Blind Emotion [See Problem 11 in Section 10.2A.] When the area of the brain responsible for vision is destroyed, individuals experience cortical blindness. Patients with cortical blindness are unaware of any visual stimulus including light. In a 52-year-old male patient with cortical blindness (as a result of two strokes within a 38-day timeframe), a series of visual stimuli were presented on a computer screen. The patient was given two choices for each stimulus and asked to report what was on the screen. The patient’s responses were recorded by an individual who could not see the contents on the screen.
c. The researchers wanted to determine if the patient could identify other facial characteristics. They randomly showed male or female faces and asked the patient to identify the gender. The patient was correct in 89 of 200 trials. What does this suggest?

Verified step by step guidance

1. Step 1: Define the null hypothesis (H0) and the alternative hypothesis (H1). Here, H0 assumes the patient is guessing randomly, so the probability of a correct guess is 0.5 (since there are two choices: male or female). H1 suggests the patient can identify gender better than chance, so the probability of a correct guess is greater than 0.5.
2. Step 2: Identify the sample size (n = 200) and the number of correct responses (x = 89). Calculate the sample proportion of correct guesses as \(\hat{p} = \frac{x}{n} = \frac{89}{200}\).
3. Step 3: Use the sampling distribution of the sample proportion under the null hypothesis. The mean of this distribution is \(p_0 = 0.5\), and the standard error (SE) is calculated as \(SE = \sqrt{\frac{p_0(1 - p_0)}{n}} = \sqrt{\frac{0.5 \times 0.5}{200}}\).
4. Step 4: Calculate the test statistic (z-score) using the formula \(z = \frac{\hat{p} - p_0}{SE}\). This measures how many standard errors the observed proportion is away from the hypothesized proportion under H0.
5. Step 5: Compare the calculated z-value to the critical value from the standard normal distribution for the chosen significance level (commonly 0.05). If the z-value is less than the critical value for a one-tailed test, we fail to reject H0; otherwise, we reject H0, suggesting the patient can identify gender better than chance.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence to reject a null hypothesis. It involves formulating a null hypothesis (e.g., the patient guesses gender at random) and an alternative hypothesis, then using sample data to assess the likelihood of observing the results if the null is true.

Binomial Distribution

The binomial distribution models the number of successes in a fixed number of independent trials with two possible outcomes, such as correct or incorrect guesses. It helps calculate probabilities of different numbers of successes, which is essential for evaluating if the patient’s correct responses differ from chance.

Statistical Significance and p-value

Statistical significance measures whether an observed effect is likely due to chance. The p-value quantifies the probability of obtaining results at least as extreme as those observed, assuming the null hypothesis is true. A low p-value suggests the patient’s performance is unlikely by chance, indicating possible unconscious recognition.