Question

An online survey asked 397 how much extra in taxes they would be willing to pay to protect the environment. The sample average was $599 with a sample standard deviation of $180. Is it appropriate to use a normal distribution to approximate a confidence interval for the population mean? If it’s inappropriate, indicate why.

Select one:

a. Yes.

b. No, because it was not a random sample.

c. No, because n(p-hat) < 10 or n(q-hat) < 10.

d. No, because the sample size wasn’t at least 30 and the population wasn’t normally distributed.

e. No, because we already know the population mean.

Answer 1

Answer : b.No, because it was not a random sample.

Explanation: In order to use normal distribution for confidence interval, the data must satisfy following conditions :

Randomization Condition: The data must be sampled randomly.

Independence Assumption: The sample values must be independent of each other. This means that the occurrence of one event has no influence on the next event. Usually, if we know that people or items were selected randomly we can assume that the independence assumption is met.

10% Condition: When the sample is drawn without replacement (usually the case), the sample size, n, should be no more than 10% of the population.

Sample Size Condition: The sample size must be atleast 30.

In our case, it is clearly said that it was an online survey, so only those people's opinion is captured in the cited sample who visited that particular website. So we can clearly claim that the sample is not random and therefore can not use normal distribution for confidence interval of population mean.

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