Your mathematics instructor claims that, over the years, 88% of his students have said that math is their favorite subject. In this year's class, however, only 21 out of 32 students named math as their favorite class. The teacher decides to conduct a test of the hypothesis H0 : P = .88. What's the correct value of the standard deviation of σ for this test.
0.045
0.057
0.064
0.088
0.073
To find the correct value of the standard deviation (σ) for this test, we need to calculate the standard error of the proportion.
The formula for the standard error of the proportion (σp) is given by:
σp = √[(p * (1 - p)) / n],
where p is the proportion of students who said math is their favorite subject, and n is the total number of students in the sample.
In this case, p is given as 0.88 (88%) and n is given as 32.
σp = √[(0.88 * (1 - 0.88)) / 32] = √[(0.88 * 0.12) / 32].
Calculating the value inside the square root:
√[(0.88 * 0.12) / 32] = √[0.1056 / 32] ≈ √(0.0033) ≈ 0.057.
Therefore, the correct value of the standard deviation (σ) for this test is approximately 0.057.
So, the answer is 0.057.