Part 1 of 4 Victoria, an accomplished marathon runner, claims that the standard deviation for her time to run a 26.2 mile marathon is less than 17.5 minutes. To test her claim, Victoria looks up 11 of her race times (in minutes): 227.2, 233.3, 259.7, 265.8, 252.1, 228.8, 222.6, 202.9, 214.5, 237.2, 267.7 Perform a hypothesis test using a 9% level of significance to test Victoria's claim. Step 1: State the null and alternative hypotheses. Ho:o 2v 17.5 17.5 (So we will be performing a left-tailed test.) Part 2 of 4 Step 2: Assuming the null hypothesis is true, determine the features of the distribution of test statistics. Because we are testing the population standard deviation, we will use a x v degrees of freedom. distribution with 10 Part 3 of 4 Step 3: Find the p-value of the test statistic. Sample Mean: = 237.4364 Sample Standard Deviation: 8 = 21.37 P(X s 17.5 =0.73 p-value = 12.2114286 x

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Confidence Intervals

When we calculate intervals in probability and statistics, it can be simply termed as finding out a confidence interval. The confidence interval is usually calculated from the data set which is observed. The value of the parameter that needs to be calculated is present here only.