Question

Suppose that the number of hot dogs a competitive eater can eat in ten minutes has a known standard deviation of 4.04.0 hot dogs. A producer for a cable television food show wants to know if the mean number of hot dogs consumed in ten minutes during regional qualifying rounds for an international hot dog eating contest exceeds 1515 hot dogs. She takes a simple random sample of 2424 competitors during regional qualifying rounds across the country and obtains the following results.

13,15,11,9,12,14,16,10,16,13,15,10,18,14,12,16,11,9,8,15,13,17,11,1413,15,11,9,12,14,16,10,16,13,15,10,18,14,12,16,11,9,8,15,13,17,11,14

Is the producer justified in using a one-sample ?z‑test for the mean number of hot dogs eaten in all qualifying rounds of the hot dog eating contest?

a.No, because the population distribution is not known to be normal.

b.Yes, because the data come from a simple random sample and contain no outliers, the sample standard deviation may be computed from the data, the population appears to be approximately normal, and the sample size is large enough.

c.No, because the sample is biased.

d.No, because the sample data has a significant outlier.

e.Yes, because the population standard deviation is known, the data come from a simple random sample and contain no outliers, the population appears to be approximately normal, and the sample size is large enough.

Answer 1

e.Yes, because the population standard deviation is known, the data come from a simple random sample and contain no outliers, the population appears to be approximately normal, and the sample size is large enough.

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