In a psychology experiment in which 100 volunteers were asked to read a paragraph about an engineer, 65 assumed that the engineer was male despite the fact that the paragraph did not specify gender (and avoided gendered pronouns such as “he” or “she”).
If the null hypothesis here is that there is no gender bias, what is the two-sided p-value associated with this result? Use a normal approximation to solve this.
a. P=.0001
b. p=.003
c. p=.10
d. p=.05
e. p=.99
0.05
D. 0.05 is incorrect
a is not right either
0,003
To determine the two-sided p-value associated with this result, we need to perform a hypothesis test. The null hypothesis is that there is no gender bias, meaning that the proportion of volunteers assuming that the engineer was male is equal to 0.5 (assuming an equal likelihood of assuming male or female).
To solve this using a normal approximation, we can calculate the test statistic, which is the z-score. The formula to calculate the z-score for a proportion is:
z = (p - p0) / sqrt((p0*(1-p0))/n)
Where:
p = proportion in the sample assuming the engineer was male
p0 = hypothesized proportion assuming no gender bias (0.5)
n = sample size (100)
In this case, p = 65/100 = 0.65.
Using the formula, we can calculate the z-score:
z = (0.65 - 0.5) / sqrt((0.5*(1-0.5))/100)
= 0.15 / sqrt((0.25)/100)
= 0.15 / sqrt(0.0025)
= 0.15 / 0.05
= 3
The z-score tells us how many standard deviations the sample proportion (p) is away from the hypothesized proportion (p0). In this case, we have a z-score of 3, indicating that the sample proportion is 3 standard deviations away from the hypothesized proportion.
To find the p-value associated with this result, we need to calculate the probability of observing a test statistic as extreme as the one we obtained (z = 3) under the null hypothesis. Since this is a two-sided test, we need to consider both tails of the normal distribution.
Using a standard normal distribution table or a calculator, we can find that the probability of observing a z-score of 3 or greater (in either tail) is approximately 0.0013.
Since this is a two-sided test, we need to consider both tails. Therefore, we multiply this probability by 2 to get the p-value:
p-value = 2 * 0.0013
= 0.0026
Therefore, the two-sided p-value associated with this result is approximately 0.0026, which is equivalent to p = 0.002.
So, the correct option is b. p = 0.003.