Respuesta :
a) The null hypothesis is: p = 0.8 and the alternative hypothesis is p ≠ 0.8.
b) p-value is 0.0838
c) We accept the null hypothesis
What are null and alternative hypothesis?
The null hypothesis of a test always predicts no effect or no relationship between variables, while the alternative hypothesis states your research prediction of an effect or relationship.
What is p-value?
A p-value is a statistical measurement used to validate a hypothesis against observed data.
a. Let p be the proportion of 8 out of 10 dentists.
The null hypothesis is
[tex]H_0 : p=\frac{8}{10}=0.8[/tex]
The alternative hypothesis is
[tex]H_1:p\neq 0.8[/tex]
b. The sample proportion [tex]\hat p=\frac{73}{85}\approx 0.86\\[/tex]
Z-score, the test statistic is
[tex]Z=\frac{\hat p-p}{\frac{\sqrt{p(1-p)}}{n} } \\\\Z=\frac{0.86-0.8}{\frac{\sqrt{0.8(1-0.8)}}{85} }\\ \\Z=\frac{0.06}{0.043386}\\ \\Z=1.3829\\\\Z\approx 1.38[/tex]
P(Z > 1.38) = 1 - P(Z < 1.38)
∴ P(Z > 1.38) = 1 - 0.9162 = 0.0838
p-value is 0.0838
c. Since the p-value is greater than the level of significance α=0.05, we reject the alternative hypothesis and accept the null hypothesis
For more information on null hypothesis: https://brainly.com/question/19263925
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