of students in a university. The university has 10,000 students. If you want to achieve a margin of error of no more than 2 inches with 95% confidence, what sample size should you select?

One study claimed that 88 % of college students identify themselves as procrastinators. A professor believes that the claim regarding college students is too high. The professor conducts a simple random sample of 272 college students and finds that 231 of them identify themselves as procrastinators. Does this evidence support the professor's claim that fewer than 88 % of college students are procrastinators? Use a 0.02 level of significance. Step 2 of 3: Compute the value of the test statistic. Round your answer to two decimal places.

One study claimed that 86% of college students identify themselves as procrastinators. A professor believes that the claim regarding college students is too high. The professor conducts a simple random sample of 238 college students and finds that 193 of them identify themselves as procrastinators. Does this evidence support the professor’s claim that fewer than 86% of college students are procrastinators? Use a 0.05 level of significance.   Step 2 of 3 :   Compute the value of the test statistic. Round your answer to two decimal places.