critical thinking

Examples of critical thinking in the following topics:

• Critical Thinking

  • The essential skill of critical thinking will go a long way in helping one to develop statistical literacy.
  • The essential skill of critical thinking will go a long way in helping one to develop statistical literacy.
  • Critical thinking is a way of deciding whether a claim is always true, sometimes true, partly true, or false.
  • Critical thinking is an inherent part of data analysis and statistical literacy.
  • Interpret the role that the process of critical thinking plays in statistical literacy.

• Inference for a single proportion exercises

  • (c) A random sample of 60 young Americans where 85% think they can achieve the American dream would be considered unusual.
  • (d) A random sample of 120 young Americans where 85% think they can achieve the American dream would be considered unusual.
  • (c) A critic points out that this 95% confidence interval is only accurate if the statistic follows a normal distribution, or if the normal model is a good approximation.
  • (d) A news piece on this survey's findings states, "Majority of Americans think marijuana should be legalized."
  • (c) Calculate a 90% confidence interval for the proportion of Americans who think the Civil War is still relevant.

• Testing a Single Mean

  • A statistics instructor thinks the mean score is lower than 65.
  • The criteria for the inferential test stated above: Think about the assumptions and check the conditions.
  • There is no reason to think the score of one exam has any bearing on the score of another exam.
  • Sketch the test statistic and critical region: Look up the probability on the table shown in .
  • This graph shows the critical region for the test statistic in our example.

• Statistical Literacy

  • Critics have said that extreme events in reality are more frequent than would be expected assuming normality.

• Testing a Single Proportion

  • The criteria for the inferential test stated above: Think about the assumptions and check the conditions.
  • There is no reason to think how many cell phones one household owns has any bearing on the next household.
  • Sketch the test statistic and critical region: Look up the probability on the table, as shown in:
  • Since the probability is greater than the critical value of 5%, we will fail to reject the null hypothesis.
  • This image shows a graph of the critical region for the test statistic in our example.

• Testing a Single Variance

  • We may think of $s$ as the random variable in this test.
  • One of his best students thinks otherwise.
  • In other words, we do not think the variation in waiting times is 7.2 minutes, but lower.
  • This image shows the graph of the critical region in our example.

• 95% Critical Values of the Sample Correlation Coefficient Table

• Examples

  • In other words, you do not think Jeffrey swims the 25-yard freestyle in 16.43 seconds but faster with the new goggles.
  • Historical Note: The traditional way to compare the two probabilities, α and the p-value, is to compare the critical value (z-score from α) to the test statistic (z-score from data).
  • The graph shows α, the p-value, and the test statistics and the critical value.
  • A statistics instructor thinks the mean score is higher than 65.
  • Since the instructor thinks the average score is higher, use a "> ".

• One-sample means with the t distribution exercises

  • Find the degrees of freedom and the critical t value (t?
  • Do you think this is reasonable?

• Logistic regression

  • An investigation into the cause of the disaster focused on a critical seal called an O-ring, and it is believed that damage to these O-rings during a shuttle launch may be related to the ambient temperature during the launch.
  • (d) Based on the model, do you think concerns regarding O-rings are justified?
  • The investigation found that the ambient temperature at the time of the shuttle launch was closely related to the damage of O-rings, which are a critical component of the shuttle.