In each of the following scenarios, tell if the researcher has committed a Type I error, a Type II error, or made a correct decision.
a. A researcher is testing to determine if .31 of all families own more than one car. His null hypothesis is that the population proportion is .31.He randomly samples 600 families and obtains a sample proportion of .33 that own more than one car. Based on this sample data, his decision is to fail to reject the null hypothesis. The actual population proportion is .31.
b. Suppose it is generally known that the average price per square foot for a home in a particular U.S. suburb is $73.A researcher believes that due to the economy, the average may now be less than that. To test her belief, she takes a random sample of 45 homes in this community, resulting in a sample mean of $70 per square foot. The researcher’s decision based on this sample information is to fail to reject the null hypothesis. The actual average price per square foot is now $68.
c. Suppose a utility researcher knows from past experience that the average water bill for a 2000-square-foot home in a large Midwest City is $25 per month. The utility researcher wants to test to determine if this figure is still true today. Her null hypothesis is that the population mean is $25.To test this, she randomly samples 63 homes, resulting in a sample mean of $29.From this, she decides to reject the null hypothesis. The actual average is $27.
d. According to PR Newswire, 71% of all expectant mothers wish they had to go to only one source to get their baby information. Suppose in your region of the country, you think that this figure is too high so you conduct a test of 358 expectant mothers. In your study, only 66% of the expectant mothers wish they had to go to only one source to get their baby information. Based on this, your decision is to reject the null hypothesis. It turns out that in actuality, 71% of all expectant mothers in your region of the country wish they had to go to only one source to get their information.