Name: ______Date: ______

Statistics & Probability Ms. Parent

Review for Confidence Intervals Test

ONE SAMPLE / TWO SAMPLE
Standard Deviation / Formula / Standard Deviation / Formula
Large Sample Mean
Small Sample Mean
Proportions

Review Examples:

  1. A psychologist gave a test measuring anxiety level, the State-Trait Anxiety Inventory, to a sample of 60 children and found that 22 had above-average anxiety levels. Determine the proportion of all children with above-average anxiety levels using a 90% confidence interval.
  2. Can measurements of the petal length of flowers be of value when you need to determine the species of a certain flower? Below are the summary statistics from measurements of the petals of two species of flowers. Write a 95% confidence interval for this difference and interpret your answer. Based on your results, is there evidence of a difference in petal length?

Flower Species 1 / Flower Species 2
Sample Size / 35 / 40
Mean / 55.52 / 43.22
SD / 5.519 / 5.362
  1. In August 2004, Time magazine, reporting on a survey of men’s attitudes, noted that “Young men are more comfortable than older men talking about their problems.” The survey reported that 80 of 129 surveyed 18 to 24 year old men and 98 of 184 surveyed 25 to 34 year old men said they were comfortable. What do you think? Is Time’s interpretation justified by these numbers? Use a 99% confidence interval to prove your answer.
  2. Is it a good idea to listen to music when studying for a big test? In a study conducted by some Statistics students, people were randomly assigned to listen to rap music, music by Mozart, or no music while attempting to memorize objects pictured on a page. They were then asked to list all the objects they could remember. Here are summary statistics for each group:

Rap / Mozart / No Music
Count / 29 / 20 / 13
Mean / 10.72 / 10.00 / 12.77
SD / 3.99 / 3.19 / 4.73
  1. Create a 90% confidence interval for the mean difference in memory score between students who study Mozart and those who listen to no music at all. Interpret your interval.
  2. Based on your interval in part a., can you make a claim that studying to Mozart improves your memory score? Why or why not?
  1. In your work for a national health organization, you are asked to monitor the amount of sodium in Honey Nut Cheerios. You find that a random sample of 52 cereal servings has a mean sodium content of 232 milligrams and you know the population standard deviation is 10 milligrams.
  1. Construct a 99% confidence interval for the true mean sodium content in Honey Nut Cheerios.
  2. What would happen to the interval if you used a 89% confidence interval instead? Why?
  1. A restaurant association says the typical household in the US spends a mean of $2116 per year on food away from home. You are a consumer reporter for a national publication and want to test this claim. You randomly select 12 US households and find out how much each spent on food away from home per year.
  1. Using the data below, calculate a 95% confidence interval for the true mean amount per year spent on food away from home.

34741262 853 1988 27882283 2797 1916 3415 2645 2726 2948

  1. Based on your interval, what do you think of the restaurateur’s claim?