Question

Suppose that the number of hot dogs a competitive eater can eat in ten minutes has a known standard deviation of 3.3 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 15 hot dogs. She takes a simple random sample of 20 competitors during regional qualifying rounds across the country and obtains the following results.

13, 16, 18, 15, 14, 13, 16, 17, 14, 19, 14, 15, 17, 13, 15, 15, 16, 19, 10, 12

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. 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.
b. No, because the sample data has a significant outlier. No, because the sample is biased.
c. 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.
d. No, because the population distribution is not known to be normal.

Answer 1

The producer can use a one-sample z-test for evaluating the mean number of hot dogs eaten since the population standard deviation is known, the sample comes from a simple random sampling, and the sample size is adequate.

Step-by-step explanation:

The producer is 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. This conclusion is based on the information provided that the population standard deviation is known and the sample size is sufficient. Moreover, the data comes from a simple random sample and is assumed to be from a population that is approximately normally distributed, which are all conditions that validate the use of a z-test. Therefore, the correct option is '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'.