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

MATLAB: An Introduction with Applications
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ISBN:9781119256830
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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
H:o <v 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
distribution with 10
v degrees of freedom.
Part 3 of 4
Step 3: Find the p-value of the test statistic.
Sample Mean: T =
237.4364
Sample Standard Deviation: s =
21.37
P(x s 17.5
0.73
p-value =
12.2114286 ×
Question Help: D Post to forum
Transcribed Image Text: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 H:o <v 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 distribution with 10 v degrees of freedom. Part 3 of 4 Step 3: Find the p-value of the test statistic. Sample Mean: T = 237.4364 Sample Standard Deviation: s = 21.37 P(x s 17.5 0.73 p-value = 12.2114286 × Question Help: D Post to forum
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