Final answer:
To assess whether an advertising claim that an unknown population mean is at least 20 is correct, one must conduct hypothesis testing, selecting the appropriate statistical test based on sample size and known population parameters, while ensuring the sampling method is random and representative to make valid conclusions.
Step-by-step explanation:
To determine if the advertising label is correct and to support the claim that the unknown population mean is at least 20, one must perform hypothesis testing. Depending on the sample size and whether the population standard deviation is known, one would typically use a t-test or z-test. Accurate conclusions also depend on how representative and random the sample is, which can be affected by the sampling method used (e.g., convenience sampling, simple random sampling). For instance, if a marketing team surveys 150 households and 43 have three cell phones, and they want to test if this supports a different proportion from 30 percent, they would use a binomial or normal distribution depending on the sample size and approximation conditions.
When a study reports a population mean, for example, 13, and you collect a sample with a mean of 12.8 and a standard deviation of two from 20 individuals, if the population is normally distributed, a t-test would be appropriate since the sample is < 30 and the population standard deviation is unknown. Similarly, with a proportion in a taste test, if you have a sample of 100 people with 39 percent preferring Brand A and you want to test this against a population proportion of 42 percent, you would use a normal distribution for the hypothesis test if the sample size is sufficient for the normal approximation to the binomial distribution to hold.
In cases like convenience sampling at a concert or publishing an article with disease prevalence statistics, the representativeness, and potential biases must be critically examined before drawing conclusions about the entire population from the samples collected.