``````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)``````

[A single sample t-test tests whether the population mean is statistically different from a hypothesized value.]

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

[H0: the difference between the mean of June satisfaction level and goal satisfaction level is zero (µJune-µgoal = 0)]

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

[t=(x ̅-μ_0)/(s⁄√n)=(5.6-6)/(0.5/√100)=-8.00]

``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)``

[> pt(-8,99)
 1.200152e-12]

``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)``

[We would reject the null hypothesis since the p-value is less α = 0.05. In the context of the question, the stand-up paddling rental company did not meet their goal in June.]

Sample Solution