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Statistics Exercises and Hypothesis Testing, Quizzes of Advanced Data Analysis

Ohio State University (OSU) - NewarkAdvanced Data Analysis

A set of statistics exercises covering topics such as hypothesis testing, probability, and distributions. It includes problems related to calculating probabilities, determining critical values, evaluating null hypotheses, and understanding statistical concepts like power and effect size. The exercises are designed to test understanding of statistical principles and their application in real-world scenarios, making it a useful resource for students studying introductory statistics. A practical approach to learning and reinforcing statistical concepts through problem-solving.

Typology: Quizzes

2024/2025

Uploaded on 10/23/2025

annika-osu
annika-osu 🇺🇸

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1. An online grocery shop claims that the mean delivery time for all grocery stores is 120
minutes with a standard deviation of 30 minutes. Their store states that they have an average
delivery time of 100 minutes. Is the online grocery store significantly faster? Use alpha of .05.
a. State the null and alternative hypotheses in words.
b. Set up the criteria for making a decision. That is, find the critical value(s).
c. Compute the appropriate test statistic. Show your work.
d. Based on your answers above, evaluate the null hypothesis.
Reject Fail to reject (circle one)
e. State your conclusion in words.
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  1. An online grocery shop claims that the mean delivery time for all grocery stores is 120 minutes with a standard deviation of 30 minutes. Their store states that they have an average delivery time of 100 minutes. Is the online grocery store significantly faster? Use alpha of .05. a. State the null and alternative hypotheses in words. b. Set up the criteria for making a decision. That is, find the critical value(s). c. Compute the appropriate test statistic. Show your work. d. Based on your answers above, evaluate the null hypothesis. Reject Fail to reject (circle one) e. State your conclusion in words.
  1. The mean points scored per game by all players from all the teams in the National Basketball Association (NBA) is 10 with a standard deviation of 3 points. You survey a sample of 32 basketball players who have played for the Cleveland Cavaliers basketball team recently and find a mean of 13 points scored per game. Use an alpha level of 0.05 to determine whether players on the Cleveland Cavaliers team score more points per game when compared to all players in the NBA. a. State the null and alternative hypotheses in symbols. b. Set up the criteria for making a decision. That is, find the critical value(s). c. Compute the appropriate test statistic. Show your work. d. Based on your answers above, evaluate the null hypothesis. Reject Fail to reject (circle one) e. State your conclusion in words.
  1. A researcher has discovered several new planets and is interested in the possibility of life on these planets. Of the 90 planets he is investigating, 40 of them contain water. Only 10 of those that contain water are in a habitable region around their respective stars. Half of the planets that do not contain water are in the habitable region. Contain s Water Does not Contain Water Habitable Region Non-habitable Region Please leave answers to two decimal places! a. What is the probability that a planet is in the habitable region and contains water? b. What is the probability that a planet is not in the habitable region? c. What is the probability that a planet has water, given that it is also in the habitable region?
  2. On Halloween, a bored parent decides to count the types of costumes that kids are wearing in his neighborhood. He counts 5 skeletons, 4 princesses, 10 superheroes, and 18 scary clowns. Please leave answers to two decimal places! a. What is the probability that one of the kids asking for candy is wearing a skeleton or superhero costume? b. What is the probability of that two of the scary clowns will ask for candy in a row (with replacement)? c. What is the probability of a princess and then a superhero asking for candy (without replacement)?

Multiple Choice

  1. Sample size does what to power? A.) Increases it B.) Decreases it C.) Does not affect it D.) Not enough information
  2. Assuming α= .05, a 2-tailed hypothesis test will be more conservative than a 1-tailed test because the calculated critical region will be _______for a 2-tailed test than a 1-tailed test and consequently the test statistic needed to reject the null hypothesis has to be _____ for a 2-tailed test than a 1-tailed test. A.) smaller; larger B.) larger; smaller C.) smaller; smaller D.) None of the above
  3. Assuming all other factors remain constant, during hypothesis testing, if we decrease our alpha from .05 to .01, we will make it _______difficult to reject the null hypothesis but ______our probability of publishing a bad result. A.) More; decrease B.) Less; increase C.) More; increase D.) Less; decrease E.)
  4. For a two-tailed t-test with an alpha of 0.05, what percentage of the distribution is in the rejection region of one tail? A.) 5% B.) 10% C.) 2.5% D.) 50%
  5. An increase in which of the following makes you more likely to reject the null? A.) n B.) s

C.) μ

  1. OSU’s average GPA is 3.6 while the national average is 3.5 with a standard deviation of 0.3. Calculate the effect size.