Question

The American Academy of Periodontology released a survey, revealing that 27% of US adults admit they lie to their dentist about how often they floss their teeth. Periodontist Dr. Garcia believes that the percentage seems low, so he decides to conduct his own hypothesis test to determine the true proportion. What should he write as the null and alternative hypotheses for this situation?

H0: p = 0.27; Ha: p > 0.27

H0: p = 0.27; Ha: p < 0.27

H0: p = 0.27; Ha: p ≠ 0.27

H0: μ = 0.27; Ha: μ > 0.27

H0: μ = 0.27; Ha: μ < 0.27

Answer 1

Null Hypothesis,
`H_0` : p = 0.27

Alternate Hypothesis,
`H_A` : p > 0.27

Explanation:

We are given that the American Academy of Period ontology released a survey, revealing that 27% of US adults admit they lie to their dentist about how often they floss their teeth.

Periodontist Dr. Garcia believes that the percentage seems low, so he decides to conduct his own hypothesis test to determine the true proportion.

Let p = % of US adults who admit they lie to their dentist about how often they floss their teeth

So, Null Hypothesis,
`H_0` : p = 0.27

Alternate Hypothesis,
`H_A` : p > 0.27

Here, null hypothesis states that the % of US adults who admit that they lie to their dentist about how often they floss their teeth is equal to 27%.

On the other hand, alternate hypothesis states that the % of US adults who admit that they lie to their dentist about how often they floss their teeth seems low and is more than 27%.

Also, the test statistics that would be used for conducting this hypothesis test will be One-sample z proportion statistics.