According to MessageLabs Ltd., 80% of all email sent in July 2010 was spam. A system manager at a large corporation believes that the percentage at his company may be greater than 80%, and he wants to run a hypothesis test to see if there is evidence to support his belief. He examines a random sample of 500 emails received at an email server and finds that 420 of the messages are spam. Calculate the test statistic. Keep as many decimal places as you can when you are working with the denominator. Round the final answer to two decimal places.

Any basketball fan knows that Shaquille O'Neal, one of the NBA's most dominant centers of the last twenty years, always had difficulty shooting free throws. Over the course of his career, his overall made free-throw percentage was 53.3%. During one off- season, Shag had been working with an assistant coach on his free-throw technique. During the next season, a simple random sample showed that Shaq made 26 of 39 free-throw attempts. Test the claim that Shaq has significantly improved his free-throw shooting using a 0.05 significance level. Check the conditions of the Central Limit Theorem for this scenario. Calculate the number of expected successes.

In a simple random sample of 1200 young​ people, 86​% had earned a high school diploma. What is the standard error for this estimate of the percentage of all young people who earned a high school​ diploma?

Suppose the null hypothesis is not rejected. State the conclusion based on the results of the test. Six years​ ago, 11.1​% of registered births were to teenage mothers. A sociologist believes that the percentage has decreased since then.

A researcher is studying psychological factors in artistic achievement among teenage girls. One variable he is particularly interested in is perseverance. What information does a measure of variability for the variable perseverance convey? Check all that apply. What is the central tendency for the variable perseverance among teenage girls? What is the most common value for the variable perseverance among teenage girls? How spread out are the values for perseverance amoung teenage girls? Do all teenage girls have the same amount of perseverance?