2. Sarah claims she can long jump 20 ft on average, but her coach suspects her jump distances aren't far enough to win. a. Use your Pre-Activity work to complete a hypothesis test outlined in the steps below. Step 1: State hypotheses. Step 2: We need to verify that the appropriate sampling distribution for the test is the t-distribution. Do this by answering the following questions: O How do we know the data are a random sample? How do we know the population size is at least 10 times the sample size? Since the sample size is n = 16, the sample distribution must be approximately normal or only mildly skewed with no outliers. The shape of the sample dis- tribution from the Pre-Activity is and there (circle outliers, so this condition (circle one) is is not met. Step 3: Calculate the t-test statistic value and label the picture of the t-sampling distribution below with the null value and test statistic value on the x-axis, and shade the area corresponding to the p-value. one) are are no Since df = 15, the notation for this specific t-distribution is t(15). In R, pt(t,df) will give the area under the t-distribution to the left of t:. p-value since the alternative hypothesis specifies "less than." Step 4: State the conclusion using a significance level of a = 0.05. and this is the