According to NAFSA, 1.55% of all college students in the US studied abroad during the 2014-2015 academic year. Being the location of our country's capital, a researcher believes that a higher proportion of students study abroad in the District of Columbia than elsewhere in the country. Suppose a random sample of 250 college students from D.C. had 15 who studied abroad. a. State the hypotheses in symbols and words to test the researcher's claim. b. Calculate the test statistic. c. Calculate the p-value. d. Interpret the p-value e. State the conclusion of the test.

6. Can professional astrologers reliably determine when a person was born based on their personality? In a 1985 study designed to answer this question, 116 participants filled out questionnaire to determine their personality profiles. Astrologers were then presented with the personality profiles and asked to determine which season (Spring, Summer, Fall, or Winter) that a person was born in. The astrologers in the study were able to pick the correct personality profile 35 times out of 116. If there is really no connection between birth data and personality, we would expect the astrologers to be correct 1/4 of the time just by guessing (if we make the reasonable assumption that one-fourth of the population is born in each season). Perform a one-tailed hypothesis test of the claim that astrologers can match birth seasons to personality profiles better than chance. a. State the null hypothesis in symbols and words.b. State the alternative hypothesis in symbols and words. c. What is the…

Consider the following hypothe basketball records for college A and college B. Answer parts a through c. College A College B Home Games 10 wins, 19 losses 12 wins, 4 losses Away Games 9 wins, 19 losses 56 wins, 20 losses a. Give numerical evidence to support the claim that college A has a better team than college B. Choose the correct answer below. OA. College A won 10 of their home games, whereas college B won 9 of their home games. OB. College A won about 34.5% of their home games and about 75% of their away games, whereas college B only won about 32.1% of their home games and about 73.7% of their away games. OC. College A lost only 23 games, whereas college B lost 39 games. b. Give numerical evidence to support the claim that college B has a better team than college A. Choose the correct answer below. OA. College B won 65 games, whereas college A only won 22 games. B. College B won about 62.5% of the games they played, whereas college A only won about 48.9% of the games they played.…

4. In an advanced ballet dance class, it is claimed that 42% of dancers can successfully perform a double pirouette turn. We randomly select 27 advanced level ballet dancers and only 13 of them can successfully do a double. Has the proportion increased? a) State the null and alternative hypotheses. b) Find the test statistic. Round to two decimal places. c) Find the p-value. Round to four decimal places. ļ d) Suppose we chose a 5% significance level. What is your decision?