Question

The American Academy of Health and Fitness released a survey, revealing that 35% of US adolescents admit they lie to their doctor about how often they eat vegetables. Dr. Vincent believes that the percentage is different than what is shown by the survey results. She decides to conduct her own hypothesis test to determine the true proportion. What should she write as the null and alternative hypotheses for this situation?

H0: μ = 0.35; Ha: μ > 0.35

H0: μ = 0.35; Ha: μ < 0.35

H0: p = 0.35; Ha: p > 0.35

H0: p = 0.35; Ha: p < 0.35

H0: p = 0.35; Ha: p ≠ 0.35

Answer 1

The null and the alternate hypothesis are:

H0: p = 0.35; Ha: p ≠ 0.35

Given that:

$p = 35\%$

$p = 0.35$

The percentage that lie are not 35% means that they are not equal to 35%

Not equal to is represented as: $\ne$

So, the alternate hypothesis is:

Ha: p ≠ 0.35

The null hypothesis will be the direct opposite, i.e. equal to 35%

So, the null hypothesis is:

H0: p = 0.35;

Hence, the null and the alternate hypotheses are:

H0: p = 0.35;

Ha: p ≠ 0.35

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