Approximately $19 \%$ of physics majors in the US are women. To test whether your college differs significantly from this national average, you take a random sample of 50 physics majors at your college and find that 11 are female. Calculate the appropriate test statistic to determine whether your college differs significantly from the national rate. 0.64 $-0.34$ 0.54 0.48 $-0.59$

Step 1 ：The problem is asking for a test statistic to determine whether the proportion of female physics majors at a specific college differs significantly from the national average. The test statistic in this case would be a z-score, which measures how many standard deviations an element is from the mean.

Step 2 ：To calculate the z-score, we need to use the formula: \(z = \frac{(p - P)}{\sqrt{(P * (1 - P)) / n}}\) where: p is the sample proportion (number of successes in the sample divided by the sample size), P is the population proportion (national average), and n is the sample size.

Step 3 ：In this case, the sample proportion p is calculated as the number of successes in the sample divided by the sample size, which is \(p = \frac{11}{50} = 0.22\).

Step 4 ：The population proportion P is the national average, which is \(P = 0.19\).

Step 5 ：The sample size n is 50.

Step 6 ：Substituting these values into the formula, we get \(z = \frac{(0.22 - 0.19)}{\sqrt{(0.19 * (1 - 0.19)) / 50}} = 0.54\).

Step 7 ：The calculated z-score is approximately 0.54. This means that the proportion of female physics majors at the college is approximately 0.54 standard deviations above the national average.

Step 8 ：Final Answer: The appropriate test statistic is approximately \(\boxed{0.54}\).