COVID-19 in the U.S

 

Since people have been getting vaccinated against COVID-19 in the U.S., a stand-up paddling rental company in Santa Barbara wants to know whether in the month of June, renters (n = 100) were satisfied enough with their experience. Renters rated their satisfaction on a 7-point scale, and in June, this satisfaction level was, on average, 5.6, with a standard deviation of 0.5. Their goal satisfaction level is 6.0. This company hired us to see whether they met their goal or if the discrepancy between 5.6 and 6 is probably due to sampling error. (10 points)

Why would the company want to run a single sample t-test to test their hypothesis? Explain in the context of the question. (1 point)

If the researcher conducts a two-tailed test, what is the null hypothesis? (1 point)

Calculate the t-test statistic. Show your work. (3 points)

Using R, calculate the probability of a test statistic as extreme as yours in a null hypothesis world. Paste the code. Instructions for how to do this are in the lecture. (1 point)

Using an α = .05, would you reject or fail to reject the null hypothesis? Interpret what this means in the context of the question. (2 points)

Calculate the effect size. Interpret this effect size according to Cohen’s d guidelines. (2 points)

A researcher wants to know whether reading fiction versus non-fiction books boosts creativity. They hypothesize that there will be a difference in levels of creativity between individuals who read a novel versus a biography once a week for two months. They have one sample of college students (n1=38) read a novel per week for two months, and they have a second sample of college students (n2=35) read a biography per week for two months. The novel reading sample score an average of 7.8 (s1= 2.4) on a creativity scale that ranges from 1-10, and the biography reading sample score an average of 5.3 (s2= 2.1). (12 points)

Why would the researcher run an independent samples t-test to test their hypothesis? Explain in the context of the question. (1 point)

If the researcher conducts a two-tailed test, what is the null hypothesis? (1 point)

Calculate the t-test statistic. Show your work. (5 points)

Using R, calculate the probability of a test statistic as extreme as yours in a null hypothesis world. Paste the code. Instructions for how to do this are in the lecture. (1 point)

Using an α = .05, would you reject or fail to reject the null hypothesis? Interpret what this means in the context of the question. (2 points)

Calculate the effect size. Interpret this effect size according to Cohen’s d guidelines. (2 points)

 

Sample Solution

In this essay I will discuss the connections between leadership, motivation and teamwork theories, how they connect to practice in organisations and their limitations, offering solutions where impracticalities arise. The essay aims to draw conclusions on the suitability of Fiedler’s Contingency Theory of Leadership, Tuckman’s Model of Group Development, Belbin’s Team Theory, and Herzberg’s Two Factor Theory in practice, and how complexities like power and influence shape how they can be applied to best suit the situation a leader faces.

Leadership
Contingency based theories of leadership suggest that there is no correct or best way to lead a group, or organisation, due to the significant number of constraints on a situation (Flinsch-Rodriguez, 2019). Fiedler, in his Contingency Theory of Leadership (Fiedler, 1967), suggests that the effectiveness of a group is dependent on the leadership styles of the leader and their favourability to the situation. Much of the theory is established around the least preferred co-worker scale (LPC). The LPC aims to quantify a potential leaders approach to a task on a scale of relationship motivated to task motivated, where the leader fits on the scale allows their most favourable situation to be deduced, and thus allows the identification of suitable leaders for tasks. The favourableness of the situation depends on three characteristics: leader-member relations, the support and trust the leader as from the group; task structure, the clarity of the task to the leader; and positional power, the authority the leader has to assess a groups performance and give rewards and punishments (Fiedler, 1967). If the leaders approach matches what is required from the situation then success is predicted for the group.
Fiedler’s contingency model offers a very austere categorisation of leadership, clearly defining which situations will and will not result in success for a potential leader. At the senior management level of a hierarchal structure within an organisation the theory can be applied freely, firstly due to the ease at which persons can be replaced if their LPC score does not match that required of the situation (Pettinger, 2007). Secondly, and most importantly, is to ensure that the senior management are best equipped to lead the organisation successfully. However, further down the hierarchy Fielder’s contingency theory begins to hold much less relevance, it becomes impractical from a organisational perspective due to the number of people at this level of leadership. The logistics of matching the leader with their least preferred co-worker is impossible to consistently achieve, so a more continuum based approach is required.

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