My teacher has a theory that 40% of students at the university are female.

I needed to survey 30 random students and asked them if they think 40% of students are female. 22 said yes while 8 said no. I need to carry out a hypothesis test to claim his theory that 40% of students are female. I came up with this.

It is claimed that 40% of students are female. I interviewed a random sample of 30 students. Of these, 22 students believe that 40% of are indeed female. Test whether or not the claim that 40% of students are female or not.

Null and alternative: Hypotheses: Ho : p = .4 HA : p ≠ .4

Model: Random Sample: Stated

10% condition

22 ≥ 10 = success

30 ≥ 10 = failure

Specify the sampling distribution model: √.4(.6)/30 = 0.08944

Tell the test you plan to use: Test I plan to use is one-proportion z-test.

Mechanics: Test statistics (z-score and p-value)

z score = 22/30 - .4 / .08944 = 3.727 p value = 1.94

Conclusion: ???

I know how to do all the work, but the conclusion. I just feel like my success and failures aren't correct. And how can a z-score be 3.727? Did I ask the wrong questions because I just asked if they believed if 40% were female. I got either a yes or no.