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Nat2105 [25]
3 years ago
14

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?
Answer Options:
A: H0: p = 0.27; Ha: p > 0.27

B: H0: p = 0.27; Ha: p < 0.27

C: H0: p = 0.27; Ha: p ≠ 0.27

D: H0: μ = 0.27; Ha: μ > 0.27

E: H0: μ = 0.27; Ha: μ < 0.27
Mathematics
1 answer:
Y_Kistochka [10]3 years ago
5 0

Answer:

A: H0: p = 0.27; Ha: p > 0.27

Step-by-step explanation:

The parameter is the population proportion.

According to the survey conducted by the American Academy of Periodontology, the proportion of of US adults who admit they lie to their dentist about how often they floss their teeth is 27%.

This means the null hypothesis is :

H_0: p=0.27

Periodontist Dr. Garcia believes that the percentage seems low, so his claim is that the percentage should be more than 27%.

This means, the alternate hypothesis is

H_{a}:p \: > \: 0.27

Therefore the correct choice is A.

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Kisachek [45]

Answer:

P=0.369

Step-by-step explanation:

In this binomial probability case, the success is to pick a burrito with hot peppers, there are 7 out of 17, the probability is p=7/17=0.4118. The formula is

P=_nC_kp^k(1-p)^{n-k}

Where n is the number of burritos taken at random, k is the number of success (burrito with hot peppers), p is the probability of success. _nC_k denotes the number of combinations and its formula is:

_nC_k=\frac{n!}{k!(n-k)!}

At least two burritos have hot peppers means having two or three burritos, these two cases are calculated and sum to get the probability of at least two burritos that have hot peppers.

P=_nC_kp^k(1-p)^{n-k}=\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k}

P_2=\frac{3!}{2!(3-2)!}(0.4118)^2(1-0.4118)^{3-2}=\frac{3\times2!}{2!1!} (0.1696)(0.5882)^1\\P_2=3 (0.1696)(0.5882)=0.2993

P_2=\frac{3!}{3!(3-3)!}(0.4118)^3(1-0.4118)^{3-3}=\frac{1}{0!} (0.0698)(0.5882)^0\\P_2=1 (0.0698)(1)=0.0698

P=P_2+P_3=0.2993+0.0698=0.3691

Round to three decimal places: P=0.369

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