Statistics 200_ Lab Activity for Section 4.1

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Pennsylvania State University *

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Apr 3, 2024

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Statistics 200: Lab Activity for Section 4.1 Activity 1: Statistical test or confidence interval? In each scenario below, indicate a) whether the researchers should use a statistical test or confidence interval and b) what the population parameter(s) of interest is/are. 1.Polling 1000 people in a large community to determine the proportion who have a Netflix subscription. a. Researchers should use a statistical test or confidence interval i. Confidence interval b. What the population parameter(s) of interest is/are i. P (single proportion) 2.Testing 100 high school freshmen and 100 high school seniors on the same algebra exam to determine if there is evidence for the claim that seniors score higher on average. a. Researchers should use a statistical test or confidence interval i. Statistical test b. What the population parameter(s) of interest is/are i. Mu (single mean) 3.Conduct an experiment with 50 people in a driving simulator to find the mean reaction time to hit the brakes when an object is seen in the view ahead. a. Researchers should use a statistical test or confidence interval i. Confidence interval b. What the population parameter(s) of interest is/are i. Mu (single mean) Activity 2: Hypothesis Keywords. What are keywords or phrases that help you decide if the alternative hypothesis includes a >, <, or a ≠? Symbol Key Words or Phrases > “positive” < “negative” ≠ “different” Activity 3: Writing Hypotheses Write down the hypotheses for the test in each case below (use proper notation): 1. Does the proportion of people who support gun control differ between males and females? H0: p1 = p2 Ha: p1 ≠ p2 2. Is the average hours of sleep per night for college students less than 7? H0: mu1 > mu2 Ha: mu1 < mu2 3. Is there evidence that the mean of group A is not the same as the mean of group B? H0: mu1 = mu 2 Ha: mu1 ≠ mu2 4. Is there a negative correlation between hours per week spent studying and number of parties attended per week? H0: rho = 0 Ha: rho ≠ 0

Activity 4: Evidence for The Claim. You will need to use the data in the Minitab file “Hypothetical Data for Section 4.1 Lab” for this activity. The file is available in Canvas. Use the Minitab guide to help you with creating the summaries. 1. We are interested in testing to see if there is evidence that the population mean for mathematics placement exam scores is greater than 25. a. Write the correct null and alternative hypotheses for this situation: H0: mu = 25 Ha: mu > 25 b. The data for four hypothetical samples (e.g., ‘Math Scores A’ is one sample) for the math placement exam scores is included in the Minitab data set. Create summaries, either numerical or graphical, to evaluate which of the samples provides the most or least amount of evidence against the null and for the alternative. What kind of summaries did you create? 5 number summary c. Which of the possible sample results provide the most evidence for the alternative hypothesis? Math scores C d. Which of the possible sample results provide no evidence for the alternative hypothesis? All other samples do not provide evidence 2. Researchers in a hypothetical town are trying to see if there is evidence that an upcoming ballot measure for a tax increase will pass with more than 50% of the vote. a. Write the correct null and alternative hypotheses for this situation: H0: p = 0.5 Ha: p > 0.5 b. They take four hypothetical samples (e.g., ‘Opinion A’ is one sample) of the same size and record whether individuals will vote ‘yes’ or ‘no’. Their hypothetical data is included in the same dataset you used for the above question. Again, use these data to decide which of the samples provides the most or least amount of evidence against the null and for the alternative. What kind of summaries did you create? Frequency table c. Which of the possible sample results provide the most evidence for the alternative hypothesis? Opinion A d. Which of the possible sample results provide no evidence for the alternative hypothesis? The rest of the opinions 3. We are interested in testing to see if there is evidence that the correlation between exam grades (in percentages) and hours spent playing video games is negative for a population of students. a. Write the correct null and alternative hypotheses for this situation: H0: p = 0 Ha: p > 0

Below are four scatterplots of hypothetical samples collected to investigate the claim: a. Which of the possible sample results provide the most evidence for the alternative hypothesis? Sample D b. Which of the possible sample results provide no evidence for the alternative hypothesis? Sample C and B

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