Test proportion against 1.0

#1
Hi folks.

Can you help me?

Is there a way I can I test a proportion against an expected value of 1.0?

Made up example (slightly silly):
Dichotomous Yes/No question...

Would you like me to hit you very hard on the head with this hammer?
Expected proportions: No = 1.00, Yes = 0.00
Observed proportions: No = 0.85, Yes = 0.15


How can I test if the observed No proportion of 0.85 is different from the expected No proportion of 1.0?

To be clear the null hypothesis is that there would be unanimity, that all participants would respond "no", so expected
proportion under the null hypothesis = 1.0.

Can't use a one proportion z test, as I will get 0 for my denominator, i.e. sqrt[(p_0 * (1 - p_0))/n]

Where...
p_0 = probability associated with the null hypothesis, i.e. "p" with subscript zero to indicate the null hypothesis expected proportion

Any help gratefully received.

Mike
 
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