10.4 Warm Up

A marine biologist wants to estimate the average weight of a population of dolphins living in a certain region of the ocean. The biologist will collect a random sample of dolphins and use the sample weights to create the estimate. Which of the following is an appropriate method for the biologist to use for inference to the population?

• A one-sample t-interval for a population mean

• A one-sample t-interval for a sample mean

• A one-sample z-interval for a population proportion

• A matched-pairs t-interval for a mean difference

• A two-sample t-interval for a difference between means

Answer explanation

Correct. Weight is a quantitative variable. The appropriate procedure for estimation is the one-sample -interval for a population mean.

A machine is used to fill bags with a popular brand of trail mix. The machine is calibrated so the distribution of the weights of the bags of trail mix is normal, with mean 240 grams and standard deviation 3 grams. Of the following, which is the least weight of a bag in the top 5 percent of the distribution?

• 234 grams

• 240 grams

• 243 grams

• 246 grams

• 248 grams

Answer explanation

A city planner is investigating traffic congestion at a certain intersection. To collect data, a camera will record the number of cars that pass through the intersection at different hours of the day and on different days of the week. Which of the following best describes the type of investigation being conducted by the city planner?

• The investigation is an experiment because the cars go through the intersection at random.

• The investigation is an experiment because the hours and the days are the treatments and the cars are the units.

• The investigation is an observational study because treatments are not imposed.

• The investigation is an observational study because only a sample of cars can go through the intersection on any given day.

• The investigation is a sample survey because the cars that are recorded will inform the city planner about the population of cars on city roads.

Answer explanation

Correct. No treatments are imposed or assigned to the cars. The number of cars going through the intersection is observed.

A marketing agency selected a random sample of television viewers to test the claim that the proportion of viewers who watch a particular show is less than 0.20 at a level of significance of 0.05. The test yielded a p-value of 0.47. Assuming all conditions for inference were met, which of the following is the correct conclusion?

• At the level of significance of 0.05, the null hypothesis is not rejected. There is not convincing evidence to suggest the true proportion of television viewers who watch the show is less than 0.20.

• At the level of significance of 0.05, the null hypothesis is not rejected. There is convincing evidence to suggest the true proportion of television viewers who watch the show is less than 0.20.

• At the level of significance of 0.05, the null hypothesis is rejected. There is convincing evidence to suggest that the true proportion of television viewers who watch the show is less than 0.20.

• At the level of significance of 0.05, the null hypothesis is rejected. There is not convincing evidence to suggest that the true proportion of television viewers who watch the show is greater than 0.20.

• At the level of significance of 0.05, the null hypothesis is rejected. There is convincing evidence to conclude that the null hypothesis is true.

Answer explanation

Correct. The p-value of 0.47 is very large and greater than any reasonable significance level (including 0.05), so the null hypothesis is not rejected. There is not convincing evidence to support the claim that the proportion of viewers who watch the show is less than 0.20.

• No, the condition for independence has not been met because random samples were not selected from each location.

• No, the condition for independence has not been met because the sample sizes are too large when compared to the corresponding population sizes.

• Yes, all conditions for making statistical inference have been met.

Answer explanation