M140: You must complete this exam alone and You may not collaborate with other students: Introducing statistics Assignment, OU, UK

You must complete this exam alone. You may not collaborate with other students. Collusion on this exam is detectable, so please do not do it.

Section 1

1. Your friend hypothesizes that football teams with higher salaries are more likely to win matches. He collects the average salary for players on each of the 51 teams in the European Women’s World Cup qualifier. For each team, he randomly selects one match that the team played during the qualifier, and he records whether that team won or lost the match. If the result was a draw, he randomly selects another match, until he chooses either a win or a loss for each team. So, when he is finished, his data includes 51 teams, the average salary for each team, and a win or a loss for each team. He asks you to assess whether teams with higher salaries are more likely to win. What test would you use? Why?

2. You are studying how three different soil amendments affect soil pH. You measure 180 g of acidic soil into each of 60 pots and then wet each pot to 50% water-filled pore space. For each soil amendment, you select 10 untreated pots and mix in 3.7 g of the amendment. Then, for each amendment, you select another 10 untreated pots and mix in 11 g of the amendment. So, in the end, you have six treatment groups – low lime amendment, high lime amendment, low basalt amendment, high basalt amendment, and so on – and 10 pots in each group. After 4 weeks, you measure the soil pH in each pot. You want to know whether the amendment type and amount affect the soil pH. What test would you use? Why?

3. You are interested in whether social media shapes people’s political opinions. You enroll 100 Twitter users in a study. You ask each person to rate how they feel about Boris Johnson on a scale of 0 to 10. Then, you divide the participants randomly between two groups. You ask one group to follow 10 prominent Tory-leaning Twitter accounts, and you ask the other group to follow 10 prominent Labour-leaning Twitter accounts. After one month, you ask each person to rate how they feel about Boris Johnson again, and you compute the difference in each participant’s ratings. So, for each person, you have two pieces of information: which treatment they received, and how their opinion of Boris Johnson changed. You want to know if the treatment affected their view of Boris Johnson. What test would you use? Why?

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