An amateur long distance runner knows his time taken to complete a 10km race has a standard deviation of 1 minute 51 seconds. The runner claims that his long-standing average is 42 minutes. If, for his last 15 races, he averaged 41 minutes 5 seconds, is this evidence that his mean time has improved? Test the claim at the 4% level of significance. What is the p-value for the test?

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An amateur long distance runner knows his time taken to complete a 10km race
has a standard deviation of 1 minute 51 seconds. The runner claims that his
long-standing average is 42 minutes. If, for his last 15 races, he averaged 41
minutes 5 seconds, is this evidence that his mean time has improved? Test the
claim at the 4% level of significance. What is the p-value for the test?

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